数学物理方法 第3版
2002-7
Cambridge
Jeffeys & Jeffeys,Cambridge Mathematical Library
718
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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.
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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