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Methods of Applied Mathematics - N413013

Title:	Metody aplikované matematiky
Guaranteed by:	Department of Mathematics (413)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2013 to 2019
Semester:	summer
Points:	summer s.:4
E-Credits:	summer s.:4
Examination process:	summer s.:
Hours per week, examination:	summer s.:2/1, C+Ex [HT]
Capacity:	unknown / unknown (unknown)
Min. number of students:	unlimited
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Level:
Note:	course can be enrolled in outside the study plan enabled for web enrollment

Guarantor:	Janovská Drahoslava prof. RNDr. CSc.
Class:	Předměty pro matematiku
Is interchangeable with:	M413003

Examination dates Schedule

Annotation -

Our aim is to fill gaps in knowledge of students, namely in the field of Functional Analysis, in such a way that they will be able to understand the mathematical features of the Finite Element Method. The Finite Element Method is a modern numerical method that enables us to approximate continuously the solution of partial differentia equations. Students will also try to apply the method (including software) for solving particular simple problems.

Last update: Janovská Drahoslava (29.08.2013)

Literature -

R: Kubíček Milan, Dubcová Miroslava, Janovská Drahoslava: Numerické metody a algoritmy, VŠCHT Praha, 2005 (druhé vydání).

A: Suli Endre: Lecture notes of Finite Element Method for Partial Differential Equations, http://people.maths.ox.ac.uk/suli/fem.pdf

Last update: Janovská Drahoslava (29.08.2013)

Teaching methods -

Lectures and seminars, each student solves 3 small project and presents them in seminars.

Last update: Janovská Drahoslava (29.08.2013)

Syllabus -

1. The method of weighted residuals.

2. Introduction to the Finite Element Method.

3. Short introduction to the Functional Analysis

4. Sobolev Spaces

5. Variational formulation of the boundary problems.

6. A simple one dimensional example.

7. Element point of wiev.

8. Global stiffness and mass matrix.

9. Selected methods of the Numerical Linear Algebra.

10. Variational formulation of the boundary problems in two and three dimensions.

11. Numerical realization.

12. Different types of elements.

13. The finite element method for three dimensional problems.

14. Numerical solution of systems of linear algebraic equations.

Last update: Janovská Drahoslava (29.08.2013)

Learning resources -

http://www.vscht.cz/mat/MAM/FEM_UM.pdf

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

Suli Endre: Lecture notes of Finite Element Method for Partial Differential Equations, http://people.maths.ox.ac.uk/suli/fem.pdf

Last update: TAJ413 (05.09.2013)

Learning outcomes -

Students will get acquainted with mathematical principles of methods that continuously approximate the solution of partial differential equations, in particular they will study the method of weighted residuals and the Finite Element Method.

Last update: Janovská Drahoslava (29.08.2013)

Registration requirements -

Basic course MI and MII, the advantage is also passing the course on Numerical Methods and the course MIII.

Last update: Janovská Drahoslava (29.08.2013)

Teaching methods
	Activity	Credits	Hours
	Účast na přednáškách	1	28
	Práce na individuálním projektu	1.5	42
	Příprava na zkoušku a její absolvování	1	28
	Účast na seminářích	0.5	14
		4 / 4	112 / 112

Coursework assessment
Form	Significance
Regular attendance	20
Defense of an individual project	20
Report from individual projects	40
Oral examination	20