Course objectives:
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The aim of this course is an introduction to the classical theory of partial differential equations. Students will be acquainted with the basic classification of partial differential equations and they will study general properties and fundamental methods of solving linear equations of the first and second orders, namely the transport, wave, diffusion and Laplace equations. Attention will be also paid to the derivation and physical interpretation of the studied models. This course is lectured in English, its subject is equivalent to KMA/PDR. Students should be familiar with the theory of ordinary differential equations to the extent of the course KMA/ ODR.
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Requirements on student
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Demonstrate knowledge of fundamental properties of linear partial differential equations and basic methods of their solving. The ability to apply theoretical results in solving problems on the topics in the syllabus.
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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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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Recommended:
Drábek, Pavel; Holubová, Gabriela. Elements of partial differential equations. Berlin ; Walter de Gruyter, 2007. ISBN 978-3-11-019124-0.
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Recommended:
Míka, Stanislav; Kufner, Alois. Parciální diferenciální rovnice. Praha : SNTL, 1983.
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Recommended:
Drábek, Pavel; Holubová, Gabriela. Parciální diferenciální rovnice : úvod do klasické teorie. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-766-1.
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Recommended:
Vejvoda a kol. Parciální diferenciální rovnice II. SNTL Praha, 1987.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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52
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Preparation for an examination (30-60)
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60
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Presentation preparation (report in a foreign language) (10-15)
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10
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Preparation for comprehensive test (10-40)
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40
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Preparation for formative assessments (2-20)
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20
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Total
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182
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
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. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
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.
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Skills demonstration during practicum |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture supplemented with a discussion |
Interactive lecture |
Task-based study method |
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