M8110 Partial Differential Equations

Faculty of Science
Autumn 2025
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
prof. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 M3,01023
  • Timetable of Seminar Groups:
M8110/01: Mon 14:00–15:50 M3,01023, M. Veselý
Prerequisites
!( M8300 Part. diff. equations || NOW( M8300 Part. diff. equations ))
Differential and integral calculus in several variables, basic methods for solving ordinary differential equations
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main aim of the course is to analyse the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, heat equation, wave equation, and transport equation).
Learning outcomes
At the end of the course, in particular, students will be able to:
solve first-order equations;
use the Fourier method;
formulate relevant mathematical theorems and statements and to explain methods of their proofs in the theory of the studied second-order equations;
apply problems from the theory of the studied second-order equations.
Syllabus
  • Classification of second-order equations
  • Transport equation
  • Separation of variables
  • Theorem of Cauchy-Kowalevskaya
  • Nonlinear first-order equations, method of characteristics
  • Method of Fourier's transformation
  • Laplace's and Poisson's equation, harmonic functions
  • Heat equation
  • Wave equation
Literature
    recommended literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • STRAUSS, Walter A. Partial differential equations : an introduction. [New York]: John Wiley & Sons, 1992, ix, 425. ISBN 0471548685. info
    not specified
  • TREVES, François. Analytic partial differential equations. Cham: Springer, 2022, xiii, 1228. ISBN 9783030940546. info
  • Computational partial differential equations for engineering sciences. Edited by Bernardino D'Acunto. New York: Nova Science Publishers, 2012, xvi, 569 p. ISBN 9781617614019. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
  • PETROVSKIJ, Ivan Georgijevič. Parciální diferenciální rovnice. 1. vyd. Praha: Přírodovědecké vydavatelství, 1952, 276 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further Comments
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Spring 2000, Autumn 2010 - only for the accreditation, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2025/M8110