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Lectures on partial differential equations

Author: Vladimir Igorevitch Arnol'd; Roger Cooke
Publisher: Berlin ; Heidelberg ; New York : Springer, cop. 2004.
Series: Universitext (1979)
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's equation and the wave equation, although the heat equation and the Korteweg-de Vries  Read more...
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Document Type: Book
All Authors / Contributors: Vladimir Igorevitch Arnol'd; Roger Cooke
ISBN: 3540404481 9783540404484
OCLC Number: 492526841
Description: 1 v. (X-157 p.) : ill. ; 23 cm.
Contents: 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.
Series Title: Universitext (1979)
Responsibility: Vladimir I. Arnold ; translated by Roger Cooke.
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Abstract:

An illustrated text that covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. This title includes a large number of problems, and a full set of problems  Read more...

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From the reviews of the German edition: "This book provides an introductory text (in German) to basic partial differential equations, based on the author's lectures at Moscow University. [...] Most Read more...

 
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