M8110 Partial Differential Equations I

Faculty of Science
Autumn 2005
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Martin Kolář, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Timetable
Tue 17:00–18:50 UM
  • Timetable of Seminar Groups:
M8110/01: Tue 19:00–19:50 UM, L. Adamec
Prerequisites
M5160 Differential Eqs.&Cont. Models
Differential and integral calculus in several veriables, 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 aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations. The first part contains a theory for first order equations, solutions using power series, local existence and uniqueness, classification of second order linear equations. the second part contains analysis of the fundamental equations of mathematical physics - the heat equation, wave equation and Laplace equation. Techniques for solving appropriate initial and boundary value problems are discussed - Separation of variables, integral transformations, use of characteristics, Green's function, maximum principles and uniqueness of solutions.
Syllabus
  • I. Introduction First order equations Cauchy problem for k-th order equations Classification of second order equations and canonical forms Derivation of the basic equations of mathematical physics and initial and boundary conditions II Classical methods Method of characteristics Separation of variables Integral transformations Maximum principles, harmonic functions and uniqueness of solutions
Literature
  • ARSENIN, Vasilij Jakovlevič. Metody matematičeskoj fiziki i special'nyje funkcii. 2. perer. i dop. izd. Moskva: Nauka, 1984, 382 s. info
  • PETROVSKIJ, Ivan Georgijevič. Parciální diferenciální rovnice. 1. vyd. Praha: Přírodovědecké vydavatelství, 1952, 276 s. info
Assessment methods (in Czech)
Výuka : přednáška a cvičení, Zkouška : ústní
Language of instruction
Czech
Follow-Up Courses
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 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 (Autumn 2005, recent)
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