Worked Problems in Applied Mathematics - Brossura

Lebedev, Nikola-I Nikolaevich And

Brossura

ISBN 10: 0486637301 ISBN 13: 9780486637303

Casa editrice: Dover Pubns, 2010

Riassunto

This book is an unparalleled collection of worked problem material in applied mathematics consisting of 566 problems and answers impossible to find in any other single source. Covering a wide range of topics in a particularly accessible manner, the problems apply many different mathematical methods to questions drawn from  mechanics, the theory of heat conduction, and the theory of electric and magnetic phenomena.
The first five chapters are suitable for anyone with a minimal background in applied mathematics. Topics covered are the derivation of equations and formulation of problems, some special methods for solving hyperbolic and elliptic equations, steady state harmonic oscillations, the Fourier method, and the eigenfunction method for solving inhomogeneous problems. The remaining three chapters are suitable for students with a more advanced background. These more complicated problems deal with integral transforms, curvilinear coordinates, and integral equations. Certain problems indicated throughout the text are solved in detail in a solutions section at the end of the text chapters. Included are a mathematical appendix and a supplement by Prof. E. L. Reiss titled "Variational and Related Methods," containing 51 additional problems, most with solutions. A particularly complete and valuable bibliography is also included.
This volume is another in the popular series of fine translations from the Russian by Richard A. Silverman, formerly of the Courant Institute of Mathematical Sciences of New York University. Students of applied mathematics and scientists whose researches require its use will find this book invaluable. Teachers will find it an exceptional sourcebook of problems.
"I judge this to be a useful . . . book, and one well worth reprinting. It collects a considerable amount of material that would otherwise be available only from rather scattered sources." — Jack Schwartz, Courant Institute of Mathematical Sciences, N.Y.U.

Su questo libro

Contenuti

Part 1 PROBLEMS 1 DERIVATION OF EQUATIONS AND FORMULATION OF PROBLEMS 1. Mechanics 2. Heat Conduction 3. Electricity and Magnetism 2 SOME SPECIAL METHODS FOR SOLVING HYPERBOLIC AND ELLIPTIC EQUATIONS 1. Hyperbolic Functions 2. Elliptic Equations: The Green's Function Method 3. Elliptic Equations: The Method of Conformal Mapping 3 STEADY-STATE HARMONIC OSCILLATIONS 1. Elastic Bodies: Free Oscillations 2. Elastic Bodies: Forced Oscillations 3. Electromagnetic Oscillations 4 THE FOURIER METHOD 1. "Mechanics: Vibrating Systems, Acoustics" 2. "Mechanics: Statics of Deformable Media, Fluid Dynamics" 3. Heat Conduction: Nonstationary Problems 4. Heat Conduction: Stationary Problems 5. Electricity and Magnetism 5 THE EIGENFUNCTION METHOD FOR SOLVING INHOMOGENEOUS PROBLEMS 1. Mechanics: Vibrating Systems 2. Mechanics: Statics of Deformable Media 3. Heat Conduction: Nonstationary Problems 4. Heat Conduction: Stationary Problems 5. Electricity and Magnetism 6. INTEGRAL TRANSFORMS 1. The Fourier Transform 2. The Hankel Transform 3. The Laplace Transform 4. The Mellin Transform 5. Integral Transforms Involving Cylinder Functions of Imaginary Order 7. CURVILINEAR COORDINATES 1. Elliptic Coordinates 2. Parabolic Coordinates 3. Two-Dimensional Bipolar Coordinates 4. Spheroidal Coordinates 5. Paraboloidal Coordinates 6. Toroidal Coordinates 7. Three-Dimensional Bipolar Coordinates 8. Some General Problems on Separation of Variables 8. INTEGRAL EQUATIONS 1. Diffraction Theory 2. Electrostatics PART 2 SOLUTIONS MATHEMATICAL APPENDIX 1. Special Functions Appearing in the Text 2. Expansions in Series of Orthogonal Functions 3. Some Definite Integrals Frequently Encountered in the Applications 4. Expansion of Some Differential Operators in Orthogonal Curvilinear Coordinates Supplement. VARIATIONAL AND RELATED METHODS 1. Variational Methods 1.1 Formulation of Variational Problems 1.2 The Ritz Method 1.3 Kantorovich's Method 2. Related Methods 2.1 Galerkin's Method 2.2 Collocation 2.3 Least Squares 3. References BIBLIOGRAPHY NAME INDEX SUBJECT INDEX

Product Description

Book by Nikolai Nikolaevich Lebedev

Dettagli dell'edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 0486637301
• ISBN 13: 9780486637303
• Rilegatura: Copertina flessibile
• Numero di pagine: 448
• Contatto del produttore: non disponibile
• Persona responsabile: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italia