Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMA145F valid from Autumn 2018

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  • 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.
  • 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.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • be able to account for the basics of distribution theory and the theory of Sobolev spaces.

    be able to describe the three main classes of second order equations: elliptic, parabolic and hyperbolic, and describe the properties of their solutions.

Competences and Skills
  • For a passing grade the doctoral student must
  • be able to formulate and prove the most important theorems.

    be able to use the method of characteristics to solve first order linear equations.
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.
Types of Instruction
  • Lectures
  • Seminars
Examination Formats
  • Written exam
  • Oral exam
  • Written assignments
  • Failed, pass
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.
Assumed Prior Knowledge
Selection Criteria
  • Evans, Lawrence C.: Partial Differential Equations. American Mathematical Soc., 2010. ISBN 9780821849743.
Further Information
Course code
  • FMA145F
Administrative Information
  • 2018-04-24
  • Professor Thomas Johansson

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