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Lecturer(s)
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Fiurášek Jaromír, prof. Mgr. Ph.D.
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Course content
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1) Derivation of selected equations of mathematical physics 2) Partial differential equations of first order 3) Classification of second-order linear partial differential equations, transformation to canonical form 4) Types of problems according to the initial and boundary conditions 5) Solution of wave equation, d'Alembert formula, Poisson formula, Kirchhoff formula 6) Principle of superposition and its application to construction of solution of PDEs 7) Cauchy problem for heat transport equation, integral transform method 8) Green function method 9) Harmonic functions, the maximum principle 10) Method of potentials, volume potential, surface potentials 11) Numerical solutions of PDEs 12) Finite elements method
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
- Homework for Teaching
- 50 hours per semester
- Preparation for the Exam
- 48 hours per semester
- Attendace
- 52 hours per semester
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Learning outcomes
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Introductory course on equations of mathematical physics. Students shall become familiar with the classification and properties of linear partial differential equations of second order and with the methods how to solve them.
Subject focused on the acquisition of knowledge. Knowledge of basic types of linear partial differential equations of second order and methods to solve them, ability to define the main ideas and conceptions of the subject, describe the main approaches to solving the equations. Ability to apply the theoretical knowledge when solving specific problems.
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Prerequisites
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Knowledge of integral and differential calculus and Fourier transform.
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Assessment methods and criteria
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Oral exam
Attendance of exercises is obligatory, attendance of lectures is voluntary but recommended. Course credit prior to examination is awarded for attendance at the exercises and for solving sets of homework probelems. Oral exam covers the tought topics as specified in the Content.
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Recommended literature
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Dont, M. (2008). Úvod do parciálních diferenciálních rovnic. Praha.
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Franců, J. (2003). Parciální diferenciální rovnice. Brno.
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