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Data for 2018/2019

Numerical Methods

Credits 7
Hours per week 3 / 2 / 0
Examination C+Ex
Study Language English
Level Bachelor subject
Guarantor RNDr. Miroslava Dubcová, Ph.D.
Supplemental electronic materials available at UCT Prague's e-learning

Summary

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.

Syllabus

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.

Literature

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

UCT Prague
Technická 5
166 28 Prague 6 – Dejvice
IČO: 60461373
VAT: CZ60461373

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