SubjectsSubjects(version: 853)
Course, academic year 2019/2020
  
Numerical Methods - S413005
Title: Numerical Methods
Guaranteed by: Department of Mathematics (413)
Actual: from 2011
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 [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Level:  
For type:  
Guarantor: Dubcová Miroslava RNDr. Ph.D.
This subject contains the following additional online materials
Annotation
Last update: TAJ413 (19.07.2013)
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.
Aim of the course
Last update: TAJ413 (19.07.2013)

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.

Literature
Last update: Dubcová Miroslava RNDr. Ph.D. (15.07.2013)

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

Learning resources
Last update: Dubcová Miroslava RNDr. Ph.D. (26.06.2013)

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

Teaching methods
Last update: TAJ413 (19.07.2013)

Lectures and exercise classes.

Syllabus
Last update: TAJ413 (19.07.2013)

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.

Registration requirements
Last update: Dubcová Miroslava RNDr. Ph.D. (15.07.2013)

Mathematics I, Mathematics II.

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

 
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