Teaching GuideTerm
Faculty of Computer Science
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Mestrado Universitario en Matemática Industrial (2013)
 Subjects
  Numerical methods and programming
   Contents
Topic Sub-topic
Introduction to programming 1. Introduction to matlab. Commands and basic functions.
2. Vectors and matrices in Matlab. Sparse matrices. Graphical representation.
3. Files .m and programming. Data structures in Matlab.
4. Introduction to Fortran 90: data types and flow control.
5. “Arrays” in Fortran 90. Proceedings, modules and interfaces.
6. Input/output of data in Fortran 90.
Numerical methods 7. Numerical solution of linear systems: Conditioning of a system of linear equations. Direct methods: LU, LL^t, LDL^t y QR. Classical iterative methods: Jacobi, Gauss­-Seidel, SOR and SSOR. Convergence tests. Numerical methods for the calculus of eigenvalues and eigenvectors.

8. Numerical solution of systems of nonlinear equations: review of numerical methods for solving nonlinear equations. Fixed point iteration method. Newton method. Computationanl comments.

9. Interpolation. Lagrange interpolation. Hermite interpolation. Runge effect. Approximation using splines.

10. Numerical differentiation and integration. Numerical derivatives of polynomial interpolation type. Numerical integration in one variable. Formulas of Newton-Cotes. Gauss formulas. Compound formulas.

11. Interpolation and numerical integration in several variables.
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