SubjectsSubjects(version: 853)
Course, academic year 2019/2020
  
Numerical Methods for Engineering - P413003
Title: Numerické metody pro inženýry
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0 other [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
For type: doctoral
Note: course is intended for doctoral students only
can be fulfilled in the future
you can enroll for the course in winter and in summer semester
Guarantor: Dubcová Miroslava RNDr. Ph.D.
Červená Lenka RNDr. Ph.D.
Interchangeability : D413002
Is interchangeable with: AP413003
Annotation -
Last update: Dubcová Miroslava RNDr. Ph.D. (21.09.2018)
The course covers a number of numerical problems the student encounters during the doctoral studies at UCT: numerical methods of linear algebra, interpolation, solution of nonlinear algebraic equations, solution of ordinary and partial differential equations and evaluation of experimental data.
Aim of the course -
Last update: Dubcová Miroslava RNDr. Ph.D. (21.09.2018)

Students will learn to choose a suitable numerical method for solution a mathematical model consisting of algebraic or differential equations.

Literature -
Last update: Dubcová Miroslava RNDr. Ph.D. (18.10.2018)

Z: M. Kubíček, M. Dubcová, D. Janovská, Numerické metody a algoritmy, VŠCHT Praha 2005, ISBN 80-7080-558-7

J. F. Apperson, An Introduction to Numerical Methods and Analysis, John Wiley & Sons, 2001, ISBN 0-471-31647-4

J. Stoer, R. Bulirsh: Introduction to Numerical Analysis, 3rd ed., Springer New York, 2002,ISBN 978-1441930064

G. I. Marčuk: Metody numerické matematiky, Academia Praha, 1987

E. Vitásek: Numerické metody, SNTL Praha, 1987

M. Holodniok, A. Klíč, M. Kubíček,M. Marek: Metody analýzy nelineárních dynamických modelů, ACADEMIA, 1986

Further literature individually.

Learning resources -
Last update: Dubcová Miroslava RNDr. Ph.D. (21.09.2018)

http://www.vscht.cz/mat/NM/NMAplikace/NMAplikace.html

Teaching methods -
Last update: Dubcová Miroslava RNDr. Ph.D. (21.09.2018)

Studying literature and a individual project.

Syllabus -
Last update: Dubcová Miroslava RNDr. Ph.D. (21.09.2018)

1. Interpolation, interpolation by spline functions.

2. Difference formulas, quadrature formulas.

3. Methods of linear algebra.

4. Systems of nonlinear equations. Newton method.

5. Initial value problem for ODE´s. One-step methods.

6. Multistep methods. Stability. Error estimation.

7. Stiff systems. A-stable methods.

8. Boundary value problem for ODE´s. Finite-difference methods.

9. Shooting methods.

10. Finite-difference methods for linear PDE´s of parabolic type.

11. Finite-difference methods for nonlinear PDE´s of parabolic type.

12. Methods of lines.

13. Finite-difference methods for PDE´s of elliptic type.

14. Linear and nonlinear regression.

15. Individual projekt.

Registration requirements -
Last update: Mareš Jan doc. Ing. Ph.D. (03.10.2018)

none

Course completion requirements -
Last update: Dubcová Miroslava RNDr. Ph.D. (21.09.2018)

Individual project, written exam, oral exam

Coursework assessment
Form Significance
Defense of an individual project 20
Examination test 40
Oral examination 40

 
VŠCHT Praha