| Course Unit Code | 470-4114/01 |
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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 | 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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| BOU10 | prof. RNDr. Jiří Bouchala, Ph.D. |
| VOD03 | doc. Mgr. Petr Vodstrčil, Ph.D. |
| Summary |
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| The course is offered throughout the university. Within the course the students are introduced into weak formulations of various kinds of elliptic boundary value problems, solvability conditions as well as fundamental properties of the weak solutions. The correct understanding of these notions is necessary to succeed with solution of various engineering problems. |
| Learning Outcomes of the Course Unit |
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| Students, who pases the course, will be able to define a weak solution for various kinds of elliptic boundary value problems, to prove the existence of a unique solution and master a couple of approaches to solve it numerically. |
| Course Contents |
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Lebesgue Integral.
Lebesgue Spaces.
Distributions.
Sobolev Spaces.
Trace Theorem.
Weak Solutions of Boundary Value Problems.
Lax Milgram Theorem.
Existence and Uniqueness of Weak Solutions.
Regularity of Weak Solution.
Energy Functional.
Ritz and Galerkin Methods. |
| Recommended or Required Reading |
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| Required Reading: |
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M. Renardy, R. C. Rogers: An introduction to partial differential equations, Springer-Verlag, New York, 1993.
E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995.
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J. Bouchala: Variační metody, http://am.vsb.cz/bouchala
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| Recommended Reading: |
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| E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995. |
K. Rektorys: Variační metody v inženýrských problémech a v problémech matematické fyziky, Academia, Praha, 1999.
O. John, J. Nečas: Rovnice matematické fyziky, MFF UK, Praha, 1977.
M. Renardy, R. C. Rogers: An introduction to partial differential equations, Springer-Verlag, New York, 1993.
S. Míka, A. Kufner: Parciální diferenciální rovnice I. Stacionární rovnice, SNTL, Praha, 1983.
E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995. |
| Planned learning activities and teaching methods |
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| Lectures, 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 | 10 |
| Examination | Examination | 70 | 21 |