M4010 Equations of mathematical physics

Faculty of Science
Spring 2026
Extent and Intensity
3/2/0. 4 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
Mgr. Jakub Záthurecký, Ph.D. (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
Mon 16. 2. to Fri 22. 5. Wed 13:00–15:50 M2,01021
  • Timetable of Seminar Groups:
M4010/01: Mon 16. 2. to Fri 22. 5. Thu 17:00–18:50 F3,03015
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
Abstract
The discipline is a part of the fundamental course of mathematical analysis for students of physics. It is devoted to classical methods to solving partial differential equations.
Learning outcomes
At the end of this course, students should be able to:
classify partial differential equations;
select an appropriate classical analytic method of solution depending on type of equation;
find solution in terms of integral or infinite series for basic equations.
Key topics
  • 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.
Study resources and literature
  • FRANCŮ, Jan. Parciální diferenciální rovnice. 3. vyd. Brno: CERM, 2003, 155 s. ISBN 802142334X. info
  • OLVER, Peter J. Introduction to partial differential equations. Cham: Springer, 2014, xxv, 636. ISBN 9783319020983. info
  • TREVES, François. Analytic partial differential equations. Cham: Springer, 2022, xiii, 1228. ISBN 9783030940546. 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
  • HABERMAN, Richard. Applied Partial Differential Equations. 5th ed. Pearson, 2012, 792 pp. ISBN 978-0-321-79706-3. info
  • DRÁBEK, Pavel and Gabriela HOLUBOVÁ. Parciální diferenciální rovnice. Online. 2011. URL info
  • AGARWAL, Ravi P. and Donal O'REGAN. Ordinary and partial differential equations : with special functions, Fourier series, and boundary value problems. New York, NY: Springer, 2009, xiv, 410. ISBN 9780387791456. info
  • RENARDY, Michael and Robert C. ROGERS. An Introduction to Partial Differential Equations. 2nd ed. Springer New York, NY, 2004, 434 pp. ISBN 978-0-387-00444-0. info
  • HASSANI, Sadri. Mathematical methods : for students of physics and related fields. New York: Springer Verlag, 2000, xv, 659. ISBN 0387989587. info
  • EVANS, Gwynne; Jonathan M. BLACKLEDGE and Peter YARDLEY. Analytic methods for partial differential equations. London: Springer-Verlag, 1999, xii, 299. ISBN 3540761241. 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
Approaches, practices, and methods used in teaching
Lecture and class exercises with demonstrative and individual solution of tasks. The teaching is carried out by contact form.
Method of verifying learning outcomes and course completion requirements
Written examination and subsequent oral one. One half of possible points in the written part is necessary to pass.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.
The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.
Assessment in all cases may be in Czech and English, at the student's choice.
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 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (recent)
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