A Course in Mathematical Analysis: Variation of Solutions Partial Differential Equations of the Second Order: Volume 3 - Rilegato

Goursat, Edouard

Rilegato

ISBN 10: 0486446522 ISBN 13: 9780486446523

Casa editrice: Dover Pubns, 2013

Riassunto

Edouard Goursat's three-volume A Course in Mathematical Analysis remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition. The first volume in this series addresses derivatives and differentials, definite integrals, expansion in series, and applications to geometry; the succeeding volume explores functions of a complex variable and differential equations. This, the third and final volume, examines variation of solutions and partial differential equations of the second order in its first part. The second part investigates integral equations and calculus of variations.
Topics related to variations of solutions and partial differential equations of the second order include equations of Monge-Ampère; linear equations inn variables; linear equations of the hyperbolic and elliptic types; and harmonic functions in three variables. Subjects relevant to integral equations and calculus of variations include the solution of integral equations by successive approximations; Fredholm's equation; the fundamental functions; applications of integral equations; and the calculus of variations. The text concludes with a note on conformal representation by Paul Montel.

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Contenuti

Part One: I. Variation of Solutions 1. Equations of Variation 2. Periodic and Asymptotic Solutions Stability II. Equations of Monge-Ampère 1. Characteristics. Intermediate Integrals 2. Laplace's Method. Classification of Linear Equations III. Linear Equations in n Variables 1. Classification of Equations in n Variables 2. Applications to a Few Examples IV. Linear Equations of the Hyperbolic Rype 1. Study of Some Problems Relating to the Equation s=f(x,y) 2. Successive Approximations. Riemann's Method 3. Equations in More than Two Variables V. Linear Equations of Elliptic Type 1. Harmonic Functions. Poisson's Integral 2. Dirichlet's Problem. Green's Function 3. General Equation of the Elliptic Type VI. Harmonic Functions in Three Variables 1. Dirichlet's Problem in Space 2. Newtonian Potential VII. The Heat Equation Part Two: VIII. Solution of Integral Equations by Successive Approximations 1. Linera Integral Equations with Variables Limits 2. Linear Integral Equations with Fixed Limits IX. Fredholm's Equation 1. Fredholm's Theorems 2. Study of the Resolving Kernel X. The Fundamental Functions XI. Applications of Integral Equations 1. Applications to Differential Equations 2. Applications to Partial Differential Equations XII. The Calculus of Variations 1. First Variation. Extremals 2. Second Variation. Necessary Conditions for the Extremum 3. Extremal Fields. Sufficient Conditions 4. Weiersstrass's Theory. Discontinuous Solutions Note on Conformal Representation by Paul Montel

Product Description

Book by Edouard Goursat

Dettagli dell?edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 0486446522
• ISBN 13: 9780486446523
• Rilegatura: Copertina rigida
• Numero di pagine: 389
• Contatto del produttore: non disponibile