310-3146/01 – Partial differential equations for engineers (PDEI)
| 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 equations of mathematical physics. Students will acquire advanced knowledge and skills of given parts of mathematics adapted to the needs of practical modeling in engineering practice. The course focuses on classical methods of solving problems expressed by partial differential equations.
Teaching methods
Lectures
Tutorials
Summary
The aim of the course is to provide an overview of mathematical modeling using partial differential equations. The subject is adapted to the use of models of equations of mathematical physics in practical engineering tasks. Students will acquire skills and competences that will enable them to understand the description of selected physical phenomena using partial differential equations and in reasonably simple situations solve these equations using classical methods.
Compulsory literature:
Recommended literature:
Ka Kit Tung: Methods for Partial Differential Equations. https://amath.washington.edu/courses/2019/spring/amath/503/a.
Way of continuous check of knowledge in the course of semester
Set of homework examples, credit test, oral exam.
E-learning
https://amath.washington.edu/courses/2019/spring/amath/503/a
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, terminology, motivational examples.
2. Equations of the first order, method of characteristics.
3. Classification of second order equations.
4. Derivation of heat conduction equation in rod and body.
5. Derivation of equation of diffusion and vibration of string.
6. Derivation of equations using the variational principle.
7. Method of characteristics for hyperbolic equations.
8. Fourier series.
9. Fourier series method.
10. Method of integral transformation.
11. Green function method.
12. Principle of maximum and uniqueness of tasks.
13. Potential method.
14. Final summary, evaluation of results, reserve.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction