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# MATH 3FF3, Winter 2019

PARTIAL DIFFERENTIAL EQUATIONS

This course introduces the student to the study of Partial Differentiation Equations primarily through an in depth examination of the simplest and most important PDE's that arise in the sciences: the wave equation, the heat equation, and Laplace's equation. Each of these classical equations is considered for the most part in the plane, where the differences in the underlying structure of solutions are most clearly exposed. The interplay between the mathematical solutions to these equations and their physical interpretations plays a crucial role in the development of the `well-posedness' of the theory. The {\em principle of causality} in the wave equation, the {\em maximum principle} and {\em principle of decreasing energy} in the heat equation, and the {\em mean value theorem} in Laplace's equation are just a few important examples of this symbiotic relationship that contributes to making the solving of PDE's a most exciting and rewarding application of mathematics to the sciences. Linear algebra and calculus both play a critical role in solving PDE's and are especially prevalent in the early stages of the course when more general PDE's are briefly considered.

INSTRUCTOR:  D. Pelinovsky

Course Website

Calendar Description
3 unit(s) First order equations, well-posedness, characteristics, wave equation, heat equation, Laplace equation, boundary conditions, Fourier series, applications.
Three lectures; one term
Prerequisite(s): MATH 2C03; and 2R03; and 2XX3 (or 2A03 or ISCI 2A18 A/B)

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Department of Mathematics & Statistics
McMaster University

Hamilton Hall, Room 218
1280 Main Street West