數(shù)學(xué)物理方法 第3版

內(nèi)容概要

In the present edition we have made changes in Chapter 1, mainly as a result of comments by Professor A. S. Besicovitch. Some theorems are stated more explicitly, a few proofs are added, and some are shortened. We are indebted to him for an elementary proof of the theorem of bounded convergence for Riemann integrals, which appears in the notes. In Chapter 6 the proof of Poisson's equation has been improved. In Chapter 17 we have discussed the Airy integral for complex argument in more detail, and have given conditions for uniformity of approximation for asymptotic solutions of Green's type for complex argument. In Chapter 23 we have added some remarks on the analytic continuation of the solutions, and a note applies them to the parabolic cylinder functions. We should like to express our thanks to several readers for drawing our attention to errors and misprints.

書籍目錄

Preface Chapter 1.The Real Variable   2.Scalars and Vectors   3.Tensors   4.Matrices   5.Multiple Integrals   6.Potential Theory   7.Operational Methods   8.Physical Applications of the Operational Method   9.Numerical Methods   10.Caloulns of Variations   11.Functions of a Complex Variable   12.Contour Integration and Bromwich‘s Integral   13.Conformal Representation   14.Fourier‘s Theorem   15.The Factorial and Related Functions   16.Solution of Linear Differential Equations of the Second Order   17.Asymptotic Expansions   18.The Equations of Potential， Waves， and Heat Conduction   19.Waves in One Dimension and Waves with Spherical Symmetry   20.Conduction of Heat in One and Three Dimensions  21.Bessel Functions  22.Applications of Bessel Functions  23.The Conflutent Hypergeomtrio Function  24.Legendre Functions and Associated Functions  25.Elliptic FunctionsNotesAppendix on NotatinIndex

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