Subjects

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Numerical Methods - N413005

Title:	Numerické metody
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2007 to 2012
Semester:	both
Points:	7
E-Credits:	7
Examination process:
Hours per week, examination:	3/2, C+Ex [HT]
Capacity:	winter:47 / unlimited (unknown) summer:unknown / unknown (unknown)
Min. number of students:	unlimited
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Level:
Additional information:	http://předmět je vyučován pouze v zimním semestru
Note:	course can be enrolled in outside the study plan enabled for web enrollment you can enroll for the course in winter and in summer semester

Guarantor:	Dubcová Miroslava RNDr. Ph.D.
Interchangeability :	Z413005

Examination dates Schedule

Annotation -

The course deals with methods for approximation of functions, derivatives and integrals, with methods for solving linear and nonlinear algebraic equations, with methods for solving ordinary/partial differential equations with initial/boundary conditions, and with methods for experimental data evaluation. By learning these numerical methods students will gain insight into problem formulation and develop the ability to derive a problem solution and estimate its accuracy.

Last update: TAJ413 (17.07.2013)

Literature -

R: M. Kubíček, M. Dubcová, D. Janovská, Numerical Methods and Algorithms, http://www.vscht.cz/mat/Ang/NM-Ang/NM-Ang.pdf

A: J. F. Epperson: An Introduction to Numerical Methods and Analysis,Wiley, New York, 2002, ISBN 0-471-31647-4

Last update: TAJ413 (15.07.2013)

Teaching methods -

Lectures and exercise classes.

Last update: TAJ413 (17.07.2013)

Syllabus -

1. Interpolation, difference formulas, quadrature formulas.

2. Methods of linear algebra.

3. Systems of nonlinear equations. Newton method.

4. Linear and nonlinear regression. Gauss-Newton method.

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

6. Multistep methods.

7. Stability. Error estimation.

8. Stiff systems. A-stable methods.

9. Boundary value problem for ODE´s.

10. Finite-difference methods.

11. Shooting methods.

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

13. Methods of lines.

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

Last update: Dubcová Miroslava (09.11.2012)

Learning resources -

http://www.vscht.cz/mat/Ang/NM-Ang/e_nm_semin.html

http://www.vscht.cz/mat/Ang/NM-Ang/NM-Ang.pdf

Last update: Dubcová Miroslava (15.07.2013)

Learning outcomes -

Students will be able to formulate mathematical models using algebraic or differential equations. They will gain an overview of the commonly used numerical methods and they will learn how to determine the accuracy of numerical solutions.

Last update: TAJ413 (16.07.2013)

Registration requirements -

Mathematics I, Mathematics II

Last update: TAJ413 (16.07.2013)