Abstract:
hat often goes by the title "Elementary Partial Differential Equations"
or "Boundary Value Problems;' The audience usually consists of students in mathematics, engineering, and the physical sciences. The topics
include derivations of some of the standard equations of mathematical physics (including the heat equation, the· wave equation, and the
Laplace's equation) and methods for solving those equations on bounded
and unbounded domains. Methods include eigenfunction expansions
or separation of variables, and methods based on Fourier and Laplace
transforms. Prerequisites include calculus and a post-calculus differential
equations course.
There are several excellent texts for this course, so one can legitimately
ask why one would wish to write another. A survey of the content of the
existing titles shows that their scope is broad and the analysis detailed;
and they often exceed five hundred pages in length. These books generally have enough material for two, three, or even four semesters. Yet,
many undergraduate courses are one-semester courses. The author has
often felt that students become a little uncomfortable when an instructor
jumps around in a long volume searching for the right topics, or only partially covers some topics; but they are secure in completely mastering a
short, well-defined introduction. This text was written to proVide a brief,
one-semester introduction to partial differential equations. It is limited
in both scope and depth compared with existing books, yet it covers the
main topics usually studied in the standard course and also provides an
introduction to using computer algebra packages to solve and understand
partial differential equations. The frontiers of mathematics and science
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