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
CE1 - Understand and use mathematical language.
CE2 - Know rigorous demonstrations of some classical theorems in different areas of Mathematics.
CE3 - Devise demonstrations of mathematical results, formulate conjectures and imagine strategies to confirm or deny them.
CE4 - Identify errors in incorrect reasoning proposing demonstrations or counterexamples.
CE5 - Assimilate the definition of a new mathematical object, relate it to others already known, and be able to use it in different contexts.
CE6 - Knowing how to abstract the properties and substantial facts of a problem, distinguishing them from those that are purely occasional or circumstantial.
CE7 - Propose, analyze, validate and interpret models of simple real situations, using mathematical tools more
adequate for the purposes pursued.
CE8 - Plan and execute algorithms and mathematical methods to solve problems in the academic, technical, financial or social domain.
CE9 - Use computer applications for statistical analysis, numerical and symbolic calculation, graphic visualization, optimization and scientific software, in general, to experiment in Mathematics and solve problems.
The previous competences, as well as those described on page 5 of the memory of the degree on the link
http://www.usc.es/export/sites/default/gl/servizos/sxopra/memorias_grao…,
are dealt with in class and evaluated according to the system described in the "Assessment system" section.
UNIT I. Introduction to the numerical analysis. Errors in the numerical calculus (approx. 6 expositive hours).
UNIT II. Approximation of the roots of a numerical equation: separation of roots, concepts of iterative method, order of convergence and local and global convergence. Description and analysis of the algorithms of dichotomy, functional iteration and Newton-Raphson (approx. 7 expositive hours).
UNIT III. Lagrange's polynomial interpolation: construction of the polynomial and error formula of Cauchy-Peano (approx. 7 expositive hours).
UNIT IV. Introduction to the numerical integration: simple and composite trapezoidal and Simpson rules; error formulae. Introduction to the numerical differentiation (approx. 6 expositive hours).
Basic:
[1] Michael METCALF, John K. REID, Malcolm COHEN. FORTRAN 95/2003 explained. Oxford University Press, 2004.
[2] Juan Manuel VIAÑO REY. Lecciones de métodos numéricos 1.- Introducción general y análisis de errores. Tórculo edicións, 1995.
[3] Juan Manuel VIAÑO REY. Lecciones de métodos numéricos 2.- Métodos de resolución de ecuaciones numéricas no lineales. Tórculo edicións, 1997.
[4] Juan Manuel VIAÑO REY, Margarita BURGUERA GONZÁLEZ. Lecciones de métodos numéricos 3.- Interpolación. Tórculo edicións, 2000.
Complementary:
[1] Richard L. BURDEN, J. Douglas FAIRES. Numerical Analysis (7th edition). Brooks/Cole Thomson Learning, cop. 2001.
[2] Eugene ISAACSON, Herbert Bishop KELLER. Analysis of Numerical Methods. John Wiley, 1994.
[3] David KINCAID, Elliot Ward CHENEY. Análisis Numérico: las Matemáticas del Cálculo Científico. Addison-Wesley Iberoamericana, 1991.
[4] Alfio QUARTERONI, Fausto SALERI. Cálculo científico con Matlab y Octave. Springer-Verlag Italia, Milano, 2006.
[5] David M. YOUNG, Robert Todd GREGORY. A Survey of Numerical Mathematics. Addison-Wesley, 1973.
To know the basic techniques of numerical calculus and their translation to algorithms.
To be able to apply the basic numerical methods of resolution of numerical equations, polynomial interpolation, differentiation and integration.
To be able to programme in a computer the studied numerical methods.
The previous competences, as well as those described on page 5 of the degree guidelines on the link
http://www.usc.es/export/sites/default/gl/servizos/sxopra/memorias_grao…,
are worked in class and evaluated according to the description in the section "Assessment system".
Depending on the scenarios, proceed as follows:
SCENARIO 1 (adapted normality): Thematic website for virtual teaching. Guided realization of small computer programs in the practical classes. Carrying out work by the student to reinforce knowledge.
SCENARIO 2 (distancing): Partially virtual teaching, according to the distribution organized by the center. For this, and if so established, MS Teams or other tools available for synchronous virtual classes will be used.
SCENARIO 3 (closure of the facilities): Teaching completely remotely through the virtual course of the subject and the MS Teams or other tools. As long as the teachers have the necessary infrastructure. To do this, MS Teams or other tools available for synchronous virtual classes will be used.
All marks (AC, AE, CF) must be understood in the 0-10 scale.
The evaluation system considers, on one hand, a continuous assessment (AC) and, on the other hand, an exam evaluation (AE).
Continuous assessment (AC) is the control of the programming assignments and tests of knowledge, which comprises two written assessments. The mark for the continuous assessment is the aritmetic means of all assessments.
The final evaluation (AE) is done through the official final exam fixed by the Faculty.
The final grade (CF) is calculated taking into account that this matter has to provide programming skills, being therefore mandatory to reach certain level of quality in the programming assignments. To that end, the final mark for the presented students is calculated by means of the following formula:
CF = MAX{AF,0.70*CF+0.30*AC} if AC>=3;
CF = MIN{4,MAX{CF,0.70*CF+0.30*AC}} otherwise.
Programming assignments will be performed in FORTRAN language, with the possible aid of MATLAB.
AC marks will be retained for the second call of course, if applicable.
On-site work work: 26 h expositive + 26 h interactive laboratory + 2 h tutorials = 54 h.
Personal work: 25 hours autonomous study + 25 hours of exercises + 25 hours of programming + 15 hours of recommended readings) = 90 hours.
To support a continued contact with the contents explained at class.
To do the proposed exercises.
Start doing practices from the first session.
Depending on the scenarios, we will proceed as follows:
SCENARIO 1 (adapted normality): Expository classes. Interactive laboratory classes. Telematic tutoring. Support through the subject's website.
SCENARIO 2 (distancing): Partially virtual teaching, according to the distribution organized by the center. For link, and if so stated, the MS Teams or other tools available for synchronous virtual classes will be used. The virtual classroom of the course will also be used. Through the virtual course, students will also be able to carry out tasks necessary for continuous assessment.
SCENARIO 3 (closure of the facilities): Teaching completely remotely through the virtual course of the subject and the MS Teams or other tools. As long as teachers have the necessary infrastructure. For link, MS Teams or other tools available for synchronous virtual classes will be used. The virtual classroom of the course will also be used. Through the virtual course, students will also be able to carry out tasks necessary for continuous assessment.
The tutorials will be attended electronically.
SCENARIO 3 (closure of the facilities):
Totally remote teaching through the means provided for this purpose and the virtual course of the subject.
The tutorials will be attended telematically
Adaptation of the evaluation system to Scenarios 2 and 3:
SCENARIO 2 (distancing):
Same procedure as described for SCENARIO 1, with the only difference that the activities that will be carried out will be telematic. The final and second chance test, if it is not possible to do it in person, will be telematic.
SCENARIO 3 (closure of the facilities):
Same procedure as described for SCENARIO 2, with the only difference that the final and second chance tests are also telematic late-night.
Jose Antonio Alvarez Dios
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813353
- joseantonio.alvarez.dios [at] usc.es
- Category
- Professor: University Lecturer
Carmen Rodriguez Iglesias
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813178
- carmen.rodriguez [at] usc.es
- Category
- Professor: University Lecturer
Juan Manuel Viaño Rey
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813188
- juan.viano [at] usc.es
- Category
- Professor: University Professor
Maria Luisa Seoane Martinez
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813230
- marialuisa.seoane [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 16:00-17:00 | Grupo /CLE_02 | Spanish | Classroom 08 |
| 16:00-17:00 | Grupo /CLIL_04 | Spanish, Galician | Computer room 4 |
| 19:00-20:00 | Grupo /CLE_01 | Spanish | Classroom 09 |
| Tuesday | |||
| 17:00-18:00 | Grupo /CLE_01 | Spanish | Classroom 07 |
| 18:00-19:00 | Grupo /CLE_02 | Spanish | Classroom 08 |
| 18:00-19:00 | Grupo /CLIL_04 | Galician, Spanish | Computer room 4 |
| Wednesday | |||
| 18:00-19:00 | Grupo /CLIL_06 | Galician | Computer room 4 |
| 19:00-20:00 | Grupo /CLIL_04 | Galician, Spanish | Computer room 2 |
| 19:00-20:00 | Grupo /CLIL_05 | Galician | Computer room 3 |
| Thursday | |||
| 15:00-16:00 | Grupo /CLIL_02 | Spanish | Computer room 4 |
| 17:00-18:00 | Grupo /CLIL_01 | Galician | Computer room 2 |
| 17:00-18:00 | Grupo /CLIL_04 | Galician, Spanish | Computer room 3 |
| 18:00-19:00 | Grupo /CLIL_03 | Galician, Spanish | Computer room 4 |
| 19:00-20:00 | Grupo /CLIL_01 | Galician | Computer room 3 |
| Friday | |||
| 14:00-15:00 | Grupo /CLIL_05 | Galician | Computer room 3 |
| 15:00-16:00 | Grupo /CLIL_03 | Spanish, Galician | Computer room 3 |
| 16:00-17:00 | Grupo /CLIL_02 | Spanish | Computer room 2 |
| 16:00-17:00 | Grupo /CLIL_06 | Galician | Computer room 3 |
| 01.25.2021 15:00-20:30 | Grupo /CLE_01 | Computer room 2 |
| 01.25.2021 15:00-20:30 | Grupo /CLE_01 | Computer room 3 |
| 01.25.2021 15:00-20:30 | Grupo /CLE_01 | Computer room 4 |
| 06.21.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |
| 06.21.2021 10:00-14:00 | Grupo /CLE_01 | Computer room 2 |
| 06.21.2021 10:00-14:00 | Grupo /CLE_01 | Computer room 3 |
| 06.21.2021 10:00-14:00 | Grupo /CLE_01 | Computer room 4 |