Introduction to the Theory of Partial Differential Equations

This one-year course is written on classical lines with a slant towards
modern methods. It will meet the requirements of senior honours under-
graduates and postgraduates who require a systematic introductory text
outlining the theory of partial differential equations. The amount of theory
presented will meet the needs of most theoretical scientists, and pure mathe-
maticians will find here a sound basis for the study of recent advances in the
subject.
Clear exposition of the elementary theory is a key feature of the book,
and the treatment is rigorous. The author begins by outlining some of the
more common equations of mathematical physics. He then discusses the
principles involved in the solution of various types of partial differential
equation. A close study of the existence and uniqueness theorem is reinforced
by proof. Second-order equations, because of their significance, are considered
in detail. Dr. Smith's approach to the analysis is traditional, but by intro-
ducing the concept of generalized functions and demonstrating their relevance,
he helps the reader to gain a better understanding of Hadamard's theory and
to pass painlessly on to the more difficult works by Courant and Hormander.
The text is reinforced by many worked examples, and problems for
solution have been included where appropriate.