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Numerical Methods - S413005

Title:	Numerical Methods
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2011 to 2020
Semester:	winter
Points:	winter s.:7
E-Credits:	winter s.:7
Examination process:	winter s.:
Hours per week, examination:	winter s.:3/2, C+Ex [HT]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
State of the course:	taught
Language:	English
Teaching methods:	full-time
Teaching methods:	full-time
Level:

Guarantor:	Dubcová Miroslava RNDr. Ph.D.

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 (19.07.2013)

Aim of the course

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 (19.07.2013)

Literature

R: 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: Dubcová Miroslava (15.07.2013)

Teaching methods

Lectures and exercise classes.

Last update: TAJ413 (19.07.2013)

Syllabus

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. Gauss-Newton method.

Last update: TAJ413 (19.07.2013)

Learning resources

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

Last update: Dubcová Miroslava (26.06.2013)

Registration requirements

Mathematics I, Mathematics II.

Last update: Dubcová Miroslava (15.07.2013)

Teaching methods
	Activity	Credits	Hours
	Konzultace s vyučujícími	0.5	14
	Účast na přednáškách	1.5	42
	Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi	2	56
	Příprava na zkoušku a její absolvování	2	56
	Účast na seminářích	1	28
		7 / 7	196 / 196

Coursework assessment
Form	Significance
Examination test	70
Continuous assessment of study performance and course -credit tests	30