布雷特·鮑敦received his undergraduate degree from the University of Wisconsin in Madison and the PhD from the University of Texas at Austin （both in Physics）. He joined the Research Department at The Naval Weapons Center in China Lake， CA in 1980. In 2002 he joined the Faculty of The Naval Postgraduate School in Monterey， CA， where he is Professor of Physics （Emeritus）. Dr Borden is a Fellow of The Institute of Physics.
圖書(shū)目錄
Preface Author biography 1 Partial differential equations Exercise 2 Separation of variables 2.1 Helmholtz equation 2.2 Helmholtz equation in rectangular coordinates 2.3 Helmholtz equation in cylindrical coordinates 2.4 Helmholtz equation in spheri.cal coordinates 2.5 Roadmap: where we are headed Summary Exercises Reference 3 Power-series solutions of ODEs 3.1 Analytic functions and the Frobenius method 3.2 Ordinary points 3.3 Regular singular points 3.4 Wronskian method for obtaining a second solution 3.5 Bessel and Neumann functions 3.6 Legendre polynomials Summary Exercises References 4 Sturm-Liouville theory 4.1 Differential equations as operators 4.2 Sturm-Liouville systems 4.3 The SL eigenvalue problem, L[y]=λwy 4.4 Dirac delta function 4.5 Completeness 4.6 Hilbert space: a brief introduction Summary Exercises References 5 Fourier series and integrals 5.1 Fourier series 5.2 Complex fonll of Fourier series 5.3 General intervals 5.4 Parseval's theorem 5.5 Back to the delta function 5.6 Fourier transform 5.7 Convolution integral Summary Exercises References 6 Spherical harmonics and friends 6.1 Properties of the Legendre polynomials, Pl(x) 6.2 Associated Legendre functions, Pml(x) 6.3 Spherical harmonic functions, Yml(θ, ψ) 6.4 Addition theorem for Yml(θ, ψ) 6.5 Laplace equation in spherical coordinates Summary Exercises References 7 Bessel functions and friends 7.1 Small-argument and asymptotic forms 7.2 Properties of the Bessel functions, J,(x) 7.3 Orthogonality 7.4 Bessel series 7.5 Fourier-Bessel transform 7.6 Spherical Bessel functions 7.7 Expansion of plane waves in spherical coordinates Summary Exercises Reference Appendices A Topics in linear algebra B Vector calculus C Power series D Gamma function, F(x) 編輯手記
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