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Numerical Methods for Engineering - AP413003

Title:	Numerical Methods for Engineering
Guaranteed by:	Department of Mathematics, Informatics and Cybernetics (446)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2021
Semester:	both
Points:	0
E-Credits:	0
Examination process:
Hours per week, examination:	3/0, other [HT]
Capacity:	winter:unknown / unknown (unknown) summer:unknown / unknown (unknown)
Min. number of students:	unlimited
Language:	English
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, P413003

Examination dates

Annotation -

Last update: Pátková Vlasta (16.11.2018)

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: Pátková Vlasta (16.11.2018)

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

Literature -

Last update: Jahoda Milan doc. Dr. Ing. (28.11.2018)

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

Further literature individually.

Learning resources - Czech

Last update: Pátková Vlasta (16.11.2018)

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

Teaching methods -

Last update: Pátková Vlasta (16.11.2018)

Studying literature and a individual project.

Syllabus -

Last update: Pátková Vlasta (16.11.2018)

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: Pátková Vlasta (16.11.2018)

none

Course completion requirements -

Last update: Pátková Vlasta (16.11.2018)

Individual project, written exam, oral exam