Partial Differential Equations

The course provides a thorough introduction to the mathematical theory of partial differential equations, both the classical theory of Laplace, Cauchy, Fourier, Gauss etc. and the modern theory based on functional analytic methods. Topics covered are first order equations, Cauchy's problems, characteristics, linear second-order equations, classification, boundary value problems for elliptic equations, perimeter and initial value problems for hyperbolic and parabolic equations, fundamental solutions, maximum principles, weak solutions and functional analytic methods.

1. Knowledge. The student masters the basic principles and methods for the analysis of partial differential equations, including first-order equations, Cauchy's problems, characteristics, linear second-order equations, classification, boundary value problems for elliptic equations, boundary and initial value problems for hyperbolic and parabolic equations, fundamental solutions, maximum principles, weak solutions and functional analytic methods. 2. Skills. The student is able to apply the techniques to study specific examples, understand the proofs and apply central proof techniques of related problems.

Lectures and exercises. Students are free to choose Norwegian or English for written assessments.