By Robert K. Nesbet
Publisher: Cambridge University Press
Print Publication Year: 2002
Online Publication Date:December 2009
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511535161.002
This part is concerned with variational theory prior to modern quantum mechanics. The exception, saved for Chapter 10, is electromagnetic theory as formulated by Maxwell, which was relativistic before Einstein, and remains as fundamental as it was a century ago, the first example of a Lorentz and gauge covariant field theory. Chapter 1 is a brief survey of the history of variational principles, from Greek philosophers and a religious faith in God as the perfect engineer to a set of mathematical principles that could solve practical problems of optimization and rationalize the laws of dynamics. Chapter 2 traces these ideas in classical mechanics, while Chapter 3 discusses selected topics in applied mathematics concerned with optimization and stationary principles.