| Course Unit Code | 470-4112/01 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Compulsory |
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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 | Winter 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 | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| KAL0063 | prof. RNDr. René Kalus, Ph.D. |
| Summary |
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| This course is devoted to the analytical methods of the solution of the partial differentia equations. All the methods will give us fruitful imagination of the qualitative behavior of the mathematical modeling. This information will be very useful tor the future modeling of more complicated problems. During this course there will be given standard set of the classical partial differential equations and their properties. Also stability and uniqueness will be discussed. |
| Learning Outcomes of the Course Unit |
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| The main aim of the subject is to formulate classical partial differential equations motivated by physical phenomena and to use classical methods for their solutions. |
| Course Contents |
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First order equations, Cauchy problem, characteristic equations.
Cauchy problem for equations of higher degrees.
Classification equations of the second order.
Formulation of the classical equations given by physical phenomenon (formulation boundary and initial conditions) like: heat eq., diffusion eq., wave eq., Laplace and Poisson eq., etc.
Solution by method of characteristic.
Solution by Fourier method.
Solution by integral transformations.
Solution by Green function.
Maximal principle and uniqueness of solution.
Solution by method of potentials.
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| Recommended or Required Reading |
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| Required Reading: |
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W. A. Strauss: Partial Differential Equations (An Introduction), John Wiley & Sons, Inc., New York 1992.
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P. Drábek, G. Holubová: Parciální diferenciální rovnice (Úvod do klasické teorie). Skripta ZČU Plzeň, 2001.
J. Franců: Parciální diferenciální rovnice. Skripta VUT Brno, 2000.
S. Míka, A. Kufner: Parciální diferenciální rovnice I. Stacionární rovnice. Edice MVŠT, sešit XX, SNTL Praha, 1983.
J. Barták, L. Herrmann, V. Lovicar, O. Vejvoda: Parciální diferenciální rovnice II. Evoluční rovnice. Edice MVŠT, sešit XXI, SNTL Praha, 1988.
W. A. Strauss: Partial Differential Equations (An Introduction), John Wiley & Sons, Inc., New York 1992.
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| Recommended Reading: |
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| Textbook for students of the PDE. |
Sbírka příkladů z parciálních diferenciálních rovnic.
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| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials |
| 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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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 30 (30) | 10 |
| 1. Písemka | Written test | 15 | 0 |
| 2. Písemka | Written test | 15 | 0 |
| Examination | Examination | 70 | 35 |