Numerical Mathematics 1

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 non-linear 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. Springer-Verlag 2000

Recommended references:

[5] A. S. Householder: The Theory of Matrices in Numerical Analysis. Blaisdell Publishing Company 1965

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Matematické inženýrství - Matematické modelování (compulsory course of the specialization)
• BS Matematické inženýrství - Matematická fyzika (compulsory course of the specialization)
• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (compulsory elective course)
• BS Informatická fyzika (compulsory elective course)
• BS Dozimetrie a aplikace ionizujícího záření (compulsory elective course)
• BS Experimentální jaderná a částicová fyzika (compulsory elective course)
• BS Inženýrství pevných látek (compulsory elective course)
• BS Diagnostika materiálů (compulsory elective course)
• BS Fyzika a technika termojaderné fúze (compulsory elective course)
• BS Fyzikální elektronika (compulsory elective course)