物理科学基础数学 第1卷：齐次边值问题傅里叶方法和特殊函数（英文）

　　本书着重讨论了齐次边值问题（BVPs），齐次意味着系统缺乏强制函数或源函数。本书中不仅仅有关于之前已经提到的相关主题的介绍，还有数学方法课程在物理课程中所起的作用以及相应的时间限制。本书的重点是解偏微分方程的方法及引入的特殊方程，解偏微分方程必须根据边界条件来进行，在系统的边界上需要满足一系列空间或时间上的附加约束。

　　布雷特·鲍敦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.

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)
编辑手记