Description
Dover Worked Problems in Applied Mathematics 2010 Edition by N.N. Lebedev, Etc., Richard Silverman
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. Table of contents :- Part 1 PROBLEMS1 DERIVATION OF EQUATIONS AND FORMULATION OF PROBLEMS1. Mechanics2. Heat Conduction3. Electricity and Magnetism2 SOME SPECIAL METHODS FOR SOLVING HYPERBOLIC AND ELLIPTIC EQUATIONS1. Hyperbolic Functions2. Elliptic Equations: The Green's Function Method3. Elliptic Equations: The Method of Conformal Mapping3 STEADY-STATE HARMONIC OSCILLATIONS1. Elastic Bodies: Free Oscillations2. Elastic Bodies: Forced Oscillations3. Electromagnetic Oscillations4 THE FOURIER METHOD1. "Mechanics: Vibrating Systems, Acoustics"2. "Mechanics: Statics of Deformable Media, Fluid Dynamics"3. Heat Conduction: Nonstationary Problems4. Heat Conduction: Stationary Problems5. Electricity and Magnetism5 THE EIGENFUNCTION METHOD FOR SOLVING INHOMOGENEOUS PROBLEMS1. Mechanics: Vibrating Systems 2. Mechanics: Statics of Deformable Media 3. Heat Conduction: Nonstationary Problems4. Heat Conduction: Stationary Problems5. Electricity and Magnetism6. INTEGRAL TRANSFORMS1. The Fourier Transform2. The Hankel Transform3. The Laplace Transform4. The Mellin Transform5. Integral Transforms Involving Cylinder Functions of Imaginary Order7. CURVILINEAR COORDINATES1. Elliptic Coordinates2. Parabolic Coordinates3. Two-Dimensional Bipolar Coordinates4. Spheroidal Coordinates5. Paraboloidal Coordinates6. Toroidal Coordinates7. Three-Dimensional Bipolar Coordinates8. Some General Problems on Separation of Variables8. INTEGRAL EQUATIONS1. Diffraction Theory2. ElectrostaticsPART 2 SOLUTIONSMATHEMATICAL APPENDIX1. Special Functions Appearing in the Text2. Expansions in Series of Orthogonal Functions3. Some Definite Integrals Frequently Encountered in the Applications4. Expansion of Some Differential Operators in Orthogonal Curvilinear Coordinates Supplement. VARIATIONAL AND RELATED METHODS1. Variational Methods1.1 Formulation of Variational Problems1.2 The Ritz Method1.3 Kantorovich's Method2. Related Methods2.1 Galerkin's Method2.2 Collocation2.3 Least Squares3. ReferencesBIBLIOGRAPHYNAME INDEXSUBJECT INDEX