Calculus of Variations

This 1927 book constitutes Scottish mathematician Andrew Russell Forsyth's attempt at a systematic exposition of the calculus of variations.

Andrew Russell Forsyth (Author)

9781107640832, Cambridge University Press

Paperback / softback, published 19 July 2012

680 pages
24.4 x 17 x 3.5 cm, 1.07 kg

Andrew Russell Forsyth (1858–1942) was an influential Scottish mathematician notable for incorporating the advances of Continental mathematics within the British tradition. Originally published in 1927, this book constitutes Forsyth's attempt at a systematic exposition of the calculus of variations. It was created as the antidote to a perceived lack of continuity in the development of the topic. Ambitious and highly detailed, this book will be of value to anyone with an interest in the calculus of variations and the history of mathematics in general.

Introduction
1. Integrals of the first order: maxima and minima for special weak variations: Euler test, Legendre test, Jacobi test
2. Integrals of the first order: general weak variations: the method of Weierstrass
3. Integrals involving derivatives of the second order: special weak variations, by the method of Jacobi
general weak variations, by the method of Weierstrass
4. Integrals involving two dependent variables and their first derivatives: special weak variations
5. Integrals involving two dependent variables and their first derivatives: general weak variations
6. Integrals with two dependent variables and derivatives of the second order: mainly special weak variations
7. Ordinary integrals under strong variations, and the Weierstrass test: solid of least resistance: action
8. Relative maxima and minima of single integrals: isoperimetrical problems
9. Double integrals with derivatives of the first order: weak variations: minimal surfaces
10. Strong variations and the Weierstrass test, for double integrals involving first derivatives: isoperimetrical problems
11. Double integrals, with derivatives of the second order: weak variations
12. Triple integrals with first derivatives
Index.

Subject Areas: Mathematics [PB]