
Numerical Methods II
Code: 103951Credits: 5
| Degree programme | Type | Course |
|---|---|---|
| Physics | OB | 3 |
Contact lecturer
- Name :
- José María Escartin Esteban
- Email :
- josemaria.escartin@uab.cat
Group languages
You can consult this information at the end of the document.
Prerequisites
It it highly recommended to have passed the subject "Mètodes Numèrics I".
It is recommended to have a good knowledge in calculus.
Objectives
Deepening knowledge in phisical systems modeling.
Deepening knowledge in the basic concpets of numerical methods: precisión, discretization, numerical error, conditioning, normalization...
To set and solve complex physical problems using numerical techniques.
To know the theoretical basis of error estimation in numerical simulations.
Learning outcomes
- Communicate complex information in an effective, clear and concise manner, either orally, in writing or through ICTs, in front of both specialist and general publics.
- Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
- Use distinct numerical methods to solve computational problems in a real variable and evaluate the numerical error in implementing these within a particular problem.
- In pseudocode, design and implement programmes for solving calculations in a real variable: integration, derivation, solving equations, solving ordinary differential equations.
- Develop programmes in a specific programming language.
- Apply finite element methods to solving specific problems in some of the most common problems.
- Use the most common numerical methods to describe complex systems and to solve some of the most usual problems.
- Control errors produced in the various numerical methods, giving a fuller analysis of these.
- Analyse and describe clearly the strategy in addressing a particular problem from the numerical point of view.
- Develop programming strategies that allow the collaborative use of the programmes developed.
- Analyse and describe physical problems from an approximate perspective, modelling complex physical systems and solving them in an approximate manner.
- Present numerical results accurately, including the processing of statistical errors.
- Identify situations in which a change or improvement is needed.
Contents
1. Basic concepts.
- Numerical error.
- Discretization.
- Normalization.
2. Solving non-linear equations.
- Newton-Raphson method.
- Systems of non-linear equations.
3. Numerical derivation.
4. Numerical integration.
5. Solving differential equations.
- Euler method.
- Runge-Kutta methods.
- Other methods (shooting, ...)
6. Solving equations with partial derivatives.
- Finite elements and differences.
- Implicit and explicit schemes.
- Systems of linear equations.
7. Modelling of complex systems.
- Concepts of modelling and simulation.
- Simulation of physical systems. Examples.
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Reports preparation | 71 | 2.84 | |
| Simulation tasks | 21 | 0.84 | |
| Personal study | 10 | 0.4 | |
| Theoretical lectures | 20 | 0.8 |
Development of reports. Students have to report on the practices and simulations, checking and analyzing the obtained simulations, and reporting the main results.
Personal study. It is necessary to study the theory, and to prepare the simulations.
Theoretical lectures. Guided lectures, the lecturer will give the key aspects of the different parts of the course. Also, the main lines to follow using bibliography and complementary media. A complete and ordered description of the course is given.
Simulation work. Students will develop several simulations and/or practices with the support of the teaching staff.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Theory exam | 30% | 3 | 0.12 | 1, 6, 7, 8, 9, 11, 12 |
| Practical 2: Simulation practical | 40% | 0 | 0 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 |
| Practical 1: Guided practical | 30% | 0 | 0 | 1, 2, 3, 4, 5, 8, 9, 10, 11, 12 |
Guided practical. The written report will be assessed taking into account the approach to the problem, its numerical resolution, and the presentation of the results. Eventually, we will also consider an interview to evaluate the knowledge and skills of the different authors of the report.
Simulation practical. The written report will be assessed taking into account the approach to the problem, its numerical resolution, and the presentation of the results. Eventually, we will also consider an interview to evaluate the knowledge and skills of the different authors of the report.
All the practicals will be done in groups. All members of the group are co-authors of all the works. They must know the content, the development, the results, and the used techniques of all the simulations in detail.
Theory exam. It will be valued the relevant theoretical concepts. (There will not be a resit for students that fail or score low in the theory exam.)
To access re-evaluation, the student has to be previously evaluated to a set of activities whose weight is at least two thirds of the total qualification. Re-evaluation consists of the resubmission of the practicals reports and, eventually, an interview with the authors of the report. The maximum qualification of the resubmitted practicals is 6 over 10.
It will be considered that there isn't enough evaluation evidence (thus the qualification will be "not evaluable") when we evaluate at most the first practical or the theory exam.
In the case of irregularities that would produce a significant variation in an assessment item, this item will be qualified as 0, independently from the disciplinary process that could be started. In the case of multiple irregularities in the evaluation activities of the subject, the final qualification of for this subject will be 0.
Single assessment: Students who opt for single assessment must deliver all the practicals and do the exam on the same day (to be determined, towards the end of the semester). Re-evaluation of single assessment students will follow the same scheme used for continuous assessment students.
Use of Artificial Intelligence (AI): In this subject, AI technologies may only be used for support tasks, such as bibliographic searches, orthographic corrections of texts, or the translation of materials. It is explicitly forbidden to use AI for the writing of reports, designing simulations, writing code or pseudo-code, or elaborating graphs or animations. The use of AI tools during the theory exam or during the practicals interviews is not allowed. All practicals reports must contain a section where the use made of AI in relation to the practical is clearly identified, and where the tools used are clearly specified. Furthermore, this section must include a critical discussion on how AI has influenced the process and the final result of the activity. Lack of transparency in the use of AI in the practicals or the use of AI for tasks where it is not allowed will be considered academic dishonesty and will result in partial or total penalties on the qualification of the activity, or greater sanctions in serious cases.
Bibliography
1. Introducción al Análisis Numérico. A. Ralston, Limusa-Wiley.
2. Análisis numérico. Las matemáticas del cálculo científico, D. Kinkaid, D. Cheney, Wesley Iberoamericana.
3. Mètodes numèrics per a la física, R. Guardiola, E. Higón, J. Ros, Materials 9, Universitat de València.
4. Métodos numéricos para la Física y la Ingeniería. Luis Vázquez, Salvador Jiménez, Carlos Aguirre, Pedro José Pascual, McGraw Hill.
Software
We will explain how to install and use the software needed.
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TE) Theory | 1 | Catalan | first semester | morning-mixed |
| (PLAB) Practical laboratories | 1 | Catalan | first semester | morning-mixed |
| (PLAB) Practical laboratories | 2 | Catalan | first semester | morning-mixed |
| (PLAB) Practical laboratories | 3 | Catalan | first semester | morning-mixed |
| (PLAB) Practical laboratories | 4 | Catalan | first semester | morning-mixed |