# Mathematical Methods in Physics

Subject classification: this is a physics resource. |

Subject classification: this is a mathematics resource. |

## Content Edit

### Second order differential equations Edit

- Introduction to 2nd order differential equations
- Solution of homogeneous equations with constant coefficients
- Solution of inhomogeneous equations with constant coefficients
- Singularities and series solutions
- Frobenius method

### Special functions Edit

- Cylindrical and spherical coordinates
- Boundary value problems
- Sturm-Liouville problem
- Legendre polynomials
- Bessel functions
- Associated Legendre functions
- Spherical harmonics
- Neumann functions
- Modified Bessel functions
- Fourier-Legendre series
- Asymptotic behaviors of certain special functions

### Complex functions Edit

- Complex numbers
- Basic operations with complex functions, analytic functions
- Cauchy theorem
- Singularities
- Taylor and Laurent series
- Residue theorem and applications
- Complex functions

### Partial differential equations Edit

- General definition
- Separation of variables method
- Wave equation
- Laplace and Poisson equations
- Diffusion equation
- Helmholtz equation
- Continuum eigenvalue spectrum