CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Numerical Analysis

Code Completion Credits Range Language
B4B01NUM Z,ZK 6 2P+2C Czech
Lecturer:
Mirko Navara (guarantor)
Tutor:
Aleš Němeček, Mirko Navara (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

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.

Requirements:

Linear Algebra, Calculus.

Syllabus of lectures:

1. Overview of the subject of Numerical Analysis.

2. Sources of errors in numerical computations.

3. Approximation of functions, polynomial interpolation.

4. Errors of polynomial interpolation and their estimation.

5. Hermite interpolating polynomial. Splines.

6. Least squares approximation.

7. Basic root-finding methods.

8. Iteration method, fixed point theorem.

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

10. Solution of systems of linear equations.

11. Numerical differentiation.

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

13. Gaussian and Romberg integration.

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. Individual work on assessment tasks.

6. Least squares approximation.

7. Individual work on assessment tasks.

8. Root-finding methods, root separation.

9. Individual work on assessment tasks.

10. Solution of systems of linear equations.

11. Numerical differentiation.

12. Numerical differentiation and integration, modification of tasks.

13. Individual work on assessment tasks; assessment.

Study Objective:

Practical use of numerical methods, also in non-standard situations, where a modification of the task is needed.

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, 2002, ISBN 0-521-75033-4.

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

[3] Maple User Manuals and Programming Guides, Maplesoft, a division of Waterloo Maple Inc. (http://www.maplesoft.com/documentation_center/)

Note:
Further information:
http://math.feld.cvut.cz/nemecek/nummet.html
Time-table for winter semester 2019/2020:
 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 roomKN:E-301Navara M.11:00–12:30(lecture parallel1)Karlovo nám.Šrámkova posluchárna K9 roomT2:C4-459Němeček A.09:15–10:45(lecture parallel1parallel nr.101)DejviceLaborator počítačeroomT2:C4-459Němeček A.11:00–12:30(lecture parallel1parallel nr.102)DejviceLaborator počítačeroomT2:C4-45914:30–16:00(lecture parallel1parallel nr.103)DejviceLaborator počítačeroomT2:C4-459Němeček A.16:15–17:45(lecture parallel1parallel nr.104)DejviceLaborator počítačeroomT2:C4-45918:00–19:30(lecture parallel1parallel nr.105)DejviceLaborator počítače
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-08-06
For updated information see http://bilakniha.cvut.cz/en/predmet4681806.html