Preface xiii
Types (1) and (2) are self-explanatory. As for type (3), there are some topics
that we choose to present as exercises. In some cases, these will be problems
that are similar enough to those already solved in the text. In others, they
may involve material which we feel is important, but which is not necessary
in later parts of the text. As some of these may be quite difficult, we make
sure to lead the student through them when necessary. Alternatively, the
instructor may choose to present the material herself in class.
Lastly, as PDEs is such a visual subject, we’ve provided a number of graph-
ical exercises. Some of these can be done by hand, but the majority are to be
performed using MATLAB©R (and these are labeledMATLAB).
MATLAB
This text has been written so that it can be used without access to software.
That said, it makes little sense to write a book on such a visual and intu-
itive subject as PDEs without taking advantage of one of the multitude of
mathematical software packages available these days. We have chosen MAT-
LAB because it is, by far, the most user-friendly of the packages we’ve tried,
because of its excellent graphics capabilities, and because it seems to be the
software-of-choice among the engineering community (while making strong
inroads in math and physics, as well). While we have used the latest version
of MATLAB, 8.0, most, if not all, of the code will run in many of the earlier
versions.
This text does not pretend to be an introduction to MATLAB.Therearea
number of good books available for that purpose (for example, that by Davis
listed in the Bibliography).For those wishing to use the MATLAB exercises,
we assume that the student is familiar with the rudiments of the package—how
to get it up-and-running, how M-files work, etc.Whatwehavedoneistouse
MATLAB to generate the tables and the more “mathematical” figures in the
book, for which we’ve supplied the MATLAB code in Appendix E, and also
on the author’s website at
http://www.faculty.fairfield.edu/mcolemanThe exercises labeledMATLAB, then, are to be done using this code, with
slight variations provided by the student (for example, changing the input
function, the viewing window, the number of steps in afor loopand the like).
Little actual programming is required of the student.