Engelska

Varje vårtermin

The overall purpose of the course is that PhD students after completing the course should have deepened the knowledge about the theory partial differential equations that they acquired during the course FMAN55 Applied Mathematics, in particular concerning general geometries and semilinear equations. The purpose is also that the PhD students should have further developed their ability to solve problems and communicate mathematical reasoning.

*The method of characteristics and nonlinear equations of the first order.

*Laplace’s equation. The heat equation. The wave equation.

*The Cauchy-Kovalevskaya Theorem.

*Sobolev spaces.

*Existence, uniqueness and regularity for weak solutions to linear second order elliptic, parabolic and hyperbolic equations.

*Maximum principles for elliptic and parabolic equations.

be able to explain in depth the concepts, theorems and methods included in the course,

be able to identify and prove the most important theorems in the course.

be able to apply and integrate knowledge from the different parts of the course in connection with problem solving,

be able to identify problems that can be solved by methods that are part of the course and use an appropriate solution method,

be able to describe the solution to a mathematical problem within the course framework in speech and writing, logically coherent and with adequate terminology.

Föreläsningar

Seminarier

Skriftlig tentamen

Muntlig tentamen

Underkänd, godkänd

FMAF01 Analytic Functions, FMAF05 Systems and Transforms, and FMAN55 Applied Mathematics.

Evans, Lawrence C.: Partial Differential Equations. American Mathematical Soc., 2010. ISBN 9780821849743.

FMAN76F

2025-01-10

Maria Sandsten