Preface
1 Mathematical Preliminaries
　1.1 InfiniteSeries
　1.2 Series ofFunctions
　1.3 Binomial Theorem
　1.4 Mathematical Induction
　1.5 Operations on Series Expansions of Functions
　1.6 Some Important Series
　1.7 Vectors
　1.8 Complex Numbers and Functions
　1.9 Derivatives andExtrema
　1.10 Evaluation oflntegrals
　1.1 I Dirac Delta Function
　AdditionaIReadings
2 Determinants and Matrices
　2.1 Determinants
　2.2 Matrices
　AdditionaI Readings
3 Vector Analysis
　3.1 Review ofBasic Properties
　3.2 Vectors in 3-D Space
　3.3 Coordinate Transformations
　3.4 Rotations in IR3
　3.5 Differential Vector Operators
　3.6 Differential Vector Operators: Further Properties
　3.7 Vectorlntegration
　3.8 Integral Theorems
　3.9 PotentiaITheory
　3.10 Curvilinear Coordinates
　AdditionaIReadings
4 Tensors and Differential Forms
　4.1 TensorAnalysis
　4.2 Pseudotensors, Dual Tensors
　4.3 Tensors in General Coordinates
　4.4 Jacobians
　4.5 DifferentialForms
　4.6 DifferentiatingForms
　4.7 IntegratingForms
　AdditionalReadings
5 Vector Spaces
　5.1 Vectors in Function Spaces
　5.2 Gram-Schmidt Orthogonalization
　5.3 Operators
　5.4 SelfAdjointOperators
　5.5 Unitaty Operators
　5.6 Transformations of Operators
　5.7 Invariants
　5.8 Summary-Vector Space Notation
　AdditionaIReadings
6 Eigenvalue Problems
　6.1 EigenvalueEquations
　6.2 Matrix Eigenvalue Problems
　6.3 Hermitian Eigenvalue Problems
　6.4 Hermitian Matrix Diagonalization
　6.5 NormaIMatrices
　AdditionalReadings
7 Ordinary DifTerential Equations
　7.1 Introduction
　7.2 First-OrderEquations
　7.3 ODEs with Constant Coefficients
　7.4 Second-Order Linear ODEs
　7.5 Series Solutions-Frobenius ' Method
　7.6 OtherSolutions
　7.7 Inhomogeneous Linear ODEs
　7.8 Nonlinear Differential Equations
　Additional Readings
8 Sturm-Liouville Theory
　8.1 Introduction
　8.2 Hermitian Operators
　8.3 ODE Eigenvalue Problems
　8.4 Variation Method
　8.5 Summary, Eigenvalue Problems
　Additional Readings
9 Partial Differential Equations
　9.1 Introduction
　9.2 First-Order Equations
　9.3 Second-Order Equations
　9.4 Separation of Variables
　9.5 Laplace and Poisson Equations
　9.6 Wave Equation
　9.7 Heat-Flow, or Diffusion PDE
　9.8 Summary
　Additional Readings
10 Green's Functions
　10.1 One-Dimensional Problems
　10.2 Problems in Two and Three Dimensions
　Additional Readings
11 Complex Variable Theory
　11.1 Complex Variables and Functions
　11.2 Cauchy-Riemann Conditions
　11.3 Cauchy' s Integral Theorem
　11.4 Cauchy' s Integral Formula
　11.5 Laurent Expansion
　11.6 Singularities
　11.7 Calculus of Residues
　11.8 Evaluation of Definite Integrals
　11.9 Evaluation of Sums
　11.10 Miscellaneous Topics
　Additional Readings
12 Further Topics in Analysis
　12.1 Orthogonal Polynomials
　12.2 Bernoulli Numbers
　12.3 Euler-Maclaurin Integration Formula
　12.4 Dirichlet Series
　12.5 Infinite Products
　12.6 Asymptotic Series
　12.7 Method of Steepest Descents
　12.8 Dispersion Relations
　Additional Readings
13 Gamma Function
　13.1 Definitions, Properties
　13.2 Digamma and Polygamma Functions
　13.3 The Beta Function
　13.4 Stirling's Series
　13.5 Riemann Zeta Function
　13.6 Other Related Functions
　Additional Readings
14 Bessel Functions
　14.1 Bessel Functions of the First Kind, ,Iv (x)
　14.2 Orthogonality
　14.3 Neumann Functions, Bessel Functions of the Second Kind
　14.4 Hankel Functions
　14.5 Modified Bessel Functions, Iv (x) and Kv (x)
　14.6 Asymptotic Expansions
　14.7 Spherical Bessel Functions
　Additional Readings
15 Legendre Functions
　15.1 Legendre Polynomials
　15.2 Orthogonality
　15.3 Physical Interpretation of Generating Function
　15.4 Associated L