Differential and Integral Calculus

7.1 INTRODUCTION	7.2.3 Solution of Euler's Differential Equation. Examples	7.3.4 Integrals Involving Higher Derivatives
7.1.1 Statement of the Problem	Exercises 7.2	7.3.5 Several Independent Variables
7.1.2 Necessary Conditions for Extreme Values	7.2.4 Identical Vanishing of Euler's Expression	Exercise 7.4
Exercises 7.1	7.3 GENERALIZATIONS	7.3.6. Problems Involving Subsidiary Conditions. Euler's Multiplier
7.2 EULER'S DIFFERENTIAL EQUATION IN THE SIMPLEST CASE	7.3.1 Integrals with More than one Argument Function	Exercise 7.5
7.2.1 Derivation of Euler's Differential Equation	7.3.2 Examples	Exercises 7.6
7.2.2 Proofs of the Lemmas	7.3.3 Hamilton's Principle. Lagrange's Equations	MISCELLANEOUS EXERCISES VII