SubjectsSubjects(version: 853)
Course, academic year 2019/2020
  
Numerical algorithms - AM413010
Title: Numerical algorithms
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
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: unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Level:  
For type: Master's (post-Bachelor)
Guarantor: Dubcová Miroslava RNDr. Ph.D.
Annotation
Last update: Dubcová Miroslava RNDr. Ph.D. (13.06.2019)
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 and boundary conditions, and with methods for experimental data evaluation. By learning these numerical algoritmuss students will gain insight into problem formulation and develop the ability to derive a problem solution and estimate its accuracy. During the course, the student elaborates two individual projects.
Aim of the course
Last update: Dubcová Miroslava RNDr. Ph.D. (13.06.2019)

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. The student will use numerical methods to solve specific application problems

Literature
Last update: Dubcová Miroslava RNDr. Ph.D. (13.06.2019)

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. (13.06.2019)

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

Teaching methods
Last update: Dubcová Miroslava RNDr. Ph.D. (13.06.2019)

individual project - assesment, written exam, oral exam

Syllabus
Last update: Dubcová Miroslava RNDr. Ph.D. (13.06.2019)

1. Interpolation, interpolation by spline functions. Difference formulas, quadrature formulas.

2. Methods of linear algebra.

3. Systems of nonlinear equations. Newton method.

4. Initial value problem for ODE´s. One-step methods. Multistep methods.

5. Stability. Error estimation. Stiff systems. A-stable methods.

6. Boundary value problem for ODE´s. Finite-difference methods.

7. Shooting methods.

8. Projekt 1.

9. Finite-difference methods for linear PDE´s of parabolic type.

10. Finite-difference methods for nonlinear PDE´s of parabolic type. Methods of lines.

11. Finite-difference methods for PDE´s of elliptic type.

12. Linear and nonlinear regression.

13.-14. Projekt 2.

Registration requirements
Last update: Dubcová Miroslava RNDr. Ph.D. (31.07.2019)

No requirements.

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
Coursework assessment
Form Significance
Defense of an individual project 20
Examination test 30
Oral examination 50

 
VŠCHT Praha