310-3147/01 – Simulation and numerical methods (SNM)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2021/2022 | Year of cancellation | |
| Intended for the faculties | FS | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The course deals with mathematical modeling based on ordinary differential equations. Students will acquire advanced knowledge and skills of given parts of mathematics adapted to the needs of practical modeling in engineering practice. The course is focused on analytical and numerical solution of ordinary differential equations.
Teaching methods
Lectures
Tutorials
Summary
The aim of the course is to provide an overview of mathematical modeling using ordinary differential equations. The course is focused on the use of these models in practical engineering tasks. Students will acquire skills and competences that will enable them to understand the description of selected models and solve them using analytical or numerical methods.
Compulsory literature:
M.T.Heath: Scientific Computing. An Introductory Survey, McGraw-Hill, New York, 2002. M.T.Heath: Scientific Computing. An Introductory Survey, McGraw-Hill, New York, 2002.
Recommended literature:
Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003.
Way of continuous check of knowledge in the course of semester
Set of homework examples, credit test, oral exam.
E-learning
Other requirements
Set of homework examples, credit test, oral exam.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Introduction, basic terminology, motivational examples.
2. Systems of ordinary differential equations, Cauchy's problem.
3. Elimination method.
4. Euler method.
5. Method of constant variance.
6. Boundary value problems for ordinary differential equations.
7. Application examples for analytical methods.
8. One-step numerical methods.
9. Multi-step numerical methods.
10. Calculations with controlled accuracy.
11. Taylor series method.
12. Method of shooting.
13. Application examples for numerical methods.
14. Final summary, evaluation, reserve.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction