●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 spherical 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,φ)
6.4 Addition theorem for Yml(θ,φ)
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,Jn(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,Γ(x)
編輯手記

本書著重討論了齊次邊值問題（BVPs），齊次意味著繫統缺乏強制函數或源函數。本書中不僅僅有關於之前已經提到的相關主題的介紹，還有數學方法課程在物理課程中所起的作用以及相應的時間。本書的重點是解偏微分方程的方法及引入的特殊方程，解偏微分方程必須根據邊界條件來進行，在繫統的邊界上需要滿足一繫列空間或時間上的附加約束。