Numerical Mathematics

The course is not on the list Without time-table
Code Completion Credits Range Language
2011049 Z,ZK 4 2P+2C Czech
Department of Technical Mathematics
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

Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2019-09-16
For updated information see http://bilakniha.cvut.cz/en/predmet10509002.html