Nonstandard Methods in the Calculus of Variations: 297 (Chapman & Hall/CRC Research Notes in Mathematics Series) - Softcover

This monograph is unique in its treatment of the application of methods of nonstandard analysis to the theory of curves in the calculus of variations. It will be of particular value to researchers in the calculus of variations and optimal control theory.

This text examines curves and integrals in the calculus of variations, combining elements from the tales of three famous mathematicians - Leonhard Euler, L.C. Young, and Abraham Robinson. The author has used Robinson's analysis to point out the connection between the approaches of Euler and Young, and to lay the foundations for a rigorous and coherent theory of curves having both the intuitive appeal of Euler's method and the rigorous generality of Young's theory. The bulk of this work is concerned with the relation between gneralized curves and their S-absolutly continuous representations, and with taking the necessary steps toward building an adequate foundation for variational problems. Some contributions to the general developmetn of nonstandard analysis are gathered along the way.