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: Second Semester
Teaching: With teaching
Enrolment: Enrollable
The study and application of numerical methods to solve linear and nonlinear systems of equations and to compute eigenvalues and eigenvectors associated to a matrix. Furthermore, in the computer lab sessions, students will analyze some of the studied algorithms by means of their implementation in FORTRAN 90 or MATLAB.
Topics (with time of expository lectures dedicated to each topic)
Overview of the subject (1hour).
Matrix overview: norms, spectral radius and Rayleigh quotient (6 hours).
The need of the numerical methods for solving linear systems of equations: direct and iterative methods; matrix condition number (3 hours).
Direct methods for solving a linear system: Gauss method, LU decomposition, partial pivoting strategy; Cholesky decomposition; Householder method and QR decomposition. Applications: computation of matrix determinants and inverses (10 hours).
Numerical approximation of matrix eigenvalues and eigenvectors; eigenvalue estimates: Gerschgorin theorem; power and inverse iteration methods (4 hours).
Iterative methods for solving a system of equations: fixed point methods; application to the linear case: Jacobi, Gauss-Seidel and relaxation methods; Newton method and variants for the nonlinear case (4 hours).
Basic bibliography
CIARLET, P. G. [1999]: Introducción á análise numérica matricial e á optimización. Servicio de Publicacións da USC.
ORTEGA, J. M. [1990]: Numerical análisis: a second course. SIAM.
Complementary bibliography
ATKINSON, K. E. - HAN, W. [2004]: Elementary numerical analysis. John Wiley and sons.
AUBANELL, A. - BENSENY, A. - DELSHAMS, A. [1991]: Eines bàsiques de càlcul numeric: amb 87 problemes results. Manuals de la Universitat Autònoma de Barcelona.
GANDER, W. – GANDER M. J. – KWOK, F. [2014]: Scientific computing – An introduction using MAPLE and MATLAB. Springer.
GOLUB, G. H. - VAN LOAN, C. [2013]: Matrix computations. 4th ed. The Johns Hopkins University Press.
HEATH, M. T. [2005]: Scientific computing: an introductory survey. 2nd ed. McGraw Hill.
HORN, R. A. - JOHNSON, C. R. [2013]: Matrix analysis. 2nd ed. Cambridge University Press.
KINCAID, D. - CHENEY, W. [1994]: Análisis numérico: las matemáticas del cálculo científico. Addison-Wesley Iberoamericana.
METCALF, M. - REID, J. - COHEN M. [2004]: Fortran 95/2003 explained. Oxford University Press.
QUARTERONI, A. [2003]: Scientific computing with MATLAB. Springer.
QUARTERONI, A. - SACCO, R. - SALERI, F. [2000]: Numerical mathematics. Springer.
STOER, J. - BULIRSCH, R. [1993]: Introduction to numerical analysis. 2nd ed. Springer-Verlag
TREFETHEN, Ll. N. - BAU, D. [1997]: Numerical linear algebra. SIAM.
WATKINS, D. S. [2010]: Fundamentals of matrix computations. 3rd ed. Wiley.
The skills listed in the Memoria de Verificación de Título do Grao en Matemáticas. Available in:
http://www.usc.es/export9/sites/webinstitucional/gl/servizos/sxopra/mem…
In the following section we indicate the skills worked with greater emphasis according to the type of meeting.
- Expository lectures (CG1, CT5, CE1, CE2).
- Interactive laboratory classes (CE8, CE9).
- Tutorials (CG3, CG4, CT3, CE4).
- During the four-month period, the student work will include to solve theoretical exercises, complete worksheets and implement computer algorithms, with the aim of training and reinforcing the student knowledge obtained during the course.
- Additionally, students will have an on-line course, with different material and complementary to the classroom teaching.
METHODOLOGICAL ADAPTATIONS (In accordance with the instructions contained in the document "Guidelines for the development of safe face-to-face teaching. Course 2020-21" prepared by the "Commission for Teaching Planning", we describe below the methodological adaptations that will be carried out out in each of the three scenarios in that document)
Scenario 1 (adapted normality)
The expository lectures and interactive teaching will be face-to-face and will be complemented with the virtual course of the subject, in which the students will find various bibliographic materials. Students will perform continuous assessment tasks through the virtual course, as described in the corresponding section. The tutorials will be in person or by email.
Scenario 2 (distancing)
Partially virtual teaching, according to the distribution organized by the Faculty of Mathematics. To facilitate the completion of computer practices, students will only use MATLAB on-line. Students will complete continuous assessment tasks through the virtual course, as described in the corresponding section. The tutorials will be attended by email or through MS TEAMS.
Scenario 3 (closure)
Completely remote teaching through the virtual course of the subject. To facilitate the completion of computer practices, students will only use MATLAB on-line. Students will perform continuous assessment tasks through the virtual course, as described in the corresponding section. Tutoring by email or MS TEAMS.
To compute the final mark (FM), the examen evaluation (EE) and the continuous assessment qualification (CAC) will be taken into account.
- The exam has an overall score of 10 points (EE) and will be carried out in the following two sessions:
1. Written final exam (theory, questions and problems), rated at 7.5 points
2. Practical final exam (programming in FORTRAN 90 or MATLAB), rated at 2.5 points.
- The continuous evaluation also has an overall score of 10 points (CAC), resulting from the two controls carried out within the time reserved for the subject.
To obtain the final mark, the following formula will be applied: FM = max {EE, 0.7 * EE + 0.3 * CAC}
The CAC mark will be added in the case that the unexcused absences in the sessions in laboratory groups do not exceed 10% and will be maintained for the second evaluation opportunity.
The same instruments allow to evaluate the skills previously mentioned.
In cases of fraudulent performance of exercises or tests (plagiarism or misuse of technologies), the provisions of the "Regulations for the evaluation of the academic performance of students" and the review of grades will apply.
Expository lectures: 28 hours
Interactive laboratory classes: 28 hours
Tutorials: 2 hours
Total hours with the teacher: 58
Self-study individual or in group: 30 hours
Programming / testing or other computer work: 50 hours
Writing exercises, conclusions or other works: 10 hours
Total hours of personal work: 90
- Daily study of the contents presented in theoretical lectures, complemented with the on-line activities and the revision of the recommended bibliography.
- Solution of the proposed exercises.
- Programming of the proposed algorithms by using the computer lab facilities.
- State doubts and questions to the teacher during the assigned time in the course.
CONTINGENCY PLAN (In accordance with the instructions contained in the document "Guidelines for the development of safe face-to-face teaching. Course 2020-21" prepared by the "Commission for Teaching Planning", we describe below the contingency plan, referred to the teaching methodology and evaluation system sections foreseen for scenarios 2 and 3)
Teaching methodology
Scenario 2 (distancing)
Partially virtual teaching, according to the distribution organized by the Faculty of Mathematics. To facilitate the completion of computer practices, students will only use MATLAB on-line. Students will perform continuous assessment tasks through the virtual course, as described in the corresponding section. The tutorials will be attended by email or through MS TEAMS.
Scenario 3 (closure)
Completely remote teaching through the virtual course of the subject. To facilitate the completion of computer practices, students will only use MATLAB on-line. Students will perform continuous assessment tasks through the virtual course, as described in the corresponding section. Tutoring by email or MS TEAMS.
Learning assessment system
Scenarios 2 (distancing) and 3 (closing)
The procedure will be the same as that just explained with the difference that the scheduled tests will be telematic. As already mentioned, students will use MATLAB on-line as a computer tool.
Juan Manuel Viaño Rey
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813188
- juan.viano [at] usc.es
- Category
- Professor: University Professor
Maria Del Pilar Mato Eiroa
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813181
- mdelpilar.mato [at] usc.es
- Category
- Professor: University Lecturer
Maria Luisa Seoane Martinez
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813230
- marialuisa.seoane [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 18:00-19:00 | Grupo /CLE_02 | Spanish | Classroom 08 |
| 19:00-20:00 | Grupo /CLE_01 | Spanish | Classroom 07 |
| Tuesday | |||
| 18:00-19:00 | Grupo /CLE_02 | Spanish | Classroom 08 |
| 19:00-20:00 | Grupo /CLE_01 | Spanish | Classroom 07 |
| Wednesday | |||
| 18:00-19:00 | Grupo /CLIL_03 | Spanish | Computer room 2 |
| 18:00-19:00 | Grupo /CLIL_04 | Spanish | Computer room 3 |
| 19:00-20:00 | Grupo /CLIL_03 | Spanish | Computer room 2 |
| 19:00-20:00 | Grupo /CLIL_04 | Spanish | Computer room 3 |
| Thursday | |||
| 18:00-19:00 | Grupo /CLIL_05 | Spanish | Computer room 3 |
| 18:00-19:00 | Grupo /CLIL_02 | Spanish | Computer room 4 |
| 19:00-20:00 | Grupo /CLIL_05 | Spanish | Computer room 3 |
| 19:00-20:00 | Grupo /CLIL_02 | Spanish | Computer room 4 |
| Friday | |||
| 12:00-13:00 | Grupo /CLIL_06 | Spanish | Computer room 4 |
| 13:00-14:00 | Grupo /CLIL_06 | Spanish | Computer room 4 |
| 16:00-17:00 | Grupo /CLIL_01 | Spanish | Computer room 3 |
| 17:00-18:00 | Grupo /CLIL_01 | Spanish | Computer room 3 |
| 06.02.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 02 |
| 06.02.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 03 |
| 06.02.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 06 |
| 06.02.2021 09:00-14:00 | Grupo /CLE_01 | Computer room 2 |
| 06.02.2021 09:00-14:00 | Grupo /CLE_01 | Computer room 3 |
| 06.02.2021 09:00-14:00 | Grupo /CLE_01 | Computer room 4 |
| 06.02.2021 09:00-14:00 | Grupo /CLE_01 | Ramón María Aller Ulloa Main Hall |
| 07.15.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 07.15.2021 16:00-20:00 | Grupo /CLE_01 | Computer room 2 |
| 07.15.2021 16:00-20:00 | Grupo /CLE_01 | Computer room 3 |
| 07.15.2021 16:00-20:00 | Grupo /CLE_01 | Computer room 4 |