Numerical Analysis

Lecturer:

Eva Feuerstein (gar.)

Tutor:

Eva Feuerstein (gar.)

Supervisor:

Department of Natural Sciences

Synopsis:

Approximation of functions, polynomial interpolation. Errors in polynomial interpolation. Error estimation. Splines. Approximation by the least square method. Numerical differentiation. Numerical integration. Romberg's method. Single-step and multi-step methods for solution of differential equations. Methods for searching roots of non-linear equations. Method of simple iteration, fixed point theorem.

Requirements:

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

Syllabus of lectures:

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

Syllabus of tutorials:

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

Study Objective:

Basic methods of approximation, numerical differentiation and integration, numerical solution to algebraic, transcendent and differential equations.

Study materials:

[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.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Fri	roomKL:B-316 Feuerstein E. 10:00–11:50 (lecture parallel1 parallel nr.1) Kladno FBMI Počítačová učebnaroomKL:B-316 Feuerstein E. 12:00–13:50 (lecture parallel1 parallel nr.2) Kladno FBMI Počítačová učebna
Thu	roomKL:B-316 Feuerstein E. 14:00–15:50 (lecture parallel1) Kladno FBMI Počítačová učebna
Fri

The course is a part of the following study plans:

• Navazující magisterský studijní obor Přístroje a metody pro biomedicínu - prezenční (compulsory elective course)