310-3143/02 – Partial Differential Equations (PDR)
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 | Optional |
Year | 1 | Semester | summer |
| | Study language | English |
Year of introduction | 2019/2020 | Year of cancellation | 2021/2022 |
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
Individual consultations
Tutorials
Project work
Summary
Studenti se seznámí s Fourierovými řadami a s klasickými metodami řešení parciálních diferenciálních rovnic.
V první kapitole jsou probírány Fourierovy řady v rozsahu potřebném pro další výuku. Ve druhé kapitole se studenti velmi stručně seznámí s parciálními diferenciálními rovnicemi prvního řádu. Teorie parciálních diferenciálních rovnic druhého řádu je zaměřena na Fourierovu metodu separace proměnných a metodu charakteristik. Jádro předmětu je v řešení lineárních parciálních diferenciálních rovnic druhého řádu (Laplaceova rovnice, vlnová rovnice, rovnice vedení tepla).
Compulsory literature:
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993
Recommended literature:
Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007.
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:
Syllabus of lecture
1. Fourier series: periodic functions, Fourier coefficients, functions of the period 2, function of the period T, even and odd functions
2. Even and odd functions, half - range cosine and sine series, convergence of Fourier series
3. Solution of 2nd order linear differential equations with constant coefficients by Fourier series
4. Partial differential equations: general discussion
5. Methods of solutions of partial differential equations of the first order
6. Methods of solutions of partial differential equations of the second order
7. Fourier´s method of separation
8. 2nd order partial linear differential equations
9. Canonical form of 2nd order partial linear differential equations
10. Laplace equation: separated solutions, boundary conditions
11. Solution of the one-dimensional wave equation: d’Alembert solution, method of the
separation of variables,
12. Solution of a boundary problem
13. Solution of the heat-conduction: one dimensional heat conduction equation, separation method.
14. Reserve
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.