Valid from: Autumn 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-04-24
Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: MATP16
Teaching language: English
The aim of is to give a thorough introduction to the modern mathematical theory for the partial differential equations that are of greatest importance in physics. For this purpose an introduction to the theory of distributions and the theory of Sobolev spaces.
Knowledge and Understanding
For a passing grade the doctoral student must
Competences and Skills
For a passing grade the doctoral student must
Judgement and Approach
For a passing grade the doctoral student must be able to explain the concept "well-posed problem" and its importance when modelling with differential equations.
Quasi-linear equations of the first order. Classification of second-order equations. The Cauchy-Kowalevski theorem. The Holmgren uniqueness theorem. The Laplace equation. The wave equation. The heat equation.
Evans, Lawrence C.: Partial Differential Equations. American Mathematical Soc., 2010. ISBN 9780821849743.
Types of instruction: Lectures, seminars
Examination formats: Written exam, oral exam, written assignments
Grading scale: Failed, pass
Examiner:
Admission requirements: For admission to the course, English B is required as well as at least 82.5 credits in mathematics in which should be included the courses MATC11 Analytic functions, 15 credits and MATM14 Ordinary Differential Equations, 7.5 credits or the equivalent.
Course coordinators:
Web page: https://liveatlund.lu.se/departments/Mathnfak/MATM19/Pages/default.aspx