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

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9780486446523: A Course in Mathematical Analysis: Variation of Solutions Partial Differential Equations of the Second Order: 3

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.

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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

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Goursat, Edouard
Editore: Dover Publications (2006)
ISBN 10: 0486446522 ISBN 13: 9780486446523
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Descrizione libro Dover Publications, 2006. Hardcover. Condizione libro: New. Codice libro della libreria DADAX0486446522

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Goursat, Edouard
Editore: Dover Pubns (2006)
ISBN 10: 0486446522 ISBN 13: 9780486446523
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Descrizione libro Dover Pubns, 2006. Hardcover. Condizione libro: Brand New. 389 pages. 8.50x5.75x1.50 inches. In Stock. Codice libro della libreria 0486446522

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