| Course Unit Code | 310-4001/01 |
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| Number of ECTS Credits Allocated | 10 ECTS credits |
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| Type of Course Unit * | Choice-compulsory |
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| Level of Course Unit * | Third Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Winter, 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. |
| Summary |
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Fourier series: orthogonal functions, Fourier coefficients, even and odd
functions, convergence of the Fourier series, complex form, solution of second
order linear differential equations.
Partial differential equations: general discussion, first-order and second-
order
partial differential equations (initial and boundary conditions, methods of
solution), second-order linear partial differential equations (method of the
characteristics, method of separation of variables), the wave equation, the
heat-conduction equation, the Laplace equation, Maxwell's equations.
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| Learning Outcomes of the Course Unit |
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Main study goals:
(i) to be acquainted with actual progress in this mathematical discipline,
(ii) to extend needed theoretical knowledge with emphasized orientation to its applicability,
(iii) to increase communication ability of specialists in different branches.
With regard to professional orientation of students learning themes modification is offered to fulfill presented aims. |
| Course Contents |
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Syllabus of lecture
1. Fourier series: periodic functions, Fourier coefficients, functions of the period 2 PI, 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. ISBN 0-201-56519-6 |
Drábek, P. - Holubová, G.: Parciální diferenciální rovnice. http://mi21.vsb.cz
Kufner, A. - Kadlec, J.: Fourierovy řady. Academia, Praha 1969.
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6 |
| Recommended Reading: |
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| Strauss, W.A.: Partial differential equations: an introduction. New York: Wiley, 1992. ISBN 0-471-54868-5 |
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
Míka, S. – Kufner, A.: Parciální diferenciální rovnice I : stacionární rovnice. SNTL, Praha 1983.
Ošťádalová, E. a kol.: Parciální diferenciální rovnice. Skriptum VŠB Ostrava, 1999. |
| 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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| Examination | Examination | | |