Mathematical Methods in Physics

Subject classification: this is a physics resource.

Subject classification: this is a mathematics resource.

Content

Second order differential equations

1. Introduction to 2nd order differential equations
2. Solution of homogeneous equations with constant coefficients
3. Solution of inhomogeneous equations with constant coefficients
4. Singularities and series solutions
5. Frobenius method

Special functions

1. Cylindrical and spherical coordinates
2. Boundary value problems
3. Sturm-Liouville problem
4. Legendre polynomials
5. Bessel functions
6. Associated Legendre functions
7. Spherical harmonics
8. Neumann functions
9. Modified Bessel functions
10. Fourier-Legendre series
11. Asymptotic behaviors of certain special functions

Complex functions

1. Complex numbers
2. Basic operations with complex functions, analytic functions
3. Cauchy theorem
4. Singularities
5. Taylor and Laurent series
6. Residue theorem and applications
7. Complex functions

Partial differential equations

1. General definition
2. Separation of variables method
3. Wave equation
4. Laplace and Poisson equations
5. Diffusion equation
6. Helmholtz equation
7. Continuum eigenvalue spectrum

Green functions

1. For Sturm-Liouville operators
2. For 2 dimensions
3. For initial value problems
4. For boundary value problems
5. Solution of higher-order differential equations
6. Reduction to canonical form