2WA09 - Partial Differential Equations

Course: Partial Differential Equations
Vakcode: 2WA09
Semester 1, aimed at students of the Masters in Industrial and Applied Mathematics.

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Teacher	Office	Email
Prof. dr. M. A. Peletier	HG 8.55	m.a.peletier@tue.nl
Prof. dr. J. J. M. Slot	HG 8.88	J.J.M.Slot@tue.nl

Center for Analysis, Scientific Computation, and Applications: CASA@tue.nl, HG 8.38, tel. 2753.

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Time & Place

Course: Tuesdays 15.45-17.30 in AUD09 (Semester 1) and AUD16 (DIFFERENT ROOM!) (Semester 2)
Instruction: Wednesdays 13.45-15.30 in Matrix 1.44.

Content

Partial differential equations are essential tools of the trade of the applied mathematician. They describe a wide range of phenomena in engineering, physics, chemistry, biology, finance, economics, sociology, and many other fields. In this course we provide an introduction to this broad class of equations.

The course consists of two parts. In the first part we provide a short introduction to the different types of PDEs, elliptic, parabolic, and hyperbolic, and discuss their properties such as existence and uniqueness of solutions, stability, boundary conditions, maximum principles, energy principles, and more.

In the second part we zoom in on the case of linear elliptic equations on bounded domains, and we construct the theory of weak solutions via the Lax-Milgram Lemma. This gives a very complete understanding of the existence, uniqueness, and stability of solutions of this class of equations. Other topics that we discuss are the trace theorem, different boundary conditions, and solvability criteria under constraints.

Homework

Every week after the course on Tuesday a set of exercises will be made available in the Downloads directory. You are expected to hand in the worked exercises the following Monday before noon in the pigeon hole of Prof. Slot.

Examination

There will be an oral exam at the end of the semester, which will be based on the homework that you provided.

Literature

For part 1 we will use Chapter 2 of Evans, Partial Differential Equations (AMS); for part 2 we use the course notes VarMethEllEqs.pdf by Georg Prokert.