Introduction to the Calculus of Variations (Chapman and Hall Mathematics Series)

This text provides a clear concise introduction to the calculus of variations. The introduction chapter provides a general sense of the subject through a discussion of several classical and contemporary examples of the subject's use. In the second chapter the all-important Euler differential is dereived and the Lemma of Du Bois-Reymond is established. Other basic terminology is introduced and the underlying theory, which will later be extended smoothly to more complex problems, is developed. Chapters 3 through 6 are devoted to the crucial topics of necessary and sufficient conditions. The remainder of the text extends the concepts of the first half of hte book to problems involving variable boundaries, to parametic representations to the problems constrained by side conditions.