ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 102 Hours of tutorials: 6 Expository Class: 18 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Applied Mathematics, External department linked to the degrees
Areas: Applied Mathematics, Área externa M.U en Matemática Industrial
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
1. To khow the fundamentals of numerical methods (root finding, interpolation, differentiation and integration)
2. To know the fundamentals of scientific computation and its application to implement numerical methods.
First Part: Programming
1. Introduction to Matlab; Basic commands and functions.
2. Vectors and Matrices in Matlab. Treatment of sparse matrices. Graphical representations.
3. Files .m and programming. Data structures.
4. Introduction to Fortran 90. Data types. Flow control.
5. "Arrays" in Fortran 90. Procedures. Modules and Interfaces.
6. Data input/output in Fortran 90.
Second Part: Numerical Methods
7. Numerical solution of systems of linear equations: Condition of a system of linear equations. Direct methods: LU, LL^t, LDL^t and QR. Classical iterative methods: Jacobi, Gauss-Seidel, SOR and SSOR . Convergence criteria. Numerical methods for the calculus of eigenvalues and eigenvectors.
8. Numerical solution of systems of non-linear equations: Review of methods for solving non-linear equations. Fixed-point iteration. Newton's method. Computational considerations.
9. Interpolation, numerical differentiation and integration: Lagrange interpolation. Hermite interpolation. Runge effect. Spline approximation. Numerical differentiation of polynomial interpolating type. Numerical quadrature of polynomial interpolating type. Newton-Cotes formulas. Gauss formulas. Composite quadrature.
9. Interpolation. Lagrange interpolation. Hermite interpolation. Runge effect. Spline approximation.
10. Numerical differentiation and integration. Numerical differentiation of polynomial interpolating type. Numerical quadrature of polynomial interpolating type in a single variable. Newton-Cotes formulas. Gauss formulas. Composite quadrature.
11. Numerical interpolation and integration in several variables.
Basic:
J.F. Epperson. An introduction to numerical methods and analysis. Edición revisada. John Wiley &
Sons, 2007.
J.A. Infante del Río, J.M. Rey Cabezas. Métodos numéricos: teoría, problemas y prácticas con Matlab. Piramide, 2007.
M. Metcalf, J.K. Reid. Modern Fortran Explained Oxford University Press, 2011.
Complementary:
P.G. Ciarlet. Introduction to numerical linear algebra and optimisation. Cambridge University Press, 1989.
S.J. Chapman, Fortran 90/95 for scientists and engineers. WCB/McGraw-Hill, 2004.
J.D. Faires, R. Burden. Análisis Numérico. Thomson 2011.
G.H. Golub, C.F. van Loan. Matrix Computations. John Hopkins, University Press, 1996.
Guía de programación en Matlab de MathWorks:
http://www.mathworks.com/access/helpdesk/help/techdoc/matlab_prog/matla…
D.C. Hanselman, B.L. Littlefield. Mastering Matlab 7. Prentice Hall, 2004.
T. Aranda, J.G. García. Notas sobre Matlab. Universidad de Oviedo, Servicio de Publicaciones, 1999.
C.T. Kelley. Solving Nonlinear Equations with Newton’s Method. SIAM, 2003.
D. Kincaid, W. Cheney. Análisis numérico. Las matemáticas del cálculo cienífico. AddisonWesley
Iberoamericana, 1994.
J.H. Mathews, K.D. Fink. Métodos Numéricos con Matlab. Prentice Hall , 2000.
M. Metcalf, J.K. Reid. Fortran 90/95 explained. Oxford University Press, 1999.
W.H. Press. Numerical Recipes in Fortran 90: Volume 2. Cambridge University Press, 1996.
A. Quarteroni, F. Saleri. Cálculo Científico con MATLAB y Octave. Springer, 2006.
J.M. Viaño, M. Burguera. Lecciones de métodos numéricos. 3. Interpolación. Tórculo Edicións,
1999.
J.M. Viaño. Lecciones de métodos numéricos. 2. Resolución de ecuaciones numéricas. Tórculo
Edicións, 1997.
Basic and General
CG2 Be able to apply the acquired knowledge and abilities to solve problems in new or unfamiliar environments within broader contexts, including the ability to integrate multidisciplinary R & D in the business environment;
CG4 To have the ability to communicate the findings to specialist and non-specialist audiences in a clear and unambiguous way
CG5 To have the appropriate learning skills to enable them to continue studying in a way that will be largely self-directed or autonomous, and also to be able to successfully undertake doctoral studies.
Specific:
CE4: Being able to select a set of numerical techniques, languages and tools, appropriate to solve a mathematical model.
Specialty "Numerical Simulation"
CS2: To adapt, modify and implement software tools for numerical simulation.
Theory will be taught in order for students to build small computer programs under guidance as an introduction to programming. Students will also carry out other tasks by themselves to strengthen their knowledge. The involved skills are CG2, CG4, CG5.
Students will work individually on numerical methods in order to deepen their knowledge on the subject. The involved skills are CG2, CG4, CE4, CS2.
Teaching is given via M2I videoconference system, and communications via Teams.
CRITERIA FOR THE 1ST ASSESSMENT OPPORTUNITY
The first part (50% of the qualification) will consist on the evaluation of the Matlab and Fortran practical works; both works will have the same weight to calculate the qualification of this part. The involved skills are CG2, CG4, CE4, CS2.
The second part (the remaining 50%) will correspond to the exam, where the concepts acquired in the part II of the subject will be evaluated. The involved skills are CG2, CG4, CG5.
Students must pass both parts in order to pass the subject. If one of the parts is not passed the qualification will be 4 out of 10. Besides, the practical works of Matlab and Fortran must be passed separately.
A student will be considered as “presented” when the exam and/or two practical works are presented.
CRITERIA FOR THE 2ND ASSESSMENT OPPORTUNITY
The same as for the first opportunity. The deadline for handing in the tasks will be adapted to the date of the second exam. The surpassed parts (exam, Matlab or Fortran works) in the first opportunity is conserved for the second one.
Due to an order of the Vicerreitoría de Organización Académica of the USC, the following warning must be considered: "In cases of fraudulent performance of exercises or tests, what is stated in the Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións".
6 ETCS credits
To reserve of some time periodically for the study of the subject.
To make by oneself the examples proposed by the professor.
To consult the bibliography.
To use the tutorial hours to solve doubts.
Francisco Jose Pena Brage
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813194
- fran.pena [at] usc.es
- Category
- Professor: Temporary PhD professor
| Monday | |||
|---|---|---|---|
| 12:00-14:00 | Grupo /CLE_01 | Galician | Computer room 5 |
| Thursday | |||
| 13:00-14:00 | Grupo /CLE_01 | Galician | Computer room 5 |