Course content

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.

Learning outcome

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.

Learning methods and activities

Lectures and exercises. Retake of examination may be given as an oral examination. The lectures may be given in English. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments.

Recommended previous knowledge

TMA4145 Linear Methods or equivalent.

Course materials

Will be announced at the start of the course.

Credit reductions