### Numerical Analysis

#### Numerical Analysis - B4B01NUM

 Credits 6 Semesters Winter Completion Assessment + Examination Language of teaching Czech Extent of teaching 2P+2C
Annotation
The course introduces to basic numerical methods of interpolation and approximation of functions, numerical differentiation and integration, solution of transcendent equations and systems of linear equations. Emphasis is put on estimation of errors, practical skills with the methods and demonstration of their properties using Maple and computer graphics.
Study targets
Practical use of numerical methods, also in non-standard situations, where a modification of the task is needed. Direct motivation to SRL (Self-Regulated Learning).
Course outlines
1. Overview of the subject of Numerical Analysis. Approximation of functions, polynomial interpolation.
2. Errors of polynomial interpolation and their estimation.
3. Hermite interpolating polynomial. Splines.
4. Least squares approximation.
5. Numerical differentiation. Richardson's extrapolation.
7. Error estimates and stepsize control. Gaussian and Romberg integration.
8. Integration over infinite ranges. Tricks for numerical integration.
9. Root separation. Basic root-finding methods.
10. Iteration method, fixed point theorem.
11. Finitary methods of solution of systems of linear equations.
12. Matrix norms, convergence of sequences of vectors and matrices.
13. Iterative methods of solution of systems of linear equations.
14. Reserve.
Exercises outlines
1. Instruction on work in laboratory and Maple.
2. Training in Maple.
3. Polynomial interpolation, estimation of errors.
4. Individual work on assessment tasks.
5. Least squares approximation.
6. Individual work on assessment tasks.
7. Individual work on assessment tasks.
8. Numerical differentiation and integration, modification of tasks.
9. Individual work on assessment tasks.
10. Solution of systems of linear equations.
11. Individual work on assessment tasks.
12. Solution of systems of linear equations.