# Book:A.R. Forsyth/Calculus of Variations

## A.R. Forsyth: Calculus of Variations

Published $1927$, Cambridge University Press

ISBN 978-1107640832.

### Contents

Introduction

Chapter I. Integrals of the First Order; Maxima and Minima for Special Weak Variations; Euler Test, Legendre Test, Jacobi Test.

Chapter II. Integrals of the First Order; General Weak Variations; the Method of Weierstrass

Chapter III. Integrals involving Derivatives of the Second Order; Special Weak Variations, by the Method of Jacobi; General Weak Variations, by the Method of Weierstrass

Chapter IV. Integrals involving two dependent Variables and their First Derivatives; Special Weak Variations.

Chapter V. Integrals involving two dependent Variables and their First Derivatives; General Weak Variations.

Chapter VI. Integrals with two dependent Variables and Derivatives of The Second Order; Mainly Special Weak Variations.

Chapter VII. Ordinary Integrals under Strong Variations, and the Weierstrass Test; Solid of Least Resistance; Action

Chapter VIII. Relative Maxima and Minima of Single Integrals; Isoperimetrical Problems

Chapter IX. Double Integrals with Derivatives of the First Order; Weak Variations; Minima Surfaces

Chapter X. Strong Variations and the Weierstrass Test, for Double Integrals involving First Derivatives; Isoperimetrical Problems

Chapter XI. Double Integrals, with Derivatives of the Second Order; Weak Variations

Chapter XII. Triple Integrals with First Derivatives

Index