Mathematical Physics (Notes)

Contents

• Chapter 1: Mathematical Preliminaries
• 1.1 Infinite Series
• 1.2 Series of Functions
• 1.3 Binomial Theorem
• 1.4 Mathematical Induction
• 1.5 Operations on Series Expansion of Functions
• 1.6 Some Important Series
• 1.7 Vectors
• 1.8 Complex Numbers and Functions
• 1.9 Derivatives and Extrema
• 1.10 Evaluation of Integrals
• 1.11 Dirac Delta Function
• Chapter 2: Determinants and Matrices
• Chapter 3: Vector Analysis
• Chapter 4: Tensors and Differential Forms
• Chapter 5: Vector Spaces
• Chapter 6: Eigenvalue Problems
• Chapter 7: Ordinary Differential Equations
• 7.1 Introduction
• 7.2 First-Order Equations
• 7.3 ODEs with Constant Coefficient
• 7.4 Second-Order Linear ODEs
• 7.5 Series Solutions - Frobenius Method
• 7.6 Other Solutions
• 7.7 Inhomogeneous Linear ODEs
• 7.8 Nonlinear Differential Equation
• Chapter 8: Sturm-Liouville Theory
• Chapter 9: Partial Differential Equation
• Chapter 10: Green's Functions
• Chapter 11: Complex Variable Theory
• Chapter 12: Further Topics in Analysis
• Chapter 13: Gamma Function
• Chapter 14: Bessel Functions
• Chapter 15: Legendre Functions
• Chapter 16: Angular Momentum
• Chapter 17: Group Theory
• 17.1 Introduction to Group Theory
• 17.2 Representation of Groups
• 17.3 Symmetry and Physics
• 17.4 Discrete Groups
• 17.5 Direct Products
• 17.6 Symmetric Group
• 17.7 Continuous Group
• 17.8 Lorentz Group
• 17.9 Lorentz Covariance of Maxwell's Equations
• 17.10 Space Groups
• Chapter 18: More Special Function
• Chapter 19: Fourier Series
• Chapter 20: Integral TransformIn
• Chapter 21: Integral Equations
• Chapter 22: Calculus of Variations
• Chapter 23: Probability and Statistics