Numerical Mathematics
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| 2011049 | Z,ZK | 4 | 2+2 | Czech |
- Lecturer:
- Jiří Fürst (gar.), Luděk Beneš, Marta Čertíková, Petr Sváček
- Tutor:
- Radka Keslerová, Jiří Fürst (gar.), Nataša Bendová, Luděk Beneš, Vojtěch Běták, Marta Čertíková, Jiří Holman, Jaroslav Huml, Jan Karel, Martin Kosík, Petr Louda, Olga Majlingová, Tomáš Neustupa, Petra Pořízková, Vladimír Prokop, Petr Sváček, Jakub Šístek
- Supervisor:
- Department of Technical Mathematics
- Synopsis:
- Requirements:
- Syllabus of lectures:
- Syllabus of tutorials:
- Study Objective:
-
1. Matrices; System of linear equations - direct methods; Gauss elimination for tri-diagonal systems; Principle of iterative methods; norms and spectral radius., 2. Simple and Jacobi iterative method; Gauss-Seidel method; convergence conditions., 3. Systems of nonlinear equations; Problems of existence and uniqueness of the solution; Iterative methods - Newton method; Analogy of 1D problem., 4. Principle of interpolation; Interpolation by algebraic polynomials; Existence and uniqueness of the polynomial; Interpolation by spline functions; Advantages of this interpolation; Practical applications., 5. Least squares approximation - principle of approximation by an algebraic polynomial; Derivation of the system of normal equations;, 6-8. Numerical solution of the Cauchy problem for the 1st order equation and for a system in normal form; Cauchy problem for the nth order equation; Principle of one-step methods of Euler & Runge-Kutta; Convergence; Practical application;, 9-10. The problems of the solution of the boundary value problems for an 2nd order ordinary differential equation, comparison with the Cauchy problem; Existence and uniqueness; Dirichlet problem; Principle of the mesh methods (finite difference methods), convergence; Existence and uniqueness of the solution of the associated system of linear equations; Shooting method;, 11-13. Numerical solution of the linear partial differential 2nd order equations in 2D -mesh methods; Classes of equations; Formulation of elementary problems for the equations of the mathematical physics (Laplace and Poisson equation; Heat transfer equation, Wave equation); Difference substitutions of the first and second derivative order of the approximation; Principle of the mesh method for the solution of individual types of problems; Convergence and stability;
- Study materials:
-
1. Mathews, J. H.: Numerical Methods for Mathematics, Science and Engineering, Prentice Hall International, 2nd edition,1992, 2. Gerald, C.F., Wheatley, P.O.: Applied Numerical Analysis, Addison Wesley, 6th edition, 1999
- Note:
- Time-table for winter semester 2011/2012:
- Time-table is not available yet
- Time-table for summer semester 2011/2012:
-
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Fri Thu Fri - The course is a part of the following study plans: