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:

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:

[1] A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics. Springer-Verlag 2000

[2] J.W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer Science & Business Media, 2013

Recommended references:

[3] 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:

• Aplikovaná algebra a analýza (compulsory course in the program)
• Matematické inženýrství - Matematická fyzika (PS)
• Matematické inženýrství - Matematická informatika (PS)
• Matematické inženýrství - Matematické modelování (PS)