Numerical Mathematics
Code  Completion  Credits  Range  Language 

01NM  Z,ZK  4  3+1  Czech 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The course introduces to numerical methods for solving the basic problems arising from technical and research problems. The accent is put on a good understanding of the root of theoretical methods.
 Requirements:
 Syllabus of lectures:

1. Recapitulation of necessary concepts from linear algebra and functional analysis.
2. Direct and iterative methods for solving linear algebraic equations. Matrix inversion.
3. Solving the partial eigenvalue problem.
4. Solution of the full eigenvalue problem.
5. Solving the equation f (x) = 0
6. Systems of nonlinear algebraic and transcendental equations.
7. Interpolation functions by polynomials.
8. Numerical calculation of derivatives.
9. Numerical calculation of integral
 Syllabus of tutorials:

1. Practicing rules of operations with triangular matrices, proofs of theorems on decompositions of square matrices, derivation of decomposition formulae.
2. Proof of Schur decomposition theorem. Consequences for special classes of matrices.
3. Examples of solution of systems of linear algebraic equations and matrix inversion using direct methods.
4. Examples of solution of systems of linear algebraic equations using iterative methods.
5. Examples of application of methods for solution of extremal eigenvalues and complete eigenvalue problem.
6. Examples of solution of nonlinear algebraic and transcendental equations and their systems. Numerical approximation of integrals.
 Study Objective:

Knowledge: Correct understanding of the theoretical basis for numerical algorithms is accented. Skills: Applications of numerical methods for solution of basic mathematical tasks originated from technical or scientific problems.
 Study materials:

Key references:
[4] A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics. SpringerVerlag 2000
Recommended references:
[5] A. S. Householder: The Theory of Matrices in Numerical Analysis. Blaisdell Publishing Company 1965
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: