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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
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Numerical Analysis

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Code Completion Credits Range Language
B4B01NUM Z,ZK 6 2P+2C Czech
Vztahy:
It is not possible to register for the course B4B01NUM if the student is concurrently registered for or has previously completed the course B0B01MVM (mutually exclusive courses).
Garant předmětu:
Mirko Navara
Lecturer:
Mirko Navara
Tutor:
Mirko Navara, Aleš Němeček
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. Math in Maple (B0B01MVM) is an appropriate/recommended prerequisite.

Syllabus of lectures:

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.

6. Numerical integration (quadrature).

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.

Syllabus of tutorials:

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.

13. Submission of assessment tasks.

14. 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. Direct motivation to SRL (Self-Regulated Learning).

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:
https://moodle.fel.cvut.cz/courses/B4B01NUM
Time-table for winter semester 2023/2024:
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
Wed
roomKN:E-301
Navara M.
11:00–12:30
(lecture parallel1)
Karlovo nám.
Šrámkova posluchárna K9
Thu
roomT2:A3-412
Němeček A.
09:15–10:45
(lecture parallel1
parallel nr.101)

Dejvice
Laborator
roomT2:A3-412
Němeček A.
11:00–12:30
(lecture parallel1
parallel nr.102)

Dejvice
Laborator
roomT2:C4-459

14:30–16:00
(lecture parallel1
parallel nr.103)

Dejvice
Laborator počítače
roomT2:A3-412
Němeček A.
16:15–17:45
(lecture parallel1
parallel nr.104)

Dejvice
Laborator
roomT2:C4-459

18:00–19:30
(lecture parallel1
parallel nr.105)

Dejvice
Laborator počítače
roomT2:A4-402
Němeček A.
09:15–10:45
(lecture parallel1
parallel nr.101)

Dejvice
Laborator
roomT2:A4-402
Němeček A.
11:00–12:30
(lecture parallel1
parallel nr.102)

Dejvice
Laborator
roomT2:A4-402
Němeček A.
16:15–17:45
(lecture parallel1
parallel nr.104)

Dejvice
Laborator
room412 - online

18:00–19:30
(lecture parallel1
parallel nr.115)

Dejvice
Hybridní výuka
room412 - online
Němeček A.
09:15–10:45
(lecture parallel1
parallel nr.111)

Dejvice
Hybridní výuka
room412 - online
Němeček A.
11:00–12:30
(lecture parallel1
parallel nr.112)

Dejvice
Hybridní výuka
room412 - online

14:30–16:00
(lecture parallel1
parallel nr.113)

Dejvice
Hybridní výuka
room412 - online
Němeček A.
16:15–17:45
(lecture parallel1
parallel nr.114)

Dejvice
Hybridní výuka
Fri
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-16
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet4681806.html