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Lecturer(s)
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Valentová Ivana, doc. Ing. Ph.D.
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Course content
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Week 1: Mathematical models; basic classification of PDEs; Week 2: Linear PDEs of the first order; method of characteristics; Week 3: Wave equation; derivation; Cauchy problem; Week 4: Diffusion equation; derivation; Cauchy problem; Week 5: Initial-boundary value problems; Week 6: Fourier method; Week 7: Laplace and Poisson equations in two dimensions; Week 8: Methods of integral transforms; Week 9: General principles; Week 10: Laplace and Poisson equations in three dimensions; Week 11: Diffusion equation in higher dimensions; Week 12: Wave equation in higher dimensions; Week 13: Summary and conclusion.
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, Task-based study method
- Contact hours
- 52 hours per semester
- Preparation for an examination (30-60)
- 60 hours per semester
- Preparation for formative assessments (2-20)
- 20 hours per semester
- Preparation for comprehensive test (10-40)
- 40 hours per semester
- Presentation preparation (report in a foreign language) (10-15)
- 10 hours per semester
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| prerequisite |
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| Knowledge |
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| There is no prerequisite for this course. Students should be familiar with the theory of ordinary differential equations to the extent of the course KMA/ ODR. |
| learning outcomes |
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| By the end of the course, a successful student should be able to: 1. Use notions of PDE theory in English; 2. Classify partial differential equations; 3. Formulate the initial-boundary value problem for the transport, wave, diffusion and Laplace equations; 4. Provide the physical interpretation of the above problems; 5. Explain general principles valid for the above problems; 6. Solve Cauchy problems by fundamental methods; 7. Solve initial-boundary value problems by Fourier method and methods of integral transforms; 8. Apply partial differential equations and their solutions to real problems. |
| teaching methods |
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| Lecture supplemented with a discussion |
| Interactive lecture |
| Task-based study method |
| assessment methods |
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| Combined exam |
| Skills demonstration during practicum |
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Recommended literature
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Drábek, Pavel; Holubová, Gabriela. Elements of partial differential equations. Berlin ; Walter de Gruyter, 2007. ISBN 978-3-11-019124-0.
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Drábek, Pavel; Holubová, Gabriela. Parciální diferenciální rovnice : úvod do klasické teorie. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-766-1.
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Míka, Stanislav; Kufner, Alois. Parciální diferenciální rovnice. Praha : SNTL, 1983.
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Vejvoda a kol. Parciální diferenciální rovnice II. SNTL Praha, 1987.
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