This is a textbook written for use in a graduate-level course for
students of mechanics and engineering science. It is designed to cover
the essential features of modern variational methods and to demonstrate
how a number of basic mathematical concepts can be used to produce a
unified theory of variational mechanics. As prerequisite to using this
text, we assume that the student is equipped with an introductory course
in functional analysis at a level roughly equal to that covered, for
example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock,
Rochester, 1957) and possibly a graduate-level course in continuum
mechanics. Numerous references to supplementary material are listed
throughout the book. We are indebted to Professor Jim Douglas of the
University of Chicago, who read an earlier version of the manuscript and
whose detailed suggestions were extremely helpful in preparing the final
draft. We also gratefully acknowedge that much of our own research work
on va ri at i ona 1 theory was supported by the U. S. Ai r Force Offi ce
of Scientific Research. We are indebted to Mr. Ming-Goei Sheu for help
in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude
for her excellent and painstaking job of typing the manuscript. This
revised edition contains only minor revisions of the first. Some
misprints and errors have been corrected, and some sections were
deleted, which were felt to be out of date.