SubjectsSubjects(version: 895)
Course, academic year 2021/2022
  
Numerical Methods - AB413004
Title: Numerical Methods
Guaranteed by: Department of Mathematics (413)
Actual: from 2021
Semester: winter
Points: winter s.:5
E-Credits: winter s.:5
Examination process: winter s.:
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited / unlimited (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Level:  
For type: Bachelor's
Additional information: http://předmět je vyučován pouze v zimním semestru
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Dubcová Miroslava RNDr. Ph.D.
Červená Lenka RNDr. Ph.D.
Interchangeability : B413004, N413005
Is interchangeable with: B413004
This subject contains the following additional online materials
Annotation -
Last update: Kubová Petra Ing. (22.01.2018)
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: Kubová Petra Ing. (22.01.2018)

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: Kubová Petra Ing. (22.01.2018)

R: M. Kubíček, M. Dubcová, D. Janovská, Numerical Methods and Algorithms, 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: Kubová Petra Ing. (22.01.2018)

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

http://www.vscht.cz/mat/Ang/NM-Ang/NM-Ang.pdf

Teaching methods -
Last update: Kubová Petra Ing. (22.01.2018)

Lectures and exercise classes.

Syllabus -
Last update: Kubová Petra Ing. (22.01.2018)

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 regression.

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

Students are expected to have either completed the prerequisite course 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)

Mathematics A

Course completion requirements -
Last update: Dubcová Miroslava RNDr. Ph.D. (16.02.2018)

individual project - assesment, written exam, oral exam

Teaching methods
Activity Credits Hours
Konzultace s vyučujícími 0,5 14
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 1 28
Příprava na zkoušku a její absolvování 1,5 42
Účast na seminářích 1 28
5 / 5 140 / 140
 
VŠCHT Praha