Lectures on partial differential equations

Vladimir I. Arnold ; translated by Roger Cooke

Choice Outstanding Title! (January 2006) This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.

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[目次]

  • 1. The General Theory for One First-Order Equation.- 2. The General Theory for One First-Order Equation (Continued).- 3. Huygens' Principle in the Theory of Wave Propagation.- 4. The Vibrating String (d'Alembert's Method).- 5. The Fourier Method (for the Vibrating String).- 6. The Theory of Oscillations. The Variational Principle.- 7. The Theory of Oscillations. The Variational Principle (Continued).- 8. Properties of Harmonic Functions.- 9. The Fundamental Solution for the Laplacian. Potentials.- 10. The Double-Layer Potential.- 11. Spherical Functions. Maxwell's Theorem. The Removable Singularities Theorem.- 12. Boundary-Value Problems for Laplace's Equation. Theory of Linear Equations and Systems.- A. The Topological Content of Maxwell's Theorem on the Multifield Representation of Spherical Functions.- A.1. The Basic Spaces and Groups.- A.2. Some Theorems of Real Algebraic Geometry.- A.3. From Algebraic Geometry to Spherical Functions.- A.4. Explicit Formulas.- A.6. The History of Maxwell's Theorem.- Literature.- B. Problems.- B.1. Material from the Seminars.- B.2. Written Examination Problems.

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この本の情報

書名 Lectures on partial differential equations
著作者等 Arnolʹd, Vladimir Igorevich
Cooke, Roger
Arnold Vladimir I.
書名別名 Lektsii ob uravneniyakh s chastnymi proizvodnymi
シリーズ名 Universitext
出版元 Springer
刊行年月 c2004
ページ数 x, 157 p.
大きさ 24 cm
ISBN 9783540404484
NCID BA64709317
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言語 英語
原文言語 ロシア語
出版国 ドイツ
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