Overview

Classic three-volume study. Volume 1 covers applications to geometry, expansion in series, definite integrals, and derivatives and differentials. Volume 2 explores functions of a complex variable and differential equations. Volume 3 surveys variations of solutions and partial differential equations of the second order and integral equations and calculus of variations.

Full Product Details

Author:   Edouard Goursat ,  Howard G. Bergmann
Publisher:   Dover Publications Inc.
Imprint:   Dover Publications Inc.
Dimensions:   Width: 15.00cm , Height: 4.20cm , Length: 22.50cm
Weight:   0.934kg
ISBN:  

9780486446523

ISBN 10:   0486446522
Pages:   389
Publication Date:   04 April 2013
Audience:   General/trade ,  General
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of stock  

Table of Contents

Part One: I. Variation of Solutions 1. Equations of Variation 2. Periodic and Asymptotic Solutions Stability II. Equations of Monge-Ampere 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

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