Numerical Mathematics
Code  Completion  Credits  Range  Language 

2011049  Z,ZK  4  2P+2C  Czech 
 Lecturer:
 Tutor:
 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 tridiagonal systems; Principle of iterative methods; norms and spectral radius., 2. Simple and Jacobi iterative method; GaussSeidel 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;, 68. 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 onestep methods of Euler & RungeKutta; Convergence; Practical application;, 910. 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;, 1113. 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:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 10 62 67 00 BTZI 2012 P základ (compulsory course in the program)
 11 68 73 00 BTZI 2012 K základ (compulsory course in the program)
 02 26 31 34 BSTR EPT 2012 P základ (compulsory course in the program)
 03 26 31 36 BSTR IAT 2012 P základ (compulsory course in the program)
 04 26 31 38 BSTR KPP 2012 P základ (compulsory course in the program)
 06 40 45 48 BSTR EPT 2012 K základ (compulsory course in the program)
 07 40 45 50 BSTR IAT 2012 K základ (compulsory course in the program)
 08 40 45 52 BSTR KPP 2012 K základ (compulsory course in the program)
 05 40 45 46 BSTR TZP 2012 K základ (compulsory course in the program)
 05 40 45 46 DSTR TZP 2012 K základ (compulsory course in the program)
 06 40 45 48 DSTR EPT 2012 K základ (compulsory course in the program)
 07 40 45 50 DSTR IAT 2012 K základ (compulsory course in the program)
 08 40 45 52 DSTR KPP 2012 K základ (compulsory course in the program)
 10 62 67 00 DTZI 2012 P základ (compulsory course in the program)
 11 68 73 00 DTZI 2012 K základ (compulsory course in the program)