Overview The subject of partial differential equations has an unchanging core of material but
is constantly expanding and evolving. The core consists of solution methods mainly separation
of variables for boundary value problems with constant coeffi cients in geometrically simple
domains. Too often an introductory course focuses exclusively on these core problems and
techniques and leaves the student with the impression that there is no more to the subject.
Questions of existence uniqueness and well-posedness are ignored. In particular there is a
lack of connection between the analytical side of the subject and the numerical side.
Furthermore nonlinear problems are omitted because they are too hard to deal with analytically.
Now however the availability of convenient powerful computational software has made it
possible to enlarge the scope of the introductory course. My goal in this text is to give the
student a broader picture of the subject. In addition to the basic core subjects I have
included material on nonlinear problems and brief discussions of numerical methods. I feel that
it is important for the student to see nonlinear problems and numerical methods at the
beginning of the course and not at the end when we run usually run out of time. Furthermore
numerical methods should be introduced for each equation as it is studied not lumped together
in a final chapter.
