vi Contents 12 Green's Functions and Conformal Mappings 611 12.1 Green's Theorem and Identities 612 12.2 Harmonic Functions and Green's Identities 622 12.3 Green's Functions 629 12.4 Green's Functions for the Disk and the Upper Half-Plane 638 12.5 Analytic Functions 645 12.6 Solving Dirichlet Problems with Conformal Mappings 663 12.7 Green's Functions and Conformal Mappings 674 12.8 Neumann Functions and the Solution of Neumann Problems 684 APPENDIXES A Ordinary Differential Equations: Review of Concepts and Methods A1 A.1 Linear Ordinary Differential Equations A2 A.2 Linear Ordinary Differential Equations with Constant Coefficients A10 A.3 Linear Ordinary Differential Equations with Nonconstant Coefficients A21 A.4 The Power Series Method,Part I A28 A.5 The Power Series Method,Part II A40 A.6 The Method of Frobenius A51 B Tables of Transforms A65 B.1 Fourier Transforms A66 B.2 Fourier Cosine Transforms A68 B.3 Fourier Sine Transforms A69 B.4 Laplace Transforms A70 Era References A73 Answers to Selected Exercises A75 Index o nom....m A99 po年生