Subjects

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Methods of Applied Mathematics - M413003

Title:	Metody aplikované matematiky
Guaranteed by:	Department of Mathematics, Informatics and Cybernetics (446)
Faculty:	Faculty of Chemical Engineering
Actual:	from 2021
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:	unlimited / unlimited (unknown)
Min. number of students:	unlimited
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
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
Classification:	Mathematics > Mathematics General
Interchangeability :	N413013

Examination dates Schedule

This subject contains the following additional online materials

E-learning course

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: Pátková Vlasta (09.01.2018)

Aim of the course -

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: Pátková Vlasta (09.01.2018)

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: Pátková Vlasta (09.01.2018)

Teaching methods -

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

Last update: Pátková Vlasta (09.01.2018)

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: Pátková Vlasta (09.01.2018)

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: Pátková Vlasta (09.01.2018)

Entry requirements -

Students are expected to have either completed the prerequisite courses Mathematics A and Mathematics B or possess the equivalent knowledge prior to enrolling in the course.

Last update: Borská Lucie (13.05.2019)

Registration requirements -

No requirements.

Last update: Borská Lucie (06.05.2019)

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