M4010 Equations of mathematical physics

Faculty of Science
Spring 2015
Extent and Intensity
3/2/0. 4 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Zdeněk Pospíšil, Dr.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 F4,03017, Wed 10:00–12:50 M4,01024
Prerequisites
Single- and multivariable differential and integral calculus, curve and surface integral, 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 discipline is a part of the fundamental course of mathematical analysis for students of physics. At the end of this course, students should be able to:
classify partial differential equations;
select an appropriate classical analytical method of solution depending on type of equation;
find solution in terms of integral or infinite series for basic equations.
Syllabus
  • Boundary value problems for ordinary differential equations.
  • Special functions: Gamma function, Bessel functions, Legendre, Laguerre a Hermite polynomials.
  • Distributions.
  • Methods of characteristics: quasilinear 1st order equation, canonical form of 2nd order equations, initial value problem for wave equations.
  • Methods of integral transforms: Fourier, Laplace transforms.
  • Methods of separation of variables: wave equation, heat equation, eliptic equation, Schroedinger equation.
  • Eliptic equations: harmonic functions, potentials, Green function.
Literature
  • Franců Jan. Parciální diferenciální rovnice. VUT Brno, 2000
  • EVANS, Gwynne, Jonathan M. BLACKLEDGE and Peter YARDLEY. Analytic methods for partial differential equations. London: Springer-Verlag, 1999, xii, 299. ISBN 3540761241. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
  • BARTÁK, Jaroslav. Parciální diferenciální rovnice. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1988, 220 s. URL info
  • MÍKA, Stanislav and Alois KUFNER. Parciální diferenciální rovnice. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1983, 181 s. info
  • MÍKA, Stanislav and Alois KUFNER. Okrajové úlohy pro obyčejné diferenciální rovnice. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1981, 88 s. URL info
  • TICHONOV, Andrej Nikolajevič and Aleksandr Andrejevič SAMARSKIJ. Rovnice matematické fysiky. Translated by Alois Apfelbeck - Karel Rychlík. 1. vyd. Praha: Nakladatelství Československé akademie věd, 1955, 765 s. info
Teaching methods
Lecture and class exercises with demonstrative and individual solution of tasks.
Assessment methods
Written examination and subsequent oral one. One half of possible points in the written part is necessary to pass (usually 25 points of 50 total).
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2015, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2015/M4010