Computational Physics

This course aims to provide students who take it with the numerical tools necessary to solve problems that may arise in fields related to Physics.

The specific objectives of the subject are:
• Knowledge of the theoretical bases behind any software that they may encounter in the future so that they are aware of its ranges of applicability and limitations.
• Ability to create the necessary IT tools.

Learning outcomes:
With respect to the Computational Physics subject, the student will demonstrate
• Be familiar with the different types of numerical problems that can be presented in Physics, and have the basic tools to be able to approach their study with confidence. In-depth knowledge of these numerical techniques will allow the student who later uses commercial computer packages to understand what the different algorithms are doing, their range of validity and the origin of possible errors. These problems include the resolution of systems of algebraic and differential equations (ordinary and partial derivatives), data processing, etc.

BASIC NUMERICAL METHODS. Numerical roots of equations and systems of equations. Elimination methods, Newton-Raphson, others. Numerical interpolation, differentiation and integration.

SIMULATION AND MODELING METHODS. Stochastic processes and random number generation. Monte Carlo method.

NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS. Euler method. Predictor-corrector method. Runge-Kutta method. Dynamic systems.

NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES. Finite difference methods. Finite element method.

PHYSICAL EXAMPLES.

- Numerical Recipes. W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling. Cambridge University Press (1988)

- Computational Techniques for Fluide Dynamics. C.A.J. Fletcher. Springer-Verlag (1991)

- Introducción a la programación con Python 3. Andrés Marzal, Isabel Gracia, Pedro García. Publicacions de la Universitat Jaume I (2014)
[http://repositori.uji.es/xmlui/handle/10234/102653]

- https://www.python.org/

BASIC AND GENERAL
CB1 - Students will demonstrate possession and understanding of knowledge in an area of study that is based on secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study.
CB2 - Students will know how to apply their knowledge to their work or vocation in a professional way and possess the skills that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of study.
CB3 - Students will have the ability to gather and interpret relevant data (normally within their area of study) to make judgments that include reflection on relevant issues of a social, scientific or ethical nature.
CB4 - Students will be able to transmit information, ideas, problems and solutions to both a specialized and non-specialized audience.
CB5 - Students will develop those learning skills necessary to undertake further studies with a high degree of autonomy.
CG2 - Students will have the ability to gather and interpret relevant data, information and results, obtain conclusions and issue reasoned reports on scientific, technological or other areas that require the use of knowledge of Physics.
CG3 - Students will be able to apply both the theoretical and practical knowledge acquired as well as the capacity for analysis and abstraction in the definition and formulation of problems and in the search for their solutions in both academic and professional contexts.

TRANSVERSE
CT1 - Acquire capacity for analysis and synthesis.
CT2 - Have the capacity for organization and planning.
CT3 - Master a foreign language and work in an international context.
CT4 - Be able to work as a team.
CT5 - Develop critical reasoning.
CT6 - Develop creativity, initiative and entrepreneurial spirit.

SPECIFIC
CE2 - Be able to clearly handle orders of magnitude and make adequate estimates in order to develop a clear perception of situations that, although physically different, show some analogy, allowing the use of known solutions to new problems.
CE5 - Be able to carry out the essentials of a process or situation and establish a working model of it, as well as to make the required approximations in order to reduce the problem to a manageable level. They will demonstrate critical thinking to build physical models.
CE6 - Understand and master the use of the most commonly used mathematical and numerical methods in Physics.
CE7 - Be able to use computer tools and develop software programs.
CE8 - Be able to manage, search and use bibliography, as well as any relevant source of information and apply it to research work and technical development of projects.

The introduction of theoretical content will be simultaneous with the performance of related practices, so that for each theoretical block a time will be allocated in which the appropriate programs will be developed to solve problems that exemplify the topic addressed. The programs carried out may be presented and discussed jointly in class.

The fundamental objective is for students to be able, at the end of the course, to address any numerical problem related to Physics, having the minimum theoretical tools to achieve it.

This will be the methodology followed, as long as the traditional enrollment parameters are maintained.

In the "first opportunity" it will only be possible to pass the subject in the continuous evaluation modality. The aspects to be evaluated will be practices and programs for each of the topics covered (with respect to these assignments, the teacher in charge of the subject may request additional explanations that will contribute to their grading). We will complement the evaluation with periodic release controls.

The course is splited in two parts, for each of them and in them the student will obtain grades N1 and N2, finally taking the average (N1+N2)/2 as long as each of them is equal to or greater than 3.0 (out of 10). For the student to be evaluated by this modality, they must attend a minimum of 60% (both in the first and second half of the subject) of the scheduled sessions. This percentage may be reduced in case of duly justified cause.

The evaluation in the "second opportunity" will take place on the date scheduled by the dean's office and will consist of an exam (weight: 0.2) plus the presentation and defense of (weight: 0.8) all the works requested throughout the regular academic course. The final grade will be the average of the N1 and N2 grades corresponding to the two mentioned parts, provided that each of them is equal to or greater than 3.0 (out of 10).

In cases of fraudulent completion of exercises or evaluation tests, the provisions of the “Regulations for evaluating the academic performance of students and reviewing grades” will apply:

Article 16. Fraudulent performance of exercises or tests.
The fraudulent completion of any exercise or test required in the evaluation of a subject will imply a failure grade in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. The creation of works that are plagiarized or obtained from sources accessible to the public without reworking or reinterpretation and without citations to authors and sources will be considered fraudulent, among others.

A good deal of the work to be presented will be carried out during the interactive laboratory classes; however, for optimal use of the subject, it is recommended to dedicate a certain number of additional hours of personal work. The detailed amount of work hours would be:
Interactive laboratory classes: 42 hours (100% in-person)
Independent study: 30 hours
Tutorials: 3 hours
Autonomous work on a computer and other activities: 37.5 h

This is a course that does not require too much conceptual effort but, rather, continuous work. Furthermore, it complements very well other courses that, given their nature, frequently need numerical tools to solve the problems that arise.

It is advisable that students enrolling in this subject have already taken the course on Mathematical Methods I-VI, as well as have programming knowledge in a scientific language (C, Fortran, Python, Matlab...).

In general, during the students' stay at the Center, the hygiene and individual protection measures indicated by the health authorities and by the University of Santiago de Compostela itself must be scrupulously respected.

Tutorials may be in person or online. They will require an appointment.