Lectures on the Calculus of Variations Book

Illustrated To Include 48 Figures - Chapters Include: Agreements Concerning Notation And Terminology - Vanishing Of The First Variation - The Fundamental Lemma And Euler's Differential Equation - Weirstrass's Lemma And The E-Function - Discontinuous Solutions - Boundary Conditions - Legendre's Condition - Jacobi's Theorem - Jacobi's Criterion - Geometrical Interpretation Of The Conjugate Points - Necessity Of Jacobi's Condition - Sufficient Conditions For An Extremum Of The Integral - Weirstrass's Theory Of The Problem In Parameter Representation - Formulation Of The Problem - Kneser's Theory: Gauss's Theorems On Geodesics - Construction Of A Field - Kneser's Curvilinear Coordinates -Sufficient Conditions For A Minimum In The Case Of One Moveable Endpoint - The Focal Point - Weierstrass's Theory Of The Isoperimetric Problems - Euler's Rule - The Second Necessary Condition - The Third Necessary Condition And The Conjugate Point - Hilbert's Existence Theorem - Hilbert's Construction - Properties Of Hilbert's Curve, Etc., Etc. - Addenda - Index