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Preface
“It is impossible to exaggerate the extent to which modern
applied mathematics has been shaped and fueled by the gen-
eral availability of puters with large memories. Their
impact on mathematics, both applied and pure, parable
to the role of the telescopes in astronomy and microscopes in
biology.”
— Peter Lax, Siam Rev. Vol. 31 No. 4
Congratulations! You have chosen to study partial differential equations.
That decision is a wise one; the laws of nature are written in the language
of partial differential equations. Therefore, these equations arise as models
in virtually all branches of science and technology. Our goal in this book
is to help you to understand what this vast subject is about. The book is
an introduction to the field. We assume only that you are familiar with ba-
sic calculus and elementary linear algebra. Some experience with ordinary
differential equations would also be an advantage.
Introductory courses in partial differential equations are given all over
the world in various forms. The traditional approach to the subject is to
introduce a number of analytical techniques, enabling the student to de-
rive exact solutions of some simplified problems. Students who learn about
viii Preface
computational techniques on other courses subsequently realize the scope
of partial differential equations beyond paper and pencil.
Our approach is different. We introduce analytical putational
techniques in the same book and thus in the same course. The main reason
for doing this is that puter, developed to assist scientists in solv-
ing partial differential equations, has monly available and is
currently used in all practical applications of partial differential equations.
Therefore, a modern introduction to this topic must focus on methods suit-
able puters. But these methods often rely on deep analytical insight
into the equations. We must therefore take great care not to throw away
basic