Course: Partial Differential Equations 1

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Course title Partial Differential Equations 1
Course code KMA/PDR1
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 3
Language of instruction Czech, English
Status of course Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • Fürst Tomáš, RNDr. Ph.D.
  • Horák Jiří, doc. RNDr. CSc.
  • Vodák Rostislav, RNDr. Ph.D.
Course content
1. Equations of mathematical physics. 2. Classification of equations of the second order, canonic form of the equations. 3. Derivation of the basic equations of mathematical physics. 4. Wave and heat equations and their fundamental solutions (d'Alembert method and Fourier transform). 5. Fourier method for the wave, heat and Poisson equations. 6. The maximum principle. 7. Uniqueness of solution. 8. Three potentials theorem. 9. Harmonic functions and their properties (the maximum principle, Harnack theorems).

Learning activities and teaching methods
Lecture, Demonstration
  • Attendace - 52 hours per semester
  • Preparation for the Exam - 40 hours per semester
Learning outcomes
Understand classical approach to PDE's.
Application Apply differential and intergral calculus of functions of several variables in the classic theory of PDEs.
Understanding the mathematical tools of differential and integral calculus of functions of several variables.

Assessment methods and criteria
Written exam

Credit: the student has to pass one written test (i.e. to obtain at least half of the possible points). Exam: the student has to understand the subject and be able to prove all theorems.
Recommended literature
  • A. N. Tichonov, A. A. Samarskij. (1955). Rovnice matematické fyziky. ČSAV, Praha.
  • L. C. Evans. (1998). Partial Differential Equations. University of Berkeley, 1994 a Amer.Math.Soc. Providence.
  • M. Renardy, R. C. Rogers. (1993). An Introduction to Partial Differential Equations. Springer-Verlag.
  • O. John, J. Nečas. (1977). Rovnice matematické fyziky. Skripta MFF UK Praha.
  • S. G. Michlin. (1977). Linějnyje uravněnija v častnych proizvodnych (v ruštině). Vyššaja škola, Moskva.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester