Numerical Analysis

Přednášející:

Mirko Navara

Cvičící:

Mirko Navara, Aleš Němeček

Předmět zajišťuje:

katedra matematiky

Anotace:

The course introduces to basic numerical methods of interpolation and approximation of functions, numerical differentiation and integration, solution of transcendent and ordinary differential 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.

Požadavky:

The first two courses of bachelor studies, mathematics and programming.

Osnova přednášek:

1. Overview of the subject of Numerical Analysis

2. Approximation of functions, polynomial interpolation

3. Errors of polynomial interpolation and their estimation

4. Hermite interpolating polynomial. Splines

5. Least squares approximation

6. Basic root-finding methods

7. Iteration method, fixed point theorem

8. Basic theorem of algebra, root separation and finding roots of polynomials

9. Solution of systems of linear equations

10. Numerical differentiation

11. Numerical integration (quadrature); error estimates and stepsize control

12. Gaussian and Romberg integration

13. One-step methods of solution of ODE's

14. Multistep methods of solution of ODE's

Osnova cvičení:

1. Instruction on work in laboratory and Maple

2. Individual work - 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. Root-finding methods, root separation

8. Individual work on assessment tasks

9. Solution of systems of linear equations

10. Numerical differentiation

11. Numerical differentiation and integration, modification of tasks

12. Individual work on assessment tasks

13. Solution of ODE's

14. Individual work on assessment tasks; assessment

Cíle studia:

Zvládnutí základních metod aproximace, numerické derivace a integrace, numerické řešení algebraických, transcendentních a diferencíálních rovnic.

Studijní materiály:

[1] Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T.: Numerical Recipes (The Art of Scientific Computing), Cambridge University Press, Cambridge, 1990.

[2] Knuth, D. E., The Art of Computer Programming, Addison Wesley, Boston, 1997.

Poznámka:

Rozsah výuky v kombinované formě studia: 14p+6c

Rozvrh na zimní semestr 2011/2012:

Rozvrh není připraven

Rozvrh na letní semestr 2011/2012:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů:

• Open Informatics - Computer and Information Science (povinný předmět oboru)