Syllabus for Mathematics 640:423:
Elementary Partial Differential Equations
This is an introductory course to the topic of linear "PDEs".
After a brief look at first order "transport equations",
we shall do a fair amount of "explicit solution" of the
three generic types of second order (two dimensional) PDEs: (1) the wave
equation, (2) the heat equation, and (3) the Laplace equation.
An important aspect is understanding the different (qualitative) behaviour
of the solutions.
We shall cover
the following parts of the book ``Partial Differential Equations''
2nd Ed., by W. Strauss:
Chapter 1: Where PDEs Come From.
Chapter 2: Waves and Diffusions.
Chapter 3: Reflections and Sources.
Chapter 4: Boundary Problems.
Chapter 5: Fourier Series.
Parts of Chapter 6: Harmonic Functions (time permitting).