Degree in Physics

Objectives

The aim of this module is for students to develop skills in Linear Algebra, a branch of mathematics that is essential to the study of physics. Students are expected to understand matrix calculus from a conceptual perspective and to be able to apply it to solving problems specific to their field of study.

Prerequisites

There are no prerequisites

Competencies

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK6 Understand the principles of mathematics and statistics that underpin the study of physics in classical and quantum systems

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

RC3 Acquire IT knowledge and skills enabling the development of methods and technologies applicable to the relevant fields of study

Learning outcomes

RA10 Solve typical problems in linear algebra and apply the knowledge and skills acquired in relation to physics-related concepts.

RA11 Understands the abstract structure of vector spaces and is able to tackle problems of higher dimensionality.

RA12 Analyses, evaluates and interprets the results obtained when solving systems of equations.

LA13 Reason abstractly, using logical and algorithmic thinking, when solving exercises relating to linear applications and their matrix representations

RA14 Carries out work in the field of linear algebra using knowledge of and computer tools.

Description of the content

Topic 1: Matrices and systems of linear equations

Topic 2: Vector spaces

Topic 3: Homomorphisms between vector spaces

Topic 4: Diagonalisation of endomorphisms

Topic 5: Bilinear and quadratic forms. Scalar product. Norm.

Learning activities

AP1. Participatory lectures

AP2. Seminars or practical application sessions

AP3. Practical activities (case studies, project work, simulations, etc.)

AP4. Independent study

AP5. Tutoring

AP6. Knowledge assessments

Assessment system and criteria

Without prejudice to any other requirements that may be set out in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities requiring the student’s physical or virtual presence will result in the loss of the right to continuous assessment during the standard examination period. In this case, the examination to be held during the official period set by the University will be the sole assessment criterion, with the weighting specified in the course syllabus.

----

The assessment process will consist of evaluating the extent to which the student has acquired the competences associated with the module.

REGULAR EXAMINATION PERIOD – CONTINUOUS ASSESSMENT

VERY IMPORTANT: in order for students to benefit from continuous assessment, they must attend at least 70 per cent of the scheduled class hours (SESSION, WORKSHOP). If attendance is less than 70 per cent, the module may be passed by sitting a single examination during an official examination period (ordinary or supplementary). During the ordinary examination period, in accordance with the ‘SE2 – Final Knowledge Tests’ assessment system, as set out in the report for the degree verification application, this exam will account for 60 per cent of the mark, which means that a student who has forfeited their right to continuous assessment may obtain, at most, a mark of 6.0 out of 10 for the module in that sitting; to pass the module, they must therefore achieve a mark of 8.34 out of 10 in the exam.

Continuous assessment will consist of the following components:

-- an individual portfolio (for each student), accounting for 10 per cent of the final mark for the module, which will consist of evidence of the use of computer tools such as Wolfram Alpha, GeoGebra or any other (MATLAB, Mathematica, Python with NumPy, etc.) to solve various linear algebra problems throughout the term.

-- a practical case study, accounting for 30 per cent of the final course mark, which students will undertake in small groups throughout the academic term; this practical case study will involve the submission of several deliverables (in order to analyse the progress of the different working groups), each of which will be assessed and will carry its corresponding weighting in the case study’s mark. Submission dates will be announced well in advance.

-- a mid-term exam (not a pass/fail exam), accounting for 20% of the final mark for the module. The date of this exam, which will take place during the term, will be announced well in advance; it will cover topics 1 and 2.

-- a final examination, which will take place during the ordinary examination period (January), on the date set by the university for that period. This exam will assess all the content covered in the module, and it will account for 40% of the final mark, provided that the student achieves a mark of 4.0 out of 10 or higher.

***** Only the examinations will be subject to re-marking.

Should a student have forfeited their right to continuous assessment, they may, as described above, pass the module by sitting the examination covering all the content taught in the module during the ordinary examination session. However, as already noted, this exam will account for 60 per cent of the final mark for the module, so the student will need to achieve a minimum of 8.4 out of 10 in it in order to pass.

*** The module is considered to have been passed in the ordinary examination period if the final mark is 5.0 or higher.

SUPPLEMENTARY EXAMINATION PERIOD

Regardless of their attendance during the term, in the supplementary assessment period students will be examined on all the content covered in the course in a single examination. The mark for this assessment period will be that obtained in this examination (continuous assessment will not be taken into account).

*** The module is considered passed in the supplementary examination period if the final mark is 5.0 or higher.

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Essential:

1. Juan De Burgos Román

Algebra and Geometry. Definitions, Theorems and Results

García Maroto Editores. 2010.

ISBN: 9788492976942

2. Luis Merino and Evangelina Santos

Linear Algebra using Elementary Methods

Paraninfo. 2010.

ISBN: 978-84-9732-4

Supplementary:

3.- Gilbert Strang

Introduction to Linear Algebra

Wellesley Cambridge Press. 2008.

ISBN: 8175968117

4.- Juan De Burgos Román

Linear Algebra. 80 Useful Problems

García Maroto Publishers. 2007.

ISBN: 9788493601805

Others:

5. Eugenio Hernández

Linear Algebra and Geometry

3rd ed. ADDISON WESLEY. 2012.

ISBN: 9788478291298

6. Jesús Rojo

Linear Algebra

McGraw-Hill. 2001.

ISBN: 8448130162

7. Jesús Rojo

Exercises and Problems in Linear Algebra

2nd ed. McGraw-Hill. 2005.

ISBN: 8448198581

8. Stanley I. Grossman and José Job Flores

Linear Algebra

McGraw-Hill. 2012.

ISBN: 978-607-15-07

Objectives

The aim of the module is to equip students with the mathematical tools necessary for solving problems in the field of physics.

Prerequisites

No prerequisites

Learning Outcomes

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK6 Understand the principles of mathematics and statistics that underpin the study of physics in classical and quantum systems

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

RC3 Acquire IT knowledge and skills enabling the development of methods and technologies applicable to the relevant fields of study

Learning outcomes

RA1 Solve problems involving differential calculus of a real variable.

RA2 Develops and applies abstract reasoning and logical and algorithmic thinking when working with real functions of a real variable.

RA3 Performs mental and written calculations involving real numbers, expansions using numerical sequences and series, and mathematical calculations with ease.

LA4 Produces work in the field of differential and integral calculus of a single variable through the knowledge and use of computer tools.

Description of the content

1) Real numbers.

Sequences of real numbers: convergence.

Series of real numbers: convergence criteria.

Operations on series.

2) Real functions of a real variable.

Continuity.

The derivative: Rolle’s theorem, the mean value theorem, the generalised mean value theorem, L’Hopital’s rule

.

Applications of the derivative: Taylor’s formula with its error term, representation of functions.

3) Integration.

Riemann integral: the fundamental theorem of calculus.

Integration techniques: direct integration, integration by parts, change of variable, rational, irrational and trigonometric integrals.

Applications: calculation of areas, lengths and volumes.

Teaching activities

AP1. – Participatory lectures 96 4 100

AP2. – Seminars or practical application classes 60 2.5 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 144 3 50

AP4.- Independent study 240 0 0

AP5.- Tutorials 48 0.6 30

AP6.- Knowledge assessments 12 0.5 100

TOTAL 600 10.6

Assessment system and criteria

Without prejudice to any other requirements that may be set out in the relevant course syllabus, as a general rule, failure to attend more than 70 per cent of the course’s teaching activities—which require the student’s physical or virtual presence—will result in the loss of the right to continuous assessment during the standard assessment period. In this case, the examination to be held during the official period set by the University will be the sole assessment criterion, with the weighting specified in the course syllabus.

----

SE1.- Practical activities (case studies, problem-solving and challenges, project work, etc.): 30%

SE2.- Two multiple-choice mid-term exams (a minimum mark of 4 is required to be included in the average). If the average is 5 or higher, the student is exempt from the ordinary January examination session. 50%

SE3.- Submission of exercises: 20%

The following assessments will be carried out as part of continuous assessment:

1) A first assessment on Topic 1, in early November, which will count for 10%

2) A second assessment on Topic 2, at the end of December, worth 10%

3) A third assessment on Topic 3, in January, which will account for 10%

4) The official exam in the ordinary examination session, which will account for 70% of the overall mark for the course.

Students who, for any reason, miss the continuous assessment will sit the ordinary examination, which will count for 100%

The supplementary sitting will count for 100%

Addendum

Assessment system Min. weighting % Max. weighting %

SE1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.) 20 30

SE2. Final knowledge assessments 60 60

SE4.- Portfolio 10 20

Objectives

The aim of the module is to equip students with the necessary tools to tackle fundamental problems in the field of physics (historical context, kinematics, dynamics, energy and associated theorems, systems of multiple particles), thereby providing them with the necessary foundation for subsequent modules.

Prerequisites

No prior requirements have been met.

Learning Outcomes

RK1 Understand the most important phenomena and theories in the various branches of physics, as well as their historical context

RK3 To analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RS3 Estimate orders of magnitude to interpret laboratory phenomena in the field of physics and its related disciplines, as well as in chemistry.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

RS5 Use appropriate electronic instruments and/or computer tools in modelling to find solutions to physics problems.

Learning outcomes

RA1 Identifies the relevant physical principles and, where necessary, makes simplifications and uses estimates of orders of magnitude in order to model and solve practical problems.

RA2 Handles fundamental concepts such as particles and fields, force, work, etc., with ease, in order to describe physical systems correctly.

LR3 Applies Newton’s laws appropriately to solving problems involving particles and systems of particles, and in relation to oscillatory motion.

RA4 Understands the units of the International System of Units and correctly assigns them to each of the physical quantities studied, as well as other units commonly used in the field of physics.

RC1 Work independently on the management of projects related to the different areas of physics

Description of the content

- Historical introduction.

- Particle kinematics. Types of motion.

- Particle dynamics.

- Work and energy, and associated theorems.

- Oscillatory motion.

- Systems of particles. Geometry of masses.

- Statics.

- Elasticity.

Training activities

Teaching activity No. of hours* Contact hours (8–12)** % of contact time

AP1.- Participatory lectures 50 2.78 100

AP2.- Seminars or practical application classes 30 1.67 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 72 2 50

AP4.- Independent study 180 0 0

AP5. – Tutorials 36 0.6 30

AP6.- Knowledge assessments 8 0.44 100

AP10.- Workshop and/or laboratory activities 74 4.11 100

TOTAL 450 11.60

Assessment system and criteria

Assessment system Weighting (%)

SE1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.) 30

AS2.- Final knowledge assessments 50 50

SE3.- Laboratory practical booklet 20

Timetable

Click on this link to view the detailed timetable in Excel

Objectives

The aim of the module is to equip students with the necessary programming language tools to enable them to solve more complex scientific problems.

Prerequisites

None

Learning Outcomes

RC1 To work independently on the management of projects related to the various areas of physics

RC3 Acquire the IT knowledge and skills required to develop methods and technologies applicable to the relevant fields of study

RODS Develop effective communication, teamwork, analytical thinking, creativity and ethical leadership from a cross-disciplinary perspective, clearly inspired by democratic principles and values, as well as the Sustainable Development Goals, in order to conduct oneself with integrity in the professional sphere.

Learning outcomes

RA1 Describes the fundamentals of basic general-purpose programming structures.

RA2 Uses IT tools to solve physical problems and illustrate mathematical concepts.

LA3 Formulates algorithms and models simple physical problems in order to implement them in a programming language (Python, Java or similar).

LA4 Reads and analyses programmes in order to identify the problem they solve or to detect possible errors, as well as to make modifications to adapt them to solving other similar scientific problems.

Course content

- Introduction to programming languages. Fundamentals of programming. Fundamentals of Python, Java or similar.

- Application structure. Data and expressions.

- Control structures. Classes and objects.

- Libraries. Data types and structures. Data input/output.

- Computer fundamentals. Computer architecture. Storage systems. Performance evaluation.

Training activities

Training activity No. of hours* Face-to-face hours (8–12)** % face-to-face

AP1.- Participatory lectures 48 4 100

AP2.- Seminars or practical application classes 30 2.5 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 72 3 50

AP4.- Independent study 120 0 0

AP5. – Tutoring 24 0.6 30

AP6.- Knowledge assessments 6 0.5 100

TOTAL 300 10.6

Assessment system and criteria

Assessment system Min. weighting % Max. weighting %

SE1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.) 20 30

AS2.- Final knowledge assessments 60 60

SE4.- Portfolio 10 20

Timetable

Click on this link to view the detailed timetable in Excel

Objectives

- To apply basic knowledge of statistics and probability to the analysis of data relating to physical phenomena and processes.

- To carry out statistical data analysis applied to solving real-world problems using mathematical software development packages (Python + NumPy).

- To apply probability calculations through the identification of models.

- To describe and apply the basic principles of statistical inference.

Prerequisites

No prerequisites have been set.

Competencies

RC1 Work independently on the management of projects relating to the various areas of physics

RC3 Acquire IT knowledge and skills enabling the development of methods and technologies applicable to the relevant fields of study

RODS Develop effective communication, teamwork, analytical thinking, creativity and ethical leadership from a cross-disciplinary perspective, clearly inspired by democratic principles and values, as well as the Sustainable Development Goals, in order to conduct oneself with integrity in the professional sphere.

Learning outcomes

RA5 Apply basic knowledge of statistics and probability to the analysis of data relating to physical phenomena and processes.

RA6 Performs statistical data analysis applied to the resolution of real-world cases using mathematical software development packages (Python + NumPy, SPSS or similar).

LA7 Applies probability calculations through the identification of models.

LA8 Describes and applies the basic principles of statistical inference.

Course content

Topic 1. Descriptive statistics.

Topic 2. Probability.

Topic 3. Random variables.

Topic 4. Probability distributions.

Topic 5. Statistical inference.

Teaching activities

AP1. Participatory lectures 48 4 100

AP2. Seminars or practical application sessions 30 2.5 100

AP3. Practical activities (case studies, project work, simulations, etc.) 72 3 50

AP4. Independent study 120 0 0

AP5. – Tutoring 24 0.6 30

AP6.- Knowledge assessments 6 0.5 100

Assessment system and criteria

ASSESSMENT FOR THE REGULAR EXAM SESSION

The final mark for the module will be calculated as a weighted average of projects and examinations as follows:

- Continuous assessment (40%)

+ Submission of exercises (10%)

+ Python project (30%)

- Final exam (60%)

ASSESSMENT FOR THE SUPPLEMENTARY EXAMINATION

- 100% Final exam mark for the module, based on the completion of theoretical and practical exercises in an exam.

Objectives

This module, together with Algebra I, aims not only to familiarise students with the main results of linear algebra, but also to enable them to understand matrix calculus from a conceptual perspective and to apply it to solving problems typical of physics; it therefore forms part of the mathematical foundation not only for other subjects within the degree programme, but also essential for the professional practice of a physics graduate.

Algebra II will cover what is known as linear geometry, which encompasses the study of vector spaces and Euclidean affine spaces, affine varieties, affine mappings and transformations (in particular, rigid transformations), the algebraic description of conics and quadric surfaces, and, finally, an introduction to projective geometry.

Throughout this module, students will continue to be trained in the use of computer tools for solving problems in linear algebra and, in particular, in the associated geometry.

Prerequisites

No prerequisites

Learning outcomes

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK6 Understand the principles of mathematics and statistics that underpin the study of physics in classical and quantum systems

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

RC3 Acquire IT knowledge and skills enabling the development of methods and technologies applicable to the relevant fields of study

Learning outcomes

RA15 Solves typical problems in linear geometry and applies the knowledge and skills acquired in relation to concepts associated with physics.

RA16 Demonstrates the ability to distinguish between quadratic and conic sections.

RA17 Analyses, evaluates and interprets the results obtained when solving problems in linear geometry.

LA18 Explains affine transformations and movements in an affine Euclidean space and solves related exercises.

RA19 Produces work in the field of linear geometry using knowledge of and computer tools.

Description of the content

- Euclidean vector spaces.

- Affine spaces. Linear varieties: lines and planes. Affine transformations.

- Euclidean affine spaces. Transformations in a Euclidean affine space.

- Spectral theory of symmetric and orthogonal matrices for application in the study of transformations.

- Conics and quadric surfaces.

- Projective geometry.

Teaching activities

AP1. – Participatory lectures

AP2. Seminars or practical application classes

AP3. Practical activities (case studies, project work, simulations, etc.)

AP4. Independent study

AP5. Tutoring

Assessment system and criteria

The assessment process will consist of evaluating the extent to which the student has acquired the competences associated with the module.

REGULAR EXAMINATION PERIOD – CONTINUOUS ASSESSMENT

VERY IMPORTANT: in order for students to benefit from continuous assessment, they must attend at least 70 per cent of the scheduled class hours (SESSION, WORK). If attendance is less than 70 per cent, the module must be passed by sitting a single examination during an official examination period (ordinary or supplementary). During the ordinary examination period, in accordance with the ‘SE2 – Final Knowledge Tests’ assessment system, as set out in the report for the degree verification application, this exam will account for 60% of the mark, which means that a student who has forfeited their right to continuous assessment due to attendance below 70 per cent may obtain, at most, a mark of 6.0 points for the module in that examination session; to pass the module, they must therefore achieve a mark of 8.34 points in the examination.

Continuous assessment will consist of the following components:

-- portfolio (SE4), individual, accounting for 10 per cent of the final mark for the module, which will consist of evidence of the use of computer tools such as Wolfram Alpha, GeoGebra or any other (MATLAB, Mathematica, Python with NumPy, etc.) to solve various linear algebra problems throughout the term.

-- a practical case study (SE1), accounting for 10% of the final mark for the module, which students will undertake in small groups throughout the academic term; this practical case study will involve the submission of several deliverables (in order to analyse the progress of the different working groups), each of which will be assessed and will carry its corresponding weighting in the case study’s mark. Submission dates will be announced well in advance.

-- a mid-term exam (SE1), accounting for 20% of the final mark for the module. The date of this exam, which will take place during the term, will be announced in good time; it will cover topics 1 and 2.

-- a final exam (SE2) accounting for 60% of the final mark for the module. This will take place during the ordinary examination period (January), on the date set by the university for that period. A minimum mark of 4/10 is required to pass the module.

*** The module is considered passed in the ordinary examination period if the final mark is 5.0 or higher.

EXTRAORDINARY EXAMINATION SESSION

Regardless of their attendance during the term, in the extraordinary examination period students will be examined on all the content covered in the module in a single examination. The mark for this examination period will be that obtained in this examination (continuous assessment will not be taken into account).

*** The module is considered passed in the supplementary examination period if the final mark is 5.0 or higher.

Bibliography

Essential:

1.- Juan De Burgos Román

Algebra and Geometry. Definitions, Theorems and Results

García Maroto Editores. 2010.

ISBN: 9788492976942

2. Luis Merino and Evangelina Santos

Linear Algebra using Elementary Methods

Paraninfo. 2010.

ISBN: 978-84-9732-4

Supplementary:

3.- Gilbert Strang

Introduction to Linear Algebra

Wellesley Cambridge Press. 2008.

ISBN: 8175968117

4.- Juan De Burgos Román

Linear Algebra. 80 Useful Problems

García Maroto Publishers. 2007.

ISBN: 9788493601805

Others:

5. Eugenio Hernández

Linear Algebra and Geometry

3rd ed. ADDISON WESLEY. 2012.

ISBN: 9788478291298

6. Jesús Rojo

Linear Algebra

McGraw-Hill. 2001.

ISBN: 8448130162

7. Jesús Rojo

Exercises and Problems in Linear Algebra

2nd ed. McGraw-Hill. 2005.

ISBN: 8448198581

8. Stanley I. Grossman and José Job Flores

Linear Algebra

McGraw-Hill. 2012.

ISBN: 978-607-15-07

Objectives

The aim of this module is to provide students with a sound grounding in differential and integral calculus of several variables, enabling them to tackle complex mathematical problems applied to physical phenomena. By the end of the module, students will be able to:

Understand and analyse the geometry of Euclidean space, applying concepts of vectors, planes and surfaces to the solution of physical problems.

Study functions of several variables, examining their properties relating to limits, continuity and differentiability.

Calculate higher-order derivatives and apply Taylor’s theorem in several variables to approximate functions and solve optimisation problems.

Work with vector functions, analysing trajectories and curves in space, as well as their properties of continuity and differentiability.

Calculate multiple integrals (double and triple) by applying Fubini’s theorem and the change of variables theorem, with applications to the calculation of volumes and masses.

Solve line integrals and surface integrals, applying them to the study of vector fields and flux through surfaces.

Apply the fundamental theorems of vector analysis (Green’s, Gauss’s and Stokes’s) to physics problems, such as electrostatics and fluid dynamics.

Interpret and analyse the results obtained from mathematical calculations, applying them to the modelling and solving of physical problems.

Prerequisites

No prerequisites

Competencies

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK6 Understand the principles of mathematics and statistics that underpin the study of physics in classical and quantum systems

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

RC3 Acquire IT knowledge and skills enabling the development of methods and technologies applicable to the relevant fields of study

Learning outcomes

RA5 Apply integrals in calculations associated with physics-related concepts.

RA6 Explain the geometry of multidimensional space and demonstrate three-dimensional spatial awareness.

RA7 Uses specific formal mathematical language with rigour

RA8 Produces work in the field of integral calculus through the knowledge and use of computer tools.

RA9 Analyses, evaluates and interprets the results obtained when solving problems involving differential calculus of several real variables.

Description of the content

Topic 1. The geometry of Euclidean space

Vectors in Euclidean space: magnitude, direction and vector operations.

Planes and surfaces: equations and geometric properties.

Topic 2. Functions of several variables: limits and continuity. Differentiation.

Functions of several variables: domain, range and graphs.

Limits and continuity in several variables.

Partial derivatives and differentiability.

Tangent plane and linear approximation.

Topic 3. Higher-order derivatives

Higher-order partial derivatives.

Hessian and convexity criteria.

Taylor’s theorem for several variables.

Applications in optimisation and stability analysis.

Topic 4. Functions with vector-valued outputs

Vector functions: continuity, differentiability and applications.

Parametric curves in space.

Derivatives of vector functions: velocity and acceleration.

Vector fields and lines of flow.

Topic 5. Double and triple integrals. Fubini’s theorem and the change of variables

Double and triple integrals: definition and properties.

Change of order of integration: Fubini’s theorem.

Change of variables in multiple integrals.

Applications to the calculation of areas, volumes, masses and centres of mass.

Topic 6. Integrals over curves and surfaces

Line integrals: over scalar and vector fields.

Surface integrals: flux through a surface.

Topic 7. Integration theorems in vector calculus

Green’s theorem: circulation and flux in the plane.

Gauss’s theorem (divergence): flux through closed surfaces.

Stokes’ theorem: relationship between circulation and rotational flux.

Learning activities

AP1. Participatory lectures

AP2. Seminars or practical application classes

AP3. Practical activities (case studies, project work, simulation, etc.)

AP4. Independent study

AP5. Tutoring

Assessment system and criteria

Regular examination period

VERY IMPORTANT: in order for students to benefit from continuous assessment during the ordinary assessment period, they must attend at least 70 per cent of the scheduled class hours (SESSION, WORK).

Practical group activities (20 per cent): Solving physics-related problems using analytical tools.

Submission of exercises (20 per cent): Individual exercises to consolidate theoretical and practical concepts.

Final exam (60%): A minimum mark of 4 is required to be included in the average.

Supplementary examination

The final mark for the module will correspond to 100 per cent of the mark obtained in this exam.

Bibliography

Core:

1. JERROLD E. MARSDEN and ANTHONY J. TROMBA

Vector Calculus.

Pearson. 2004.

ISBN: 9780201629354

Objectives

To provide students with the physical knowledge of fluid mechanics, electrical phenomena and magnetic fields necessary to tackle more complex physical problems.

Prerequisites

No prerequisites have been set.

Learning Outcomes

RK1 Understand the most important phenomena and theories in the various branches of physics, as well as their historical context

RK3 To analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RS3 Estimate orders of magnitude to interpret laboratory phenomena in the field of physics and its related disciplines, as well as in chemistry.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

RS5 Use appropriate electronic instruments and/or computer tools in modelling to find solutions to physics problems.

RC1 Work independently on the management of projects related to the different areas of physics

Learning outcomes

RA5 Understands, at a basic level, the limitations of so-called Classical Physics and of the experiments that led to the formulation of Special Relativity.

RA6 Applies the knowledge acquired to formulate and solve problems, identifying the relevant physical principles and using order-of-magnitude estimates in relation to fluids, thermodynamics, waves, electric fields and magnetic fields.

LA7 Interprets electrical and magnetic phenomena in nature in terms of electromagnetic fields and their interactions with matter.

RA8 Develops a broad overview of the scope of modern physics.

Course content

- Rigid bodies

- Fluids (statics and dynamics)

- Wave motion.

- Electric field.

- Magnetic field.

- Introduction to thermodynamics.

- Optics.

- Special relativity and modern physics.

Teaching activities

AP1. – Interactive lectures

AP2. Seminars or practical application classes

AP3.- Practical activities (case studies, project work, simulations, etc.)

AP4. Independent study

AP5. Tutoring

AP6. Assessment tests

AP10.- Workshop and/or laboratory activities

Assessment system and criteria

Regular assessment period

VERY IMPORTANT: in order for students to benefit from continuous assessment during the standard assessment period, they must attend at least 70 per cent of the scheduled class sessions (SESSION, LAB).

Assessment system Weighting

SE1.- Practical activities (case studies, problems and challenges, possible project to boost marks)  20 %

SE2. Final knowledge assessments (with a minimum mark of 4.5/10 to be included in the average with the other assessment methods) 50%

SE3.- Mid-term knowledge assessments (with a minimum mark of 4.5/10 to be included in the overall average) 30 %

Extraordinary examination session

The final mark for the module will correspond to 100 per cent of the mark obtained in this examination

Objectives

The objectives set out for the ‘Fundamentals of Chemistry’ module within the Bachelor’s Degree in Physics respect effective equality between women and men as laid down in Organic Law 3/2207 of 22 March, the principles of equal opportunities, non-discrimination and universal accessibility for people with disabilities, as set out in Act 51/2203 of 2 December, and promote education for peace, non-violence and human rights, as set out in Act 27/2005 of 30 November.

The specific objectives proposed for the ‘Fundamentals of Chemistry’ module are as follows:

To provide training in science, with a particular focus on chemistry, enabling students to undertake the study of technological subjects.

To ensure the acquisition of cross-curricular competences and skills that enable and enhance the application of the knowledge acquired.

To foster the capacity for innovation and the dissemination of scientific findings.

To foster a commitment to ethical standards in both professional and social contexts.

Prerequisites

No prerequisites.

Competencies

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of Physics.

RS3 Estimate orders of magnitude to interpret laboratory phenomena in the field of Physics and its sub-disciplines, as well as in Chemistry.

Learning outcomes

RA1 List, at a basic level, the principles that explain the physicochemical properties of matter.

RA2 Formulate and name simple inorganic compounds.

RA3 Describe the main mechanisms involved in a chemical reaction, identify different types of reaction, determine the quantities of reactants, and use thermodynamic potentials to characterise the reaction in terms of energy.

LA4 Determine the mechanisms responsible for chemical equilibrium and explain how the parameters on which it depends act.

RA5 Determines the acidity of a solution.

RA6 Identifies some of the main organic functional groups and determines their most important chemical reactions.

RA7 Analyses, evaluates and interprets the results obtained when solving problems.

Description of the content

- Atoms and chemical bonding. Inorganic formulae and nomenclature. Intermolecular forces.

- States of matter and phase diagrams. Fundamentals of thermochemistry. Mixtures. Solutions.

- Chemical reactions: mechanisms and rates; stoichiometry.

- Chemical equilibrium: constants; Le Chatelier’s principle. Solubility equilibrium. Acids and bases.

- Oxidation-reduction reactions and electrochemistry. Introduction to organic chemistry.

- Oxidation-reduction reactions and electrochemistry. Introduction to organic chemistry.

Teaching activities

AP1.- Interactive lectures

AP2. – Seminars or practical application classes

AP3.- Practical activities (case study sessions, project work, simulations, etc.)

AP4. – Independent study

AP5. Tutoring

AP6. Assessment tests

AP10.- Workshop and/or laboratory activities

Assessment system and criteria

REGULAR EXAM SESSION

Both parts, Chemistry and Physics: Same assessment system. The weighted average of both parts must be 5 (with a minimum mark of 4 in each part to be included in the average) to pass.

IT WILL NOT BE POSSIBLE TO PASS THE COURSE BASED ON MID-TERM EXAMS ALONE.

A) CONTINUOUS ASSESSMENT with group assignments

- 15% practicals. Minimum mark of 5.0 to pass.

- 10% Mid-term 1, treated as a group assignment

- 5% class activities (group assignments on the virtual campus)

- 5% inorganic chemistry problem-solving exam

- 5% organic chemistry problem-solving exam

B) FINAL EXAM - Two parts (Chemistry and Physics)

- Students must sit the standard exam for both the Chemistry and Physics sections.

- If a student has failed the laboratory examination for either the inorganic or organic chemistry modules, they may also retake this in the final examination.

- The mark obtained in the course activities will be retained for the calculation of the final mark.

SUPPLEMENTARY EXAMINATION SESSION

In the final exam for the supplementary sitting, the entire course (Chemistry, Physics and Practical Work) will be assessed, and the mark for this exam will account for 100 per cent of the final mark for the course.

Objectives

To carry out laboratory measurements in accordance with established protocols, involving the calibration of instruments, the estimation of systematic and random uncertainties and the identification of strategies for their elimination, the collection of data and the mathematical analysis of that data.

Establish measurement protocols, particularly those relating to the safety of the experimenter.

To prepare reports on measurement procedures, the analysis of results and the conclusions drawn.

Prerequisites

No prerequisites.

Competencies

RK1 Understand the most important phenomena and theories in the various branches of physics, as well as their historical context

RK3 Analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RS3 Estimate orders of magnitude to interpret laboratory phenomena in the field of physics and its related disciplines, as well as in chemistry.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

RS5 Use appropriate electronic instruments and/or computer tools in modelling to find solutions to physics problems.

RC1 Work independently on the management of projects related to the different areas of physics

Learning outcomes

RA9 Carries out laboratory measurements in accordance with established protocols, including the calibration of instruments, the estimation of systematic and random uncertainties (identifying strategies for their elimination), the collection of data and the mathematical analysis of that data.

LA10 Follow measurement protocols, particularly those relating to the safety of the experimenter.

RA11 Prepares reports on measurement procedures, the analysis of results and the conclusions drawn.

Description of the content

- The nature of physical phenomena and their measurement.

- Processing of experimental data and calculation of errors.

- General physics laboratory practicals related to Fundamentals of Physics I and Fundamentals of Physics II

Teaching activities

AP1.- Participatory lectures

AP2. Seminars or practical application classes

AP3. Practical activities (case studies, project work, simulations, etc.)

AP4. Independent study

AP5. Tutoring

AP6. Assessment tests

AP10.- Workshop and/or laboratory activities

Assessment system and criteria

Regular examination period

VERY IMPORTANT: in order for students to benefit from continuous assessment during the ordinary assessment period, they must attend at least 70 per cent of the scheduled class hours (SESSION, LAB).

Assessment system Weighting

SE1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.)  10

SE2. Final knowledge assessments (with a minimum mark of 4/10 to be included in the average with the other assessment components) 50

SE3. – Laboratory practical workbook (students must submit the provided scripts for the practicals carried out for assessment) 40

Extraordinary examination session

The final mark for the module will correspond to 100 per cent of the mark obtained in this examination

Objectives

To understand and apply methods for solving ordinary differential equations and linear and non-linear systems. To develop analytical skills through transforms, series and dynamic models. To encourage the practical application of theory through problems, projects and exercises.

Prerequisites

None

Competencies

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK6 Understand the principles of mathematics and statistics that underpin the study of physics in classical and quantum systems

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

Learning outcomes

LA1 Solves ordinary differential equations, linear differential equations and systems of non-linear equations.

RA2 Demonstrates proficiency in applying solution methods to basic physics equations.

RA3 Analyses the results and interprets the solutions to differential equations.

LR4 Carries out work by understanding, selecting and applying the operational method best suited to a particular problem.

Course content

- Methods for solving Ordinary Differential Equations (ODEs). ODEs with separable variables, homogeneous ODEs, exact ODEs and integral factors.

- Systems of first-order linear equations and higher-order linear equations.

- ODEs involving families of curves. Order reduction.

- Systems of linear and quasi-linear ordinary differential equations. Solving linear equations using series expansions.

- Laplace transform.

- Systems of non-linear equations: equilibria and linearisation. The logistic model: bifurcations and transition to chaos.

Training activities

Learning activity No. of hours* Contact hours

(8–12)** % Face-to-face

AP1.- Participatory lectures 24 4 100

AP2.- Seminars or practical application classes 15 2.5 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 36 3 50

AP4.- Independent study 60 0 0

AP5.- Tutoring 12 0.6 30

AP6.- Knowledge assessments 3 0.5 100

TOTAL 150 10.6

Assessment system and criteria

Assessment system Weighting (%)

AS1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.) 30

AS2.- Final knowledge assessments 60

SE4.- Portfolio 10

Bibliography

Core:

1. Dennis G. Zill

Differential Equations with Modelling Applications

Cengage Learning. 2001.

ISBN: 60-7526-631-3

2. George F. Simmons

Differential Equations: With Applications and Historical Notes

McGraw-Hill. 1993.

ISBN: 84-4810-045-X

Objectives

Students will learn the fundamental concepts of electromagnetism: its place in the history of physics, with particular emphasis on the effective application of vector calculus to relevant problems in electrostatics, magnetostatics and problems involving boundary conditions.

Prerequisites

None

Learning Outcomes

RA1 Has a firm grasp of the basic description of how electromagnetic fields are generated by charges and currents, and of the action of these fields on charges.

RA2 Understands how material media behave in the presence of electric and magnetic fields and knows how to calculate these fields.

RA3 Understands and applies analytical and numerical techniques relating to boundary value problems for potential.

RA4 Understands and is able to use Maxwell’s equations in their differential and integral forms.

Learning outcomes

o RK1 Understand the most important phenomena and theories in the various branches of physics, as well as their historical context

o RK2 Understand physically distinct phenomena and their underlying analogies, enabling the application of known solutions to new problems

o RK3 Analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

o RK7 Understand the laws and principles of physics, identifying their logical and mathematical structure, their experimental basis and the phenomena described by them

o RK11 Understand the fundamentals and basic concepts of electric and magnetic fields, as well as the interrelationship between these fields and their unification in electromagnetism

o RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

o RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

Course content

Topic 1. Electrostatics

Topic 2. Magnetostatics and Electric Current

Topic 3. Boundary value problems

Learning activities

Learning activity | No. of hours (8–12) | Contact hours | % Contact time

AP1. – Participatory lectures | 48 | 4 | 100

AP2.- Seminars or practical application classes |30 |2.5 |100

AP3.- Practical activities (case studies, project work, simulations, etc.) |72 |3 |50

AP4.- Independent study |120 |0 |0

AP5.- Tutorials | 24 |0.6 |30

AP6. – Knowledge assessments |6 |0.5 |100

TOTAL 300 10.6

Assessment system and criteria

Regular assessment period:

Assessment system Weighting %

SE1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.) 30

SE2. – Final knowledge assessments 60

SE4.- Portfolio 10

Extraordinary examination session.

In the resit, the exam will account for 100 per cent of the final mark.

Bibliography

Essential:

1. Griffiths, David J

Introduction to Electrodynamics / David J. Griffiths

Harlow, UK: Pearson. 2014.

ISBN: 1108420419

2. Richard P. Feynman, Robert B. Leighton, Matthew Sands

The Feynman Lectures on Physics, Vol. II The New Millennium Edition: Mainly Electromagnetism and Matter

Basic Books. 2011.

ISBN: 9780465024940

Objectives

Technical English is a four-level course aimed at students on technical or vocational courses, as well as employees undergoing on-the-job training. It covers the basic language and skills required to communicate effectively in various technical fields.

Course description

Key features:

• Technical concepts are presented clearly through engaging texts and illustrations.

• The topics reflect the latest technological developments and are tailored to students’ needs.

• Basic, common language is used that can be adapted to various technical disciplines.

• Grammar is practised regularly, with comprehensive sections on grammar summaries.

Assessment system and criteria

Continuous assessment

• Two written tests covering Units 1–10. Each will assess:

o Listening

o Reading comprehension

o Grammar

o Vocabulary and specialist terminology (Terminology)

• An oral test, held on a separate date.

Weighting

• Written tests (2): 70%

• Oral examination: 20%

• Assessed activities: 10%

Addendum

1. It is compulsory to sit all assessment tests during the continuous assessment period. If a student fails to sit any of the mid-term tests, they forfeit their right to continuous assessment and must sit the exam in the Ordinary Examination Session (100% of the module).

2. The topic of the oral presentation (individual or in pairs) must be agreed in advance with the lecturer.

3. The dates of the assessments will be announced in advance and, unless otherwise stated, will take place in the usual lecture theatre.

Textbook: Technical English 4, Second Edition (Pearson)

Author: David Bonamy

Other books: 1. Scientific English: A Guide for Scientists and Other Professionals

Authors: Robert A. Day & Nancy Sakaduski

2. The Scientist’s Guide to Writing (2nd Edition)

Bibliography

Basic:

1. Christopher Jacques

Technical English, 2nd Edition. Level 4. Workbook (with Answer Key and Audio CD Pack)

Pearson. 2022.

ISBN: 1292424532

2. David Bonamy

Technical English, 2nd Edition. Level 4. Coursebook and eBook

Pearson. 2022.

ISBN: 1292424494

Supplementary:

3.- Cambridge English for Scientists

Tamzen Armer

Cambridge. 2011.

ISBN: 3125351863

Objectives

This module, which together with Mechanics and Waves II forms the subject of Mechanics and Waves, has as its main objective to familiarise students with the Newtonian formulation of classical mechanics and to enable them to apply it correctly to the solution of mechanical problems. More specifically, students must understand the basic concepts of oscillatory motion, as well as the associated phenomena; they must be able to describe both the kinematics and dynamics of a rigid body in a plane and in space; and they must understand the relationship between symmetries and conservation laws in physics.

Prerequisites

None

Competencies

RK1 Understand the most important phenomena and theories in the various branches of physics, as well as their historical context

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK3 To analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RK5 To understand the scope and limitations of classical physics that led to the formulation of special and general relativity, as well as quantum mechanics, in order to address the new problems arising in modern physics.

RK7 Understand the laws and principles of physics, identifying their logical and mathematical structure, their experimental basis and the phenomena described by them

RK12 Understand the theories, laws and models governing physical phenomena related to mechanics

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

Learning outcomes

RA1 Applies the Newtonian formulation appropriately to the solution of mechanical problems.

RA2 Understands the basic concepts of wave motion, as well as the basic phenomenology of oscillatory motion, including coupled oscillations and resonance, and is able to solve problems involving free, forced and damped oscillations.

LA3 Describes both the kinematics and dynamics of a rigid body in a plane and in space, and applies this knowledge to solving problems involving rigid bodies.

RA4 Relates symmetries and conservation laws in physics, applying them to solve practical exercises.

Course content

The module covers the following topics:

1. Particle kinematics.

2. Newtonian dynamics.

3. Oscillations.

4. Non-inertial reference frames.

5. Kinematics of a rigid body.

6. Dynamics of a rigid body.

Teaching activities

Learning activity No. of hours* Contact hours

(8–12)** % Face-to-face

AP1. Participatory lectures 48 4 100

AP2.- Seminars or practical application classes 30 2.5 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 72 3 50

AP4.- Independent study 120 0 0

AP5.- Tutoring 24 0.6 30

AP6.- Knowledge assessments 6 0.5 100

TOTAL 300 10.6

Assessment system and criteria

The assessment process will consist of verifying and evaluating the student’s acquisition of the required competences.

ASSESSMENT SYSTEMS

The assessment systems for this module are:

- AS1: Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.).

- AS2: Final knowledge assessments.

- AS4: Portfolio.

ASSESSMENT CRITERIA

The assessment methods described above are set out in the following assessment criteria. There are two official examination sessions: the ordinary and the supplementary.

+++REGULAR EXAMINATION PERIOD+++

The final mark for this sitting is the weighted average of a set of assessment tasks detailed below:

- Practical activities (SE1), accounting for 20% of the final mark.

- Final knowledge assessments (SE2): two mid-term exams, each accounting for 15% of the final mark, and a final exam, accounting for 30%.

- Portfolio (SE4), accounting for 20% of the final mark. This assessment system involves completing and submitting exercises, which may be undertaken individually or in small groups.

For continuous assessment (comprising the practical activities, the portfolio and the two mid-term exams) to be taken into account, students must achieve a mark of 4.0 or higher in the final exam during the ordinary examination period. Otherwise, their mark will correspond directly to that obtained in that exam.

The module is considered passed in the ordinary examination period if the mark obtained in accordance with the above guidelines is 5.0 or higher.

+++SUPPLEMENTARY EXAMINATION PERIOD+++

If a student has not passed the module during the ordinary examination period, they may sit the extraordinary examination.

The supplementary examination session will take place during the July examination period (for further information, please consult the Academic Calendar). It consists of a single examination covering the entire syllabus of the module.

The module is considered passed in the extraordinary examination period if the final mark is 5.0 or higher.

GRADES

Article 5 of Royal Decree 1125/2003 of 5 September establishes the grading system applicable to modules within degree programmes falling within the scope of the European Higher Education Area. This system is as follows:

To obtain the corresponding credits, students must have passed the associated examinations or assessment tests.

The level of learning achieved by students will be expressed as numerical marks on a scale of 0 to 10, to one decimal place, to which the corresponding qualitative mark may be added:

- 0–4.9: Fail (SS).

- 5.0–6.9: Pass (AP).

- 7.0–8.9: Good (NT).

- 9.0–10: Distinction (SB).

The distinction ‘Honours’ shall be awarded to students who have obtained a mark of 9.0 or higher. The number of students awarded this distinction may not exceed five per cent of those enrolled on the course in the relevant academic year, unless the number of enrolled students is fewer than 20, in which case only one ‘First Class Honours’ may be awarded.

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Basic:

1. A. Fernández Rañada

Classical Dynamics

Alianza. 1994.

ISBN: 84-206-8133-4

Supplementary:

2.- J.R. Taylor

Classical Mechanics

Reverté. 2013.

ISBN: 8429143122

Others:

3. C. Kittel, W.D. Knight, M.A. Ruderman

Mechanics

Reverté. 1968.

ISBN: 978-84-291-42

4. S.T. Thornton, J.B. Marion

Classical Dynamics of Particles and Systems

Reverté. 1975.

ISBN: 9788429140941

Objectives

The aim of the module is to equip students with the necessary tools to understand thermodynamic processes and the principles and laws that govern them, so that they are able to successfully analyse and solve problems within the field of thermodynamics.

Prerequisites

None

Learning Outcomes

RK1 To be familiar with the most important phenomena and theories in the various branches of physics, as well as their historical context

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK3 To analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RK7 Understand the laws and principles of physics, identifying their logical and mathematical structure, their experimental basis and the phenomena described by them

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

RS10 Apply the principles and laws of thermodynamics involved in the analysis of physical phenomena.

Learning outcomes

RA1 Identify the essential aspects of physical phenomena, describing them quantitatively and qualitatively using thermodynamic formalism

RA2 Presents and interprets thermodynamic information (graphs, tables, etc.)

RA3 Understands the First Law as a general principle of energy conservation, with a state function, namely internal energy.

LA4 States the Laws of Thermodynamics, analyses their implications and applies them to problem-solving

RA5 Understands how entropy and its properties account for the thermodynamic behaviour of systems.

RA6 Identifies thermodynamic potentials and analyses the thermodynamic behaviour of systems.

Description of the content

- The zeroth law. The concept of temperature.

- Thermodynamic relations.

- Fundamental thermodynamic equation.

- Thermodynamic processes

- First law: work, internal energy and heat. Enthalpy.

- Second law: entropy.

- Thermodynamic potentials, equilibrium and stability.

- Open systems, phase transitions, critical points.

- Third law.

Training activities

Training activity No. of hours* Contact hours

(8–12)** % Face-to-face

AP1.- Participatory lectures 24 4 100

AP2.- Seminars or practical application classes 15 2.5 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 36 3 50

AP4.- Independent study 60 0 0

AP5.- Tutoring 12 0.6 30

AP6.- Knowledge assessments 3 0.5 100

Assessment system and criteria

Assessment system Weighting

min. % Weighting

Max. %

SE1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.) 20 20

SE2. – Final knowledge assessments 60 60

SE4.- Portfolio 20 20

Objectives

The aim of this module is to provide students with a basic understanding of electrodynamics and its relationship with special relativity.

Prerequisites

No prerequisites

Learning Outcomes

RK1 To be familiar with the most important phenomena and theories in the various branches of physics, as well as their historical context

RK2 To understand physically distinct phenomena and their underlying analogies, in order to apply known solutions to new problems

RK3 To analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RK7 Understand the laws and principles of physics, identifying their logical and mathematical structure, their experimental basis and the phenomena described by them

RK11 Understand the fundamentals and basic concepts of electric and magnetic fields, as well as the interrelationship between these fields and their unification in electromagnetism

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

Learning outcomes

RA5 Understands the relevant aspects of the propagation of electromagnetic waves in free space and in the presence of boundaries

RA6 Identifies the mechanisms of electromagnetic wave emission.

RA6 Analyses the phenomena of propagation and emission of electromagnetic waves.

LO7 Demonstrates an understanding of the close relationship between electromagnetism and the theory of relativity.

Course content

Topic 1: Conductors in electrostatic equilibrium

Topic 2: Electrodynamics

-Electromotive force

-Electromagnetic induction

-Maxwell’s equations

-Electromagnetic waves

Topic 3: Electromagnetism and relativity.

Topic 4: Electromagnetic radiation and radiating systems.

Teaching activities

AP1.- Interactive lectures

AP2.- Seminars or practical application classes

AP3. Practical activities (case studies, project work, simulations, etc.)

AP4. Independent study

AP5. Tutoring

AP6. Knowledge assessments

Assessment system and criteria

Continuous assessment

Activity Weighting (%)

SE1.- Practical activities 40

Mid-term exam (20%).

Submission of questions and problems not solved in class (20%).

SE2. Final knowledge assessments. 60

For component SE1 to count towards the final mark, a minimum mark of 4/10 must be obtained in the final exam during the regular examination period. In any other case, this component will be weighted at 0/10.

Extraordinary final assessment

In the supplementary sitting, the exam mark counts for 100 per cent of the final mark.

Bibliography

Core:

1. Griffiths, David J.

Introduction to Electrodynamics

Pearson. 2014.

ISBN: 9781292021423

2. Jackson,

J.D. Classical Electrodynamics,

Cambridge University Press. 2017.

ISBN: 9781119770763

Supplementary:

3.- R.P. Feynman, R.B. Leighton, M. Sands

The Feynman Lectures on Physics, Vol. II: The New Millennium Edition: Mainly Electromagnetism and Matter: 02

Inter-American Educational Fund. 1972.

ISBN: 9780465040841

Objectives

The aim of this course is to introduce students to experimentation in physics, data analysis and error propagation in the fields of mechanics, electromagnetism and thermodynamics.

Prerequisites

No prerequisites

Learning Outcomes

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics.

RS3 Estimate orders of magnitude to interpret laboratory phenomena in the field of Physics and its sub-disciplines, as well as in Chemistry.

RS5 Use appropriate electronic instruments and/or computer tools in modelling to find solutions to physics problems.

Learning outcomes

LA1 Understands the principles, techniques and measuring instruments, as well as the phenomena of interest in Mechanics and Waves, Thermodynamics and Electromagnetism.

RA2 Uses measuring equipment appropriately and efficiently (Mechanics and Waves, Thermodynamics and Electromagnetism), following measurement protocols, particularly those relating to the safety of the experimenter.

LA3 Is able to assess the limitations of measurement methods due to interference, the simplicity of models and the effects that are neglected in the measurement method (Mechanics and Waves, Thermodynamics and Electromagnetism).

RA4 Plots data graphically, extracts information from the plot, analyses the data, models the results and compares them with the physical laws relating to Mechanics and Waves, Thermodynamics and Electromagnetism.

RA5 Documents the measurement process in terms of its basis, the instrumentation required and the conditions under which it is valid, carrying out a complete analysis in accordance with the IMRD format (Mechanics and Waves, Thermodynamics and Electromagnetism).

RC1 Work independently on the management of projects related to the different areas of physics

Course description

Six experiments will be carried out:

Mechanics Labs:

Free fall

Thermodynamics Labs:

2. Ideal gas law

3. Thermal conductivity

4. Adiabatic gas law

Electromagnetism Labs:

5. Magnetic field in coils

6. Faraday’s law of induction

Training activities

AP1. – Participatory lectures

AP2. Seminars or practical application classes

AP3. Practical activities (case studies, project work, simulations, etc.)

AP4. Independent study

AP5. Tutoring

AP6. Assessment tests

AP10.- Workshop and/or laboratory activities

Assessment system and criteria

1. Writing of laboratory reports (SE1 + SE3, 40%), one of which must be in article format (SE2, 20%):

a PDF produced using LaTeX with the provided template and written in English.

The remaining reports may be in any format preferred by the student, although LaTeX remains compulsory............. 60%

2. Laboratory notebook (SE3)............................................................................... 20%

3. Oral exam (SE2)............................................................ 20%

Aims

The aim of this module is to provide students with a sound grounding in the fundamentals of mathematical logic, combinatorics, graph theory and number theory, equipping them to model and solve problems typical of discrete mathematics. By the end of the module, students will be able to:

1. Understand and apply the fundamentals of mathematical logic, including propositional and predicate logic, as well as rigorous methods of proof.

2. Develop structured mathematical reasoning to tackle abstract and applied problems in various contexts.

3. Analyse properties of integers using number theory, covering topics such as divisibility, modular arithmetic and congruences.

4. Understand and use relations and functions in the context of finite and infinite sets, applying them to the modelling of mathematical structures.

5. To study combinatorial structures and apply fundamental principles of combinatorics to the counting and enumeration of discrete configurations.

6. Formulate and solve problems in graph theory, including properties of graphs, paths, cycles and connectivity.

7. Apply knowledge of discrete mathematics to practical problems involving optimisation, algorithms and modelling in science and engineering.

8. Develop analytical and algorithmic skills for problem-solving using discrete approaches.

Prerequisites

No prerequisites

Competencies

RK6 Understand the principles of mathematics and statistics underpinning the study of physics in classical and quantum systems

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

RC1 Work independently on the management of projects related to the various areas of physics

RC3 Acquire IT knowledge and skills enabling the development of methods and technologies applicable to the relevant fields of study

RS5 Use appropriate electronic instruments and/or computer tools in modelling to find solutions to physics problems.

Learning Outcomes

RA1 Appreciate the foundations of logic, mathematical proofs and algorithmic reasoning.

RA2 Formulates information using logical statements.

RA3 Applies the fundamentals of number theory to problem-solving.

RA4 Relates the basic properties of trees and graphs to examples from intelligent systems.

Course description

- Basic concepts. Propositional logic. Predicate logic. Inference in predicate logic.

- Sets. Relations and functions. Combinatorics.

- Lattices and Boolean algebras. Boolean functions.

- Number theory. Graph theory.

- Binary operations. Divisibility and modular arithmetic. Counts, basic structures and rules of combinatorics. Recurrence and induction. Lists and sets.

- Applications, equivalence and order relations. Combinatorial optimisation. Application examples using mathematical software (Python, Java or similar)

Teaching activities

AP1.- Participatory lectures

AP2. Seminars or practical application sessions

AP3.- Practical activities (case studies, project work, simulation, etc.)

AP4. – Independent study

AP5. Tutoring

AP6. Knowledge assessments

Assessment system and criteria

ENG:

Continuous assessment during the regular term:

Group practical activities (10 per cent): Solving applied problems in the field of discrete mathematics and its applications.

Assignment submissions (10%): Individual exercises to reinforce theoretical and practical concepts.

One mid-term exam (20%): A minimum mark of 4 is required for it to be included in the average.

Regular term final exam (60%): A minimum mark of 4.0/10 in the regular term exam is required for it to be included in the final course mark.

In addition, continuous assessment activities will always count towards the final mark in the regular session.

Extraordinary session exam:

The exam mark will account for 100 per cent of the course mark.

ESP:

Continuous assessment in the regular session:

Group practical activities (10%): Solving applied problems in the field of discrete mathematics and its applications.

Submission of exercises (10%): Individual exercises to consolidate theoretical and practical concepts.

A mid-term exam (20%): A minimum mark of 4 is required for the mark to be included in the final average.

Main examination (60%). A minimum mark of 4.0/10 is required in the main examination for it to count towards the final mark for the module.

Furthermore, continuous assessment activities will always be factored into the mark for the ordinary examination.

Supplementary exam:

The exam mark will account for 100% of the course mark

Bibliography

Essential:

1. Johnsonbaugh, Richard

Discrete Mathematics

6th ed.: Pearson Education. 2005.

ISBN: 9702606373

Aims

This course, together with ‘Mechanics and Waves I’, forms part of the Mechanics and Waves module. Its main objective is for students to become familiar with Lagrangian mechanics and Hamiltonian mechanics, two reformulations of Newtonian mechanics upon which much of modern fundamental physics is built (including Quantum Field Theory and General Relativity). In addition to understanding the conceptual foundations of these formalisms, students should be able to apply them to solving mechanical problems.

Furthermore, an introduction to the two-body problem will be provided, and the dynamics of particles interacting via central forces and the resulting orbits will be discussed. Finally, the implications of moving away from the classical notion of absolute space and time and adopting the postulates of Special Relativity in the development of a mechanical theory will be explored.

Prerequisites

No prerequisites

Learning Outcomes

RK1 Understand the most important phenomena and theories in the various branches of physics, as well as their historical context

RK2 To understand physically distinct phenomena and their underlying analogies, enabling the application of known solutions to new problems

RK3 To analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RK5 Understand the scope and limitations of classical physics that led to the formulation of special and general relativity, as well as quantum mechanics, to address the new problems arising in modern physics.

RK7 Understand the laws and principles of physics, identifying their logical and mathematical structure, their experimental basis and the phenomena they describe

RK12 Understand the theories, laws and models governing physical phenomena related to mechanics

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

Learning outcomes

RA5 Applies the Lagrangian and Hamiltonian formulations appropriately to the solution of

mechanical problems.

RA6 Formulates the equations of motion for central forces, solving them completely and obtaining the solutions for the motion and the trajectories.

LA7 Formulates and solves the equations of a system that deviates from its equilibrium position, classifying said equilibrium.

RA8 Deepens their understanding of the fundamentals of special relativity and its most significant physical consequences, developing proficiency in the study of particle kinematics and dynamics within the context of Minkowski spacetime.

Description of the content

- Lagrangian mechanics.

- The two-body problem. Central forces. Orbits.

- Hamiltonian mechanics.

- Relativistic mechanics.

Teaching activities

AP1.- Interactive lectures

AP2. Seminars or practical application sessions

AP3.- Practical activities (case studies, project work, simulation, etc.)

AP4.- Independent study

Assessment system and criteria

ING

The assessment process will consist of verifying and evaluating the student’s acquisition of the required competencies.

ASSESSMENT SYSTEMS

The assessment systems for this course are:

- SE1: Practical activities. These consist of two mid-term exams taken during the teaching period.

- SE2: Final knowledge assessment. This consists of a final exam covering the entire course syllabus.

- SE4: Portfolio. This assessment method involves the completion and submission of approximately four sets of exercises, which may be carried out individually or in small groups depending on the progress of the course.

ASSESSMENT CRITERIA

The assessment methods described above are set out in the following assessment criteria. There are two official examination sessions: the ordinary and the extraordinary.

ORDINARY SESSION

The final mark for this session is the weighted average of the assessment components detailed below:

- Practical activities (SE1): 25% of the final mark (12.5% for each mid-term exam).

- Final knowledge assessment (SE2): 60% of the final mark.

- Portfolio (SE4): 15% of the final mark.

For the continuous assessment (comprising the portfolio and the two mid-term exams) to be taken into account, students must achieve a minimum mark of 4.0 in the final exam of the ordinary session. Otherwise, the final mark will correspond directly to the mark achieved in that exam.

The course is considered passed in the ordinary session if the final mark is 5.0 or higher.

EXTRAORDINARY SESSION

If a student does not pass the course in the ordinary session, they may sit the extraordinary session.

The supplementary session takes place during the July examination period (for further information, please consult the Academic Calendar). It consists of a single examination covering the entire course content. The mark in the supplementary session corresponds directly to the mark obtained in this examination.

The course is considered passed in the extraordinary session if the final mark is 5.0 or higher.

GRADING SYSTEM

Article 5 of Royal Decree 1125/2003, of 5 September, sets out the grading system applicable to modules within degree programmes in the European Higher Education Area.

To obtain the corresponding credits, students must pass the exams or assessment tests associated with the course.

The level of learning achieved by students will be expressed using numerical marks on a scale from 0 to 10, to one decimal place, to which a qualitative mark may be added:

- 0–4.9: Fail (SS).

- 5.0–6.9: Pass (AP).

- 7.0–8.9: Good (NT).

- 9.0–10: Excellent (SB).

The distinction ‘Honours’ (Matrícula de Honor) may be awarded to students who achieve a mark of 9.0 or higher. The number of such distinctions may not exceed five per cent of the students enrolled on the course during the relevant academic year, unless the number of enrolled students is fewer than 20, in which case only one “Honours” distinction may be awarded.

ESP

The assessment process will consist of verifying and evaluating the student’s acquisition of the required competences.

ASSESSMENT SYSTEMS

The assessment methods for this module are:

- AS1: Practical activities. These consist of two mid-term examinations held during the term.

- AS2: Final knowledge assessments. These consist of a final exam covering the entire syllabus of the module.

- AS4: Portfolio. This assessment method involves completing and submitting approximately four sets of exercises, which may be undertaken individually or in small groups depending on the progress of the course.

ASSESSMENT CRITERIA

The assessment systems described above are set out in the following assessment criteria. There are two official examination sessions: the ordinary and the supplementary.

REGULAR EXAMINATION PERIOD

The final mark for this sitting is the weighted average of the assessment components detailed below:

- Practical activities (SE1): 25% of the final mark (12.5% for each mid-term exam).

- Final knowledge assessments (SE2): 60% of the final mark.

- Portfolio (SE4): 15% of the final mark.

For continuous assessment (comprising the portfolio and the two mid-term exams) to be taken into account, students must achieve a minimum mark of 4.0 in the final exam of the ordinary assessment period. Otherwise, their mark will correspond directly to that obtained in that exam.

The module is considered passed in the ordinary examination period if the final mark is 5.0 or higher.

SUPPLEMENTARY EXAMINATION SESSION

If a student has not passed the module during the ordinary examination period, they may sit the extraordinary examination.

The supplementary examination session will take place during the July examination period (for further information, please consult the Academic Calendar). It consists of a single examination covering the entire syllabus of the module. The mark for the supplementary examination session corresponds directly to the mark obtained in this examination.

The module is considered to have been passed in the extraordinary examination session if the final mark is 5.0 or above.

GRADES

Article 5 of Royal Decree 1125/2003 of 5 September establishes the grading system applicable to modules within degree programmes falling within the scope of the European Higher Education Area. This system is as follows:

The award of the corresponding credits is conditional upon passing the associated examinations or assessment tests.

The level of learning achieved by students will be expressed as numerical marks on a scale of 0 to 10, to one decimal place, to which the corresponding qualitative mark may be added:

- 0–4.9: Fail (SS).

- 5.0–6.9: Pass (AP).

- 7.0–8.9: Good (NT).

- 9.0–10: Distinction (SB).

The distinction ‘Honours’ shall be awarded to students who have obtained a mark of 9.0 or higher. The number of students awarded this distinction may not exceed five per cent of those enrolled on the course in the relevant academic year, unless the number of enrolled students is fewer than 20, in which case only one ‘First Class Honours’ may be awarded.

Bibliography

Essential:

1. A. Fernández Rañada

Classical Dynamics

1st ed. Alianza. 1994.

ISBN: 8420681334

2. H. Goldstein

Classical Mechanics

Addison-Wesley. 1950.

ISBN: 9780201025101

3. J.R. Taylor

Classical Mechanics

Reverté. 2013.

ISBN: 8429143122

4. S.T. Thornton, J.B. Marion

Classical Dynamics of Particles and Systems

Reverté. 1975.

ISBN: 9788429140941

Objectives

To understand, study and apply the theoretical and practical results of analytic functions, in particular elementary functions and their compositions. Understand and apply the Cauchy–Gousart theorem and the Cauchy integral formula, in its various forms for functions of a complex variable, to the integration of holomorphic functions. Understand and correctly apply Cauchy’s residue theorem and its applications. Understand the discrete Fourier transform and its properties, and apply it to signal theory: the fast Fourier transform and signal filtering; and apply it to image processing and audio compression.

Prerequisites

No prerequisites.

Learning Outcomes

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK6 Understand the principles of mathematics and statistics that underpin the study of physics in classical and quantum systems

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

Learning outcomes

LA1 Solve problems involving complex functions of a complex variable and integration in the complex plane.

RA2 Explains the concepts of series convergence, singularities and residues.

RA3 Applies the residue theorem when calculating integrals to solve physics problems.

LA4 Carries out work by applying knowledge of and using the elementary complex functions that appear in various areas of physics.

LA5 Applies the Fourier transform to solve physics problems.

Course content

- Complex numbers. The complex plane. Complex functions of complex variables. Analytic functions and their properties.

- Elementary complex functions and transformations.

- Integration in the complex plane. Cauchy’s theorem. Series, singularities and residues.

- Applications of the residue theorem.

- Fourier series and their applications

- Fourier analysis. Integral Fourier transform and applications.

Teaching activities

AP1.- Interactive lectures

AP2. Seminars or practical application sessions

AP3. Practical activities (case studies, project work, simulation, etc.)

AP4. – Independent study

AP5. Tutoring

AP6. Knowledge assessments

Assessment system and criteria

Compulsory continuous assessment consists of two written examinations. Calculators and formula sheets are not permitted. These assessments do not exempt students from further coursework. They each account for 15% of the mark. Students will also be required to submit practical exercises on a specific section of the course, which account for 10% of the mark. Students will also sit the official exam in the main examination session, which will follow the same format as the assessments and account for 60% of the mark.

Students sitting the supplementary examination will sit a single exam, which accounts for 100% of the mark.

Objectives

This module will lay the foundations of electronics and electronic circuits, providing students with the knowledge required to analyse electronic circuits and understand their uses and applications. Furthermore, it will introduce students to electronic design and its applications in everyday life.

The most important electronic components will be studied, beginning with RLC circuits, covering both direct current and alternating current, followed by operational amplifiers and diodes, and concluding with BJT transistors and MOSFETs. Particular emphasis will be placed on the applications of these circuits, such as the description of power supply circuits and the main logic gates.

Prerequisites

None

Learning Outcomes

RK1 Understand the most important phenomena and theories in the various branches of physics, as well as their historical context

RK3 To analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RC4 Understand the processes involved in obtaining various types of materials, their physical principles and their applications.

Learning outcomes

RA1 Analyses direct current and alternating current circuits.

RA2 Understands the fundamental devices – diodes and bipolar and field-effect transistors – and their description using simple functional models.

RA3 Understands the main applications of the transistor in amplifier circuits: basic amplifier circuits and operational amplifiers.

LA4 Designs circuits using operational amplifiers.

LA5 Understands and uses electronic simulation software.

RA6 Understands the applications of the transistor in digital electronics.

Course content

- Ohm’s Law and Kirchhoff’s Laws; analysis of direct current circuits.

- Analysis of RLC circuits. AC circuits. Transient phenomena; analysis of AC circuits. Steady-state phenomena.

- Network analysis: Thevenin and Norton methods

- Biasing. Small-signal equivalent model. Single-stage amplifiers. Frequency response. Cascading of amplifier stages.

- Operational amplifiers and applications. Ideal operational amplifier.

- Amplifiers. Equivalent circuits of amplifiers. Feedback. Frequency-domain analysis. Amplification stages.

- Introduction to semiconductor theory. p-n junction. Diode, bipolar junction transistor (BJT) and MOSFET. Characteristic equations.

Amplifying function of the BJT and the MOSFET.

Training activities

Learning activity No. of hours* Contact hours

(8–12)** % Face-to-face

AP1.- Participatory lectures 24 4 100

AP2.- Seminars or practical application classes 15 2.5 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 36 3 50

AP4.- Independent study 60 0 0

AP5.- Tutoring 12 0.6 30

AP6.- Knowledge assessments 3 0.5 100

TOTAL 150 10.6

Assessment system and criteria

Assessment will consist of the following components:

Continuous assessment (40 per cent):

-Portfolios 10%

-Case studies/problem-solving: 30%

Objective assessment (60%):

-Term exam: 60%

Timetable

Click on this link for the detailed timetable in Excel

Bibliography

Basic:

1. Charles, K., & Alexander, S.

Fundamentals of Electrical Circuits

McGraw-Hill Interamerican. 2013.

ISBN: 978-607-15-09

Prerequisites

None

Learning outcomes

RK6 Understand the principles of mathematics and statistics that underpin the study of physics in classical and quantum systems. / Know the principles of mathematics and statistics that support the study of physics in classical and quantum systems.

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics. / Conduct calculations, assessments, studies, reports and tasks to develop high-quality work in the field of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results. / Apply mathematical and numerical methods in the modelling and explicit resolution of problems in physics and related disciplines, selecting appropriate tools and interpreting results.

RS6 Prepare reports, written works and other scientific documents in the field of physics, communicating them clearly and effectively both in writing and orally, including in English. / Prepare reports, written works and other scientific documents in the field of physics, communicating them clearly and effectively both in writing and orally, including in English.

RC1 Work independently on the management of projects related to the various areas of physics. / Develop independent work in the management of projects related to the various areas of physics.

RC3 Acquire computer knowledge and skills that enable the development of methods and technologies applicable in the relevant fields of knowledge. / Acquire computer knowledge and skills that enable the development of methods and technologies applicable in the relevant fields of knowledge.

Learning outcomes

RA1 Understands the various models and data structures and develops algorithms appropriate to the data, depending on the requirements of the problem to be solved

RA2 Applies knowledge of algorithms and computational complexity to solve problems in physical systems and related fields

RA3 Identifies and proposes solutions to problems relating to algorithm efficiency

LA4 Designs and scales algorithms for environments of varying size and complexity

RA5 Solves problems that may arise in physics by applying knowledge

relating to the structure and programming of computer systems

Course description

- Introduction, architecture, design and database models

· Abstract data type (ADT).

· Linear and associative ADTs. Tree ADTs. Graph ADTs.

· Data structures on disk.

· Analysis of algorithm efficiency.

· Algorithm design. Algorithmic techniques: greedy algorithms, divide and conquer.

· Introduction to dynamic programming.

· Applications in solving problems relating to physical systems and physics, using programming languages (Python, Java or similar).

Teaching activities

Learning activity No. of hours* Contact hours

(8–12)** % Face-to-face

AP1. – Participatory lectures 24 4 100

AP2. – Seminars or practical application classes 15 2.5 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 36 3 50

AP4.- Independent study 60 0 0

AP5.- Tutorials 12 0.6 30

AP6.- Knowledge assessments 3 0.5 100

TOTAL 150 10.6

Assessment system and criteria

Assessment system Weighting

min. % Weighting

Max. %

SE1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.) 20 30

SE2. – Final knowledge assessments 60 60

SE4.- Portfolio 10 20

Objectives

The aim of this module is for students to develop their initial skills in quantum physics, the most recent of the major branches of physics and one that is highly relevant today due to its technological applications, and, more specifically, in Old Quantum Theory. Students are expected to acquire a conceptual understanding of the physics underlying the phenomena that led humankind to the formal development of this area of knowledge, using the earliest mathematical formulations and concepts such as the quantisation of energy in interactions and the wave-particle duality-particle duality of both electromagnetic radiation and matter. Students must also be able to solve relatively complex problems in Old Quantum Theory.

Prerequisites

None

Learning Outcomes

RK1 To be familiar with the most important phenomena and theories in the various branches of physics, as well as their historical context

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK3 To analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RK5 To understand the scope and limitations of classical physics that led to the formulation of special and general relativity, as well as quantum mechanics, in order to address the new problems arising in modern physics.

RK6 Understand the principles of mathematics and statistics that underpin the study of physics in classical and quantum systems

RK7 Understand the laws and principles of physics, identifying their logical and mathematical structure, their experimental basis and the phenomena described by them

RK8 Understand the fundamental concepts of quantum physics in modelling phenomena at the atomic and subatomic scales

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

Learning outcomes

RA1 Apply the experimental foundations of quantum physics and its postulates to discuss laboratory exercises and/or experiments effectively.

RA2 Applies the mathematical formulation of quantum mechanics appropriately to simple one-dimensional and three-dimensional systems to successfully complete practical activities.

LA3 Understands the dual nature of microscopic entities and its implications for their characteristics and description.

RA4 Understands the experimental foundations of quantum physics and is proficient in handling the orders of magnitude of various physical quantities at the atomic scale.

Course content

Topic 1: Thermal radiation and Planck’s postulate.

Topic 2: Particulate properties of electromagnetic radiation.

Topic 3: de Broglie’s hypothesis and the wave properties of matter.

Topic 4: Classical and semi-classical atomic models.

Topic 5: The wave formulation of quantum mechanics.

Topic 6: The time-independent Schrödinger equation.

Topic 7: Schrödinger’s atomic model.

Training activities

Learning activity No. of hours* Contact hours

(8–12)** % Face-to-face

AP1.- Participatory lectures 48 4 100

AP2. – Seminars or practical application classes 30 2.5 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 72 3 50

AP4.- Independent study 120 0 0

AP5.- Tutoring 24 0.6 30

AP6.- Knowledge assessments 6 0.5 100

TOTAL 300 10.6

Assessment system and criteria

The assessment process will consist of evaluating the extent to which the student has acquired the competences associated with the module.

REGULAR EXAM SESSION – CONTINUOUS ASSESSMENT

Continuous assessment will consist of the following components:

-- a case study, accounting for 20% of the final mark for the module, which students will undertake in small groups throughout the term; this practical case study will involve the submission of one or more deliverables, each of which will be assessed and will carry its corresponding weighting in the case study mark. Submission dates will be announced well in advance.

-- a mid-term exam, accounting for 20% of the final mark for the module. The date of the first exam, which will cover topics 1 to 3, will be announced well in advance (it will take place during November).

-- a final exam, accounting for 60 per cent of the final mark for the module, which will cover all the content (topics) taught and will take place on the date set by the university for the ordinary examination session (officially announced at the start of the term).

***** The weighted average of all these assessment tests will be calculated only if the mark obtained in the final exam is 4.0 out of 10 or higher.

Furthermore, only the examinations will be subject to re-marking.

***** The student will have passed the module in the ordinary examination session if, and only if, they obtain a final mark (weighted average of all assessment tests) of 5.0 out of 10 or higher.

Otherwise, the student may pass the module in the supplementary examination period.

EXTRAORDINARY EXAMINATION SESSION

In this sitting, the student will be examined on all the content (topics) covered in a final examination to be held on the date set by the university for the supplementary sitting. The mark for this sitting will be solely and exclusively that obtained in this examination, and the module will be deemed passed if the mark is 5.0 out of 10 or higher.

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Essential:

1. Juan José Gómez Cadenas

Quantum Mechanics: Introduction and Applications

Ediciones Paraninfo. 2012.

ISBN: 8498825126

2. Robert Martin Eisberg and Robert Resnick

Quantum Physics: Atoms, Molecules, Solids, Nuclei and Particles

Limusa S.A. de C.V. (Mexico). 1978.

ISBN: 978-968180419

Supplementary:

3.- Alberto Galindo and Pedro Pascual

Quantum Mechanics

Reverte Publishers. 1991.

ISBN: 8429158801

4. Ramón Fernández and José Luis Sánchez

100 Problems in Quantum Physics

Alianza Editorial. 2001.

ISBN: 8420686336

Others:

5. David J. Griffiths

Introduction to Quantum Mechanics

Cambridge University Press. 2018.

ISBN: 1107189632

6. J. J. Sakurai

J. J. Sakurai – Modern Quantum Mechanics

Addison-Wesley. 2017.

ISBN: 1108422411

Objectives

The aim of this course is to introduce students to experimentation in optics and electronics.

Prerequisites

No prerequisites

Learning Outcomes

Understand phenomena of physically different nature and their underlying analogies for the application of known solutions to new problems.

RS3 Estimate orders of magnitude to interpret laboratory phenomena in the field of Physics and its related disciplines, as well as in Chemistry. / Estimate orders of magnitude to interpret laboratory phenomena in the field of Physics and its related disciplines, as well as in Chemistry.

RS4 Apply mathematical and numerical methods in the modelling and explicit solution of problems in Physics and related disciplines, selecting appropriate tools and interpreting results. / Apply mathematical and numerical methods in the modelling and explicit solution of problems in Physics and related disciplines, selecting appropriate tools and interpreting results.

RS5 Use appropriate electronic instruments and/or computer tools in modelling to find solutions to physical problems. / Use appropriate electronic instruments and/or computer tools in modelling to find solutions to physical problems.

RC1 Carry out independent work in the management of projects related to the various areas of physics. / Develop independent work in the management of projects related to the various areas of physics.

Learning outcomes

RA1 Understands the principles, techniques and measuring instruments, as well as the phenomena of interest in Mechanics and Waves, Thermodynamics and Electromagnetism.

RA2 Uses measuring instruments appropriately and efficiently (Mechanics and Waves, Thermodynamics and Electromagnetism), following measurement protocols, particularly those relating to the safety of the experimenter.

LO3 Is able to assess the limitations of measurement methods due to interference, the simplicity of models and the effects that are neglected in the measurement method (Mechanics and Waves, Thermodynamics and Electromagnetism).

RA4 Plots data graphically, extracts information from the plot, analyses the data, models the results and compares them with the physical laws relating to Mechanics and Waves, Thermodynamics and Electromagnetism.

RA5 Documents the measurement process in terms of its basis, the instrumentation required and the conditions under which it is valid, carrying out a complete analysis in accordance with the IMRD format (Mechanics and Waves, Thermodynamics and Electromagnetism).

Course description

Optics and electronics laboratory practicals. Data processing, analysis techniques and error calculation.

Training activities

Learning activity No. of hours* Contact hours

(8–12)** % Face-to-face

AP1.- Participatory lectures 6 0.33 100

AP2.- Seminars or practical application classes 6 0.33 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 18 0.5 50

AP4.- Independent study 180 0 0

AP5.- Tutorials 36 0.6 30

AP6.- Knowledge assessments 6 0.33 100

AP10.- Workshop and/or laboratory activities 198 11 100

TOTAL 450 13.09

Assessment system and criteria

SE1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.) 20

AS2.- Final knowledge assessments 40

AC3.- Laboratory practical logbook 40

Objectives

- To understand how the particle and wave nature of light has evolved with the progress of scientific research in physics.

- To recognise the different optical processes that occur when light propagates through a medium.

- To understand Fermat’s principle and its physical implications.

- To understand the principles and laws of geometrical optics.

- Determine the position and characteristics of images formed by optical systems.

- Understand how optical instruments (microscopes and telescopes) work.

- Identify the possible states of polarisation of light and how light can be polarised.

- Apply Malus’s law.

- Understand Fresnel’s equations and how to apply them.

- Calculate the rate of energy flow using the Poynting vector and its time average.

- Understand the phenomenon of interference and how to calculate intensities.

- Understand the function of the Michelson interferometer and the Fabry–Pérot interferometer.

- Understand the physical meaning of coherence and the distinction between spatial and temporal coherence.

- Describe diffraction through a single slit.

- Distinguish between the Fraunhofer and Fresnel approximations in the theory of diffraction.

- Describe how diffraction gratings work.

- Understand the mechanisms of radiation-matter interaction: absorption, spontaneous emission and stimulated emission.

- Analyse the main characteristics of laser radiation, how a laser works and some types of lasers.

Prerequisites

None

Learning Outcomes

RK1 To be familiar with the most important phenomena and theories of the various branches of physics, as well as their historical context.

RK2 Understand physically distinct phenomena and their underlying analogies, enabling the application of known solutions to new problems.

RK3 Analyse the fundamental concepts and principles of physical systems in order to make approximations that enable the construction of a simplified model.

RK4 Understand the most relevant physical principles for their practical application to the most important areas of optics.

RK7 Understand the laws and principles of Physics, identifying their logical and mathematical structure, their experimental basis and the phenomena described by them. / Understand the laws and principles of Physics, identifying their logical and mathematical structure, their experimental basis and the phenomena described by them.

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics. / Apply the most important knowledge, concepts and methods from the various branches of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting appropriate tools and interpreting results. / Apply mathematical and numerical methods in the modelling and explicit resolution of problems in physics and related disciplines, selecting appropriate tools and interpreting results.

Learning outcomes

LA1 Describes and analyses optical processes within the framework of a wave model, including the phenomena of propagation, polarisation, interference and diffraction, applying them to problem-solving.

LA2 Understands the concept of coherence.

LA3 Understands the principles underlying the various types of interferometers and diffraction gratings, and knows how to apply this knowledge to problem-solving

LA4 Describes and analyses the principles of geometric optics and their application to the study of optical systems.

RA5 Explains and analyses the fundamentals of modern optics and understands the principles underpinning laser devices and the techniques used in the generation of light pulses.

Course content

- Properties of light.

- Geometrical optics.

- Optical instruments.

- Wave optics: reflection, refraction, polarisation.

- Interference (introduction to coherence theory, superposition of fields, interferometers).

- Scalar theory of diffraction (Fraunhofer and Fresnel approximations). Resolving power of instruments. Diffraction gratings. Introduction to spatial frequency filtering.

- Emission and absorption of radiation.

- Introduction to modern optics. Amplification of stimulated radiation: the laser.

Teaching activities

Teaching activity No. of hours* Contact hours

(8–12)** % Face-to-face

AP1.- Participatory lectures 24 4 100

AP2.- Seminars or practical application classes 15 2.5 100

AP3.- Practical activities (case studies, project work, simulations, etc.) 36 3 50

AP4.- Independent study 60 0 0

AP5.- Tutoring 12 0.6 30

AP6.- Knowledge assessments 3 0.5 100

Assessment system and criteria

Assessment system Weighting (%)

SE1.- Practical activities (case studies, problem-solving and challenges, project work, oral presentations, debates, etc.) 20

AS2.- Final knowledge assessments 60

AS4.- Portfolio 20

Timetable

Click on this link to view the detailed timetable in Excel

Bibliography

Basic:

1. Guenther, Robert D.

Modern Optics/

2nd ed. Oxford University Press, 2015.

ISBN: 9780198824329

2. Hecht, Eugene

Optics

3rd ed. Pearson Addison-Wesley, 2000.

ISBN: 9788478290253

Objectives

The aim of this module is for students to solve non-linear first-order ODEs and find all their solutions, and to solve linear second-order ODEs in two variables using separation of variables and Sturm–Liouville theory

Prerequisites

PR1 Identify the basic elements, terms, and initial and boundary conditions of a partial differential equation (PDE).

RA2 Solve physics problems by formulating a partial differential equation (PDE) with its corresponding conditions

RA3 Understands the properties of the special functions most commonly used in physics and Sturm–Liouville theory.

RA4 Applies the method of separation of variables to reduce a PDE to a system of ordinary differential equations.

RA5 Assess the validity of a solution to a physical problem and correct it using appropriate methods.

Competencies

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK6 Understand the principles of mathematics and statistics that underpin the study of physics in classical and quantum systems

RS1 Apply the most important knowledge, concepts and methods from the various branches of physics.

RS2 Carry out calculations, assessments, studies, reports and tasks to produce high-quality work in the field of physics.

RS4 Apply mathematical and numerical methods to the modelling and explicit solution of problems in physics and related disciplines, selecting the appropriate tools and interpreting results.

Learning outcomes

LA1

RA2

RA3

RA4

LR5

Course description

- First-order PDEs

The linear equation. The semi-linear equation. Pfaff’s equation. The general equation. Cauchy’s problem.

The space of continuous functions

Pointwise convergence. Uniform convergence. Convergence in norm: completion of this space. Trigonometric bases: Fourier series. Some results on convergence.

Boundary value problems for ODE: Sturm–Liouville’s theorem

Introduction. Self-adjoint operators: eigenvalues and eigenfunctions. The Sturm–Liouville theorem: generalised Fourier series. Solving the boundary value problem

Solving a second-order linear PDE in two variables

Separation of variables method. Coordinate transformations.

Learning activities

AP1. – Participatory lectures

AP2. – Seminars or practical application sessions

AP3. Practical activities (case studies, project work, simulation, etc.)

AP4. – Independent study

AP5. Tutoring

AP6. Knowledge assessments

Assessment system and criteria

Compulsory continuous assessment consists of two written examinations (40 per cent) in which students must solve, using differential calculus, certain differential equations of the type explained in the course content. Calculators and formula sheets are not permitted. These assessments do not exempt students from further coursework. They carry a weighting within the established range. Students will also sit the official examination during the ordinary examination period, which has the same format as the assessments (60%). Furthermore, to be included in this weighting, students must obtain a minimum of 4 marks in the official examination.

Students who fail to meet the continuous assessment requirements, primarily due to absences, will sit the official examination and will forfeit the corresponding weighting from the other continuous assessment activities.

Students sitting the supplementary examination will sit a single exam, which will account for 100 per cent of the mark

Addendum

To follow this module, students must be able to solve ordinary differential equations covered in a previous module, which in turn requires them to be able to solve the most important types of integrals: direct integration, integration by parts, rational integrals, integration by substitution, irrational integrals and trigonometric integrals.

Objectives

To familiarise students with the fundamental concepts of the solid state.

To learn about and understand crystal structures, types of atomic bonds and their implications for the properties of solids.

To understand the mechanical, thermal, electronic and magnetic properties of solids

Prerequisites

No prerequisites

Learning outcomes

RK1 To be familiar with the most important phenomena and theories in the various branches of physics, as well as their historical context

RK2 Understand physically distinct phenomena and their underlying analogies in order to apply known solutions to new problems

RK3 To analyse the fundamental concepts and principles of physical systems in order to develop approximations that enable the construction of a simplified model

RK7 Understand the laws and principles of physics, identifying their logical and mathematical structure, their experimental basis and the phenomena described by them

RS3 Estimate orders of magnitude to interpret laboratory phenomena in the field of physics and its sub-disciplines, as well as in chemistry.

RS5 Use appropriate electronic instruments and/or computer tools in modelling to find solutions to physics problems.

RS7 Apply the principles of solid-state physics to the design of devices and circuits.

RC4 Understand the processes involved in obtaining various types of materials, their physical fundamentals and their applications.

Learning outcomes

RA1 Analyses the most common defects observed in crystals and their relationship to some of their physical properties.

RA2 Understand the relationship between structure, bonding characteristics and the properties of solids, as well as the phenomenon of vibration in crystal lattices and the models used to describe them.

RA3 Understands the emergence of cooperative phenomena such as ferromagnetism or superconductivity.

LA4 Demonstrates proficiency in the use of instrumentation (Solid-State Physics), following measurement protocols, particularly those relating to the safety of the experimenter.

RA5 Consistently documents the measurement process in the laboratory with regard to its rationale, the instrumentation required and the conditions under which it is valid, carrying out a complete analysis in accordance with the IMRD format (Solid-State Physics).

RA6 Applies the knowledge acquired to formulate and solve typical problems in solid-state physics, identifying the relevant physical principles.

Description of the content

-Topic 1: Chemical bonding (ionic, covalent, metallic, hydrogen bonding and Van der Waals forces)

-Topic 2: Crystal structure (Bravais lattices, atomic packing fraction, defects, etc.)

-Topic 3: Reciprocal lattice and X-ray and neutron diffraction patterns.

-Topic 4: Lattice vibrations.

-Topic 5: Thermal properties of solids.

-Topic 6: Free-electron model (Drude model, quasi-free electrons, Bloch’s theorem)

-Topic 7: Band theory and tight-binding theory.

-Topic 8: Introduction to electronic properties and transport (insulators, conductors and semiconductors)

-Topic 9: Cooperative phenomena (magnetism and superconductivity).

Teaching activities

AP1.- Participatory lectures

AP2.- Seminars or practical application sessions

AP4.- Independent study

AP5.- Tutoring

AP6. Knowledge assessments

AP10.- Workshop and/or laboratory activities

Assessment system and criteria

A. Continuous Assessment and Ordinary Examination:

30 per cent of the continuous assessment will consist of two problem-solving activities carried out in class, each accounting for 15 per cent.

The remaining 10 per cent of the continuous assessment will be the portfolio, comprising three submissions to be completed during the course

The ordinary examination is not part of the continuous assessment and will account for 60 per cent of the mark. The minimum mark required to be included in the average with the continuous assessment is 4.

B. Supplementary Examination:

The module may be passed in the resit by sitting a comprehensive assessment covering the entire syllabus, which will account for 100 per cent of the final mark. A mark of 5 or above is required to pass the module in this resit.