Numerical algorithms - AM413010
Title: Numerical algorithms
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2022
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 [HT]
Capacity: unlimited / unlimited (unknown)
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Level:  
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Dubcová Miroslava RNDr. Ph.D.
Classification: Mathematics > Mathematics General
Examination dates   
Annotation
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.
Last update: Dubcová Miroslava (13.06.2019)
Aim of the course

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

Last update: Dubcová Miroslava (13.06.2019)
Literature

Obligatory:

Last update: Červená Lenka (29.08.2024)
Teaching methods

individual project - assesment, written exam, oral exam

Last update: Dubcová Miroslava (13.06.2019)
Syllabus

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.

Last update: Dubcová Miroslava (13.06.2019)
Learning resources

E-learning page:

https://e-learning.vscht.cz/course/view.php?id=180

Last update: Červená Lenka (29.08.2024)
Registration requirements

No requirements.

Last update: Dubcová Miroslava (31.07.2019)
Teaching methods
Activity Credits Hours
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 1 28
Práce na individuálním projektu 1 28
Příprava na zkoušku a její absolvování 1 28
Účast na seminářích 1 28
5 / 5 140 / 140