M8110 Partial Differential Equations

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5160 Ord. Differential Equations I
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
Students will acquire techniques necessary for formulating and solving problems using partial differential equations in classical and modern setting. At the end of this course, students will be able to understand the structure and behaviour of the four fundamental linear equations of mathematical physics (Laplace's equation, Heat equation, Wave equation and transport equation) and the structure of nonlinear first order equations.
Syllabus
  • Introduction
  • Classification of second order equations
  • Laplace's and Poisson§s equations, harmonic functions
  • Fourier method
  • Separation of variables
  • Nonlinear first order equations - method of characteristics
  • Sobolev spaces
  • Second-order elliptic equations
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
Teaching methods
Lectures (theoretical explanation with practical examples) and class exercises
Assessment methods
Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
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, 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.