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Matematisa institutionen, UU


1MA053    Partiella differentialekvationer, intorduktionskurs (5.0 hp)

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  • First-order equations (the methof of characteristics, Cauchy problem for quasi-linear and fully non-linear equations, weak solutions).

  • General techniques and principles for second-order equations

  • The wave equation (d'Alembert's formula, weak solutions, reflections, Duhamel's principle, two-dimensional and three-dimensional wave equation, conservation of energy).

  • The Laplace equation (Mean Value Theorem and Maximum Principle, the fundamental solution, Green's function, Poisson kernel).

  • The heat equation (Weak maximum principle, properties of the heat kernel, properties of the solution to the pure initial value problem).


  • Robert C. McOwen, Partial Differential Equations, Methods and Applications, Prentice Hall/Pearson Education, Inc., 2003 (Second Edition)
  • * Lawrence C. Evans. Partial Differential Equations, AMS, Providence, RI. Series: Graduate Studies in Mathematics, Vol. 19, 1998.

    Instruction: Lectures and problem solving sessions.

    Examination: Written examination at the end of the course.