Math 553 Partial Differential Equations
Mon/Wed/Fri 10-11am, 241 Altgeld Hall
Course outline
The course begins with the method of characteristics for first-order
equations and then proceeds to examine the famous
second-order partial differential equations of mathematical physics, namely
the heat (or diffusion), wave and Laplace equations. The focus is initially
on finding formulas for solutions, but then moves to the qualitative theory:
how do solutions change as the initial and/or boundary data changes, what is
the speed of propagation of the solutions, how does the energy behave as time
passes, and so on. Also, how do these features differ between the three
classical equations?
Prerequisites
The course is aimed at mathematics and engineering students
who want to deepen their understanding of partial differential equations.
Many engineering graduate students have successfully taken this course.
All students need to be competent with multidimensional calculus and
undergraduate real analysis. Graduate students can take this course
without having previously studied partial differential equations, but
undergraduates who have not studied partial differential equations
should take Math 442 instead.
Assessment
This is the comprehensive exam course in the Mathematics Department for
partial differential equations, and so we will have regular homework,
a midterm and a final exam.
Textbook
Robert McOwen, Partial Differential Equations: Methods and Applications,
second edition, Prentice-Hall. We cover Chapters 1-5.