布雷特·鲍敦received his undergraduate degree from the University of WisconsiiMadisoand the PhD from the University of Texas at Austi(both iPhysics). He joined the Research Department at The Naval Weapons Center iChina Lake, CA i1980. I2002 he joined the Faculty of The Naval Postgraduate School iMonterey, CA, where he is Professor of Physics (Emeritus). Dr Bordeis a Fellow of The Institute of Physics.
目录 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
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