SubjectsSubjects(version: 853)
Course, academic year 2019/2020
  
Methods of Applied Mathematics - M413003
Title: Metody aplikované matematiky
Guaranteed by: Department of Mathematics (413)
Actual: from 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 [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
For type:  
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Janovská Drahoslava prof. RNDr. CSc.
Class: Předměty pro matematiku
Interchangeability : N413013
Examination dates   Schedule   
Annotation -
Last update: Pátková Vlasta (09.01.2018)
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.
Aim of the course -
Last update: Pátková Vlasta (09.01.2018)

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.

Literature -
Last update: Pátková Vlasta (09.01.2018)

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

Learning resources -
Last update: Pátková Vlasta (09.01.2018)

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

Teaching methods -
Last update: Pátková Vlasta (09.01.2018)

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

Syllabus -
Last update: Pátková Vlasta (09.01.2018)

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.

Entry requirements -
Last update: Borská Lucie RNDr. Ph.D. (13.05.2019)

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.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (06.05.2019)

No requirements.

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
Coursework assessment
Form Significance
Regular attendance 20
Report from individual projects 20
Examination test 20
Oral examination 40

 
VŠCHT Praha