ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Applied Mathematics
Areas: Applied Mathematics
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable
The study of numerical methods for solving optimization problems and differential equations in order to provide the students with the fundamental knowledges for their analysis, the implementation in a computer and the application to specific problems.
1. Numerical solution of differential equations. (14h)
1.1. Numerical solution of the boundary value problem for the ordinary second order linear equation: a finite differences scheme,
description and analysis. (2h)
1.2. Numerical solution of initial value problems for O.D.E. Basic methods: explicit and implicit Euler, trapezoidal rule, midpoint rule. (1h)
1.3. Concepts of consistence, stability, convergence, order and numerical stability. Stiff problems. (6h)
1.4. Runge-Kutta methods, linear multistep methods: description and properties. (5h)
2. Numerical methods in optimization. (12h)
2.1 Discrete linear least squares approximation. Existence and uniqueness of solution: normal equations. (1h)
2.2. Numerical methods in unconstrained optimization. Existence and uniqueness of solution: convex sets and convex functions, optimality conditions.(2h)
2.3. One-dimensional optimization: Goldstein and Wolfe-Powell rules. (2h)
2.4. Gradient and conjugate gradient methods. Newton and quasi-Newton methods. (4h)
2.5. Numerical methods in constrained optimization. Existence and uniqueness of solution: Lagrange multipliers and optimality conditions. Penalty methods. (3h)
Basic references on numerical methods in optimization:
J. Viaño, M. Burguera (2012): Lecciones de Métodos Numéricos: 4. Optimización. Notas de curso.
W. Sun, Y. Yuan (2006): Optimization Theory and Methods. Springer.
Basic references on numerical methods for differential equations:
E. Hairer, S. P. Nørsett, G. Wanner (1987): Solving Ordinary Differential Equations I. Non-stiff Problems. Springer.
Complementary references on numerical methods in optimization:
J. E. Dennis, R. B. Schnabel (1983): Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice Hall.
D. G. Luenberger (1973): Introduction to Linear and Nonlinear Programming. Addison-Wesley.
D. P. Bertsekas (1995): Nonlinear programming. Athena Scientific.
J. Nocedal, S. J. Wright (1999): Numerical Optimization. Springer-Verlag.
Complementary references on numerical methods for differential equations:
E. Hairer, G. Wanner (1991): Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer.
J. D. Lambert (1991): Numerical Methods for Ordinary Differential Systems. Wiley.
J. C. Butcher (2003): Numerical Methods for Ordinary Differential Equations. Wiley.
M. Crouzeix, A. L. Mignot (1989): Analyse Numérique des Équations Differentielles. Masson.
Reference on numerical methods:
W. Gander, M. J. Gander, F. Kwok (2014): Scientific computing – An introduction using MAPLE and MATLAB. Springer.
R. L. Burden, J. D. Faires (1998): Análisis Numérico. ITP Thomson.
E. Isaacson, H. B. Keller (1994): Analysis of Numerical Methods. Dover.
D. Kincaid, W. Cheney (1994): Análisis numérico: las matemáticas del cálculo científico. Addison-Wesley Iberoamericana.
The skills detailed in the Memoria de Verificación de Título do Grao en Matemáticas
(http://www.usc.es/export9/sites/webinstitucional/gl/servizos/sxopra/mem…) will be exercised.
The teaching methodology will be based on lectures where the theoretical concepts of the subject will be presented. These contents will be put into practice in computer labs where the methods presented and previously analyzed will be programmed. The student will have some additional classes that will be dedicated to the presentation of homework assignments.
The subject will have a web page on the virtual campus where various documents and activities will be posted. This platform will also be used to communicate with the students.
If it is necessary to hold a virtual session by videoconference, the Teams platform will be used.
The accomplishment of the objectives, both in terms of contents and skills, will be graded through a final exam and continuous evaluation.
In the final exam (EF, maximum of 10 points), to be held on the official date assigned by the faculty, the theoretical concepts acquired, the ability to solve questions and problems (ET, maximum of 7.5 points) as well as the programming skills (PG, maximum of 2.5 points) will be evaluated. To be more precise
EF = ET + PG.
Those students who want to avoid the programming part on the final exam day, they can replace PG with the grade obtained in the programming exam that will be held in the last computer lesson.
The grade related to continuous evaluation (EC, maximum of 10 points) will be calculated based on the intermediate theoretical and programming tests (7 points) and the works that will be defended in the additional classes with small groups (3 points).
The final grade (CF) will be obtained after calculating the maximum between EF and the weighted average between EF (70%) and EC (30%). To be more precise:
CF = max {EF, 0.7 * EF + 0.3 * EC}
The final grade in the second opportunity will be calculated with the following formula
CF = max {EF2, 0.7 * EF2 + 0.3 * EC}
where EF2 will be the grade obtained in the second-chance exam (which will have the same characteristics as the first one).
The same assessment criteria will be applied to students who repeat the course.
The grade of "no presentado" will be awarded to those students who do not carry out any evaluable activity.
For the exclusive effect of granting the Honor Registration qualification, not only the final numerical grade will be taken into account, but also the continuous evaluation.
For cases of fraudulent performance of exercises or tests, the provisions of the “Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións” may be applied.
Total hours of work with the teacher: 58h.
- Lectures: 28h.
- Interactive laboratory classes: 28h.
- Classroom tutoring: 2h.
Total hours of personal work: 90h.
- Individual or group autonomous study: 40h
- Programming / experimentation or other computer / laboratory work: 35h
- Writing of exercises, conclusions or other works: 10h
- Recommended readings and activities with bibliographic support: 5h
The total number of estimated hours to pass the subject is 90h + 58h = 148h.
- Diary study of contents covered in the class, supplemented by notes given by the teacher.
- Use of the tutorials to solve all sorts of doubts about the matter.
- Resolution of the worksheets and search of others in the recommended literature.
- Programming of the proposed algorithms, within the marked delays.
Contingency plan for the adaptation of this guide to the document "Bases para o desenvolvemento dunha docencia presencial segura no curso 2020-2021", approved by the USC Governing Council in its ordinary session held on 19 June 2020.
Both the methodology and the evaluation method described above would correspond to the so-called “scenario 1”.
In the event that the evolution of the pandemic places us in “scenario 2”, the following measures will be taken. Regarding the methodology, the expository, laboratory and tutoring classes would be taught, in the case where the number of students allowed, in the classroom. Otherwise they would be taught by video-conference through Teams. The evaluation system would not change except for the exams that would have to be carried out electronically using the Virtual Campus and the Teams platform in case the safety distance could not be maintained.
In “scenario 3” the following measures will be taken. Regarding the methodology:
- The lectures would be taught electronically through Teams.
- In the computer lessons, the students would have to prepare the practical lessons by themselves. The doubts/questions that may arise in the preparation would be resolved either by telematic sessions using the same platform or by email.
- The tutoring lessons would be carried out using Teams.
Again, the evaluation system would not change except for the exams that would have to be done electronically using the Virtual Campus and the Teams platform.
The second-chance exams will be carried out under the conditions specified above depending on the scenario.
Rafael Muñoz Sola
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813182
- rafael.munoz [at] usc.es
- Category
- Professor: University Lecturer
José Luis Ferrín González
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813191
- joseluis.ferrin [at] usc.es
- Category
- Professor: University Lecturer
Hipolito Irago Baulde
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813220
- hipolito.irago [at] usc.es
- Category
- Professor: University Lecturer
Jeronimo Rodriguez Garcia
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813355
- jeronimo.rodriguez [at] usc.es
- Category
- Professor: Temporary PhD professor
Alfredo Rios Albores
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- alfredo.rios.albores [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLIL_03 | Spanish | Computer room 4 |
| 12:00-13:00 | Grupo /CLIL_02 | Spanish | Computer room 2 |
| 13:00-14:00 | Grupo /CLIL_01 | Spanish | Computer room 3 |
| Tuesday | |||
| 11:00-12:00 | Grupo /CLIL_04 | Spanish | Computer room 2 |
| 12:00-13:00 | Grupo /CLIL_06 | Spanish | Computer room 4 |
| 13:00-14:00 | Grupo /CLIL_05 | Spanish | Computer room 3 |
| Wednesday | |||
| 11:00-12:00 | Grupo /CLE_01 | Spanish | Classroom 09 |
| 13:00-14:00 | Grupo /CLE_02 | Spanish | Classroom 07 |
| Thursday | |||
| 11:00-12:00 | Grupo /CLE_02 | Spanish | Classroom 07 |
| 12:00-13:00 | Grupo /CLIL_06 | Spanish | Computer room 2 |
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 09 |
| Friday | |||
| 09:00-10:00 | Grupo /CLIL_02 | Spanish | Computer room 2 |
| 10:00-11:00 | Grupo /CLIL_03 | Spanish | Computer room 2 |
| 11:00-12:00 | Grupo /CLIL_01 | Spanish | Computer room 2 |
| 11:00-12:00 | Grupo /CLIL_05 | Spanish | Computer room 4 |
| 12:00-13:00 | Grupo /CLIL_04 | Spanish | Computer room 4 |
| 01.26.2021 15:00-20:00 | Grupo /CLE_01 | Classroom 02 |
| 01.26.2021 15:00-20:00 | Grupo /CLE_01 | Classroom 03 |
| 01.26.2021 15:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 01.26.2021 15:00-20:00 | Grupo /CLE_01 | Computer room 2 |
| 01.26.2021 15:00-20:00 | Grupo /CLE_01 | Computer room 3 |
| 01.26.2021 15:00-20:00 | Grupo /CLE_01 | Computer room 4 |
| 01.26.2021 15:00-20:00 | Grupo /CLE_01 | Ramón María Aller Ulloa Main Hall |
| 06.22.2021 15:00-20:00 | Grupo /CLE_01 | Computer room 2 |
| 06.22.2021 15:00-20:00 | Grupo /CLE_01 | Computer room 3 |
| 06.22.2021 15:00-20:00 | Grupo /CLE_01 | Computer room 4 |
| 06.22.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |