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
……
8 Sturm-Liouville Theory
9 Partial Differential Equations
10 Green's Functions
11 Complex Variable Theory
12 Further Topics in Analysis
13 GammaFunction
14 Bessel Functions
15 Legendre Functions
16 Angular Momentum
17 Group Theory
18 More Special Functions
19 Fourier Series
20 IntegraITransforms
21 IntegraIEquations
22 Calculus of Variations
23 Probability and Statistics
Index
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