Guardian for Mathematical Physics

Chapter 1. Introduction
1.1 Trigonometric Functions
1.2 Double-and Half-angle Formulas
1.3 Hyperbolic Functions
1.4 Differentiation
1.5 Chain Rule
1.6 Integration
1.7 Complex numbers
1.8 Dirac Delta Function
1.9 Equations of Trajectory

Chapter 2. Differential Equation
2.1 Concept of Differential Equation
2.2 First Order Ordinary Differential Equation
2.3 Homogeneous Second Order Differential Equation
2.4 Inhomogeneous Second Order Differential Equation

Chapter 3. Vectors
3.1 Coordinate Systems
3.2 Vectors in Rectangular Coordinate System
3.3 Gradient, Divergence and Curl
3.4 Divergence and Stokes’ Theorem
3.5 Tensor

Chapter 4. Physical Quantities in Coordinate Systems
4.1 Spherical Coordinate System
4.2 Cylindrical Coordinate System
4.3 Curvilinear Coordinate System

Chapter 5. Infinite Series
5.1 Infinite Series
5.2 Taylor Series
5.3 Taylor Series for More Than One Variable

Chapter 6. Matrices
6.1 Matrix Representation
6.2 Operator
6.3 Eigenvalue Equation
6.4 Notation in Quantum Mechanics

Chapter 7. Special Functions
7.1 Beta and Gamma Functions
7.2 Legendre Differential Equation
7.3 Solutions for Bessel’s Equation

Chapter 8. Fourier Transformation
8.1 Fourier Series
8.2 Fourier Transform

Chapter 9. Variational Principle
9.1 Lagrange’s Equation
9.2 Lagrange Multipliers Method


Appendix
References
Index