| Course Unit Code | 310-3143/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| KUC14 | prof. RNDr. Radek Kučera, Ph.D. |
| SWA0013 | RNDr. Martin Swaczyna, Ph.D. |
| Summary |
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| Learning Outcomes of the Course Unit |
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| 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. |
| Course Contents |
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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
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| Recommended or Required Reading |
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| Required Reading: |
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James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993
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Drábek, P.- Holubová, G.: Parciální diferenciální rovnice. http://mi21.vsb.cz
Škrášek, J.-Tichý, Z.: Základy aplikované matematiky II, SNTL Praha, 1986
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993 |
| Recommended Reading: |
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| Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007. |
Franců, J.: Parciální diferenciální rovnice. Akademické nakladatelství CERM, Brno 2003. ISBN 80-214-2334-X
Drábek, P. – Holubová, G.:. Parciální diferenciální rovnice: úvod do klasické teorie. Západočeská univerzita, Plzeň 2001. ISBN 80-7082-766-1
Ošťádalová, E. a kol.: Parciální diferenciální rovnice. Skriptum VŠB Ostrava, 1988
http://mdg.vsb.cz/M
Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007. |
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Project work |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 40 | 20 |
| Examination | Examination | 60 | 25 |