Introduction to the Variational Calculus is an introduction to the
various mathematical methods needed for determining maximum and/or
minimum values associated with functions and functionals. The
material presented is suitable for a one semester course in the
subject area called calculus of variations. It is written for
mathematicians, engineers, physicists, chemistry and science majors
and is suitable for upper level college undergraduates or beginning
graduate students. It can be used as a reference book for various
calculus of variation topics.
Chapter one reviews necessary background material from the subject
area of calculus and advanced calculus. Chapter two reviews maximum
and minimum values associated with functions and functions subject
to constraint conditions. Chapter three introduces techniques for
finding extreme values associated with functionals. The
Euler-Lagrange equations are developed for a variety of
functionals.The fourth chapter develops some of the more detailed
concepts associated with the subject area of calculus of
variations. The fifth and sixth chapters consider various applied
engineering applications of the calculus of variations. Selected
applied topics are developed together with necessary solution
methods.
There are three Appendices. The Appendix A contains units of
measurements from the Systeme International Unites along with some
selected physical constants. The Appendix B contains gives the
representation of the gradient, divergence and curl in Cartesian,
cylindrical and spherical coordinates. The Appendix C contains
solutions to selected exercises. The book is 356 pages with
numerous exercises and applications presented at the end of
eachchapter.
For additional information and downloads please visit the web site
www.math.odu.edu/ jhh/counter7.html
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