M9150 Partial Differential Equations II

Faculty of Science
Spring 2009
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. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 MS2,01022
  • Timetable of Seminar Groups:
M9150/01: Mon 14:00–14:50 MS2,01022, L. Adamec
Prerequisites
M8110 Partial Differential Equations I
Calculus of several variables, basic methods of solving ordinary and partial 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
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
This course is a continuation of the course "Partial differential equations I".
The aim of the course is to aquire techniques necessary for formulating and solving problems using partial differential equations in modern setting.
At the end of this course, students should be able to understand concepts of weak solution of second-order linear partial differential equation elliptic and evolutionary.
Syllabus
  • Modern methods
  • 1) Sobolev spaces of generalized functions
  • 2) Linear seccond-order elliptic equations:
  • - Weak formulation of elliptic problems
  • - Lax-Milgram lemma and existence of solutions
  • - Regularity
  • - Maximum principle
  • 3) Linear parabolic and hyperbolic equations:
  • - Ritz-Galerkin method
  • - Regularity
  • - Semigroup theory
Literature
  • Partial differential equations. Edited by Jürgen Jost. New York: Springer-Verlag, 2002, xi, 325. ISBN 0387954287. info
  • GILBARG, David and Neil S. TRUDINGER. Elliptic partial differential equations of second order. Berlin: Springer-Verlag, 1997, x, 401 s. ISBN 3-540-08007-4-. info
  • BASSANINI, Piero and Alan R. ELCRAT. Theory and applications of partial differential equations. New York: Plenum Press, 1997, ix, 439 s. ISBN 0-306-45640-0. info
  • RENARDY, Michael and Robert ROGERS. An introduction to partial differential equations. New York: Springer-Verlag, 1992, vii, 428. ISBN 0387979522. info
Assessment methods
lectures,class exercises;
oral examination.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Spring 2005, Spring 2007.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2009/M9150