Mathematical Methods in Physics
| Subject classification: this is a physics resource . |
| Subject classification: this is a mathematics resource . |
| Resource type: this resource is a course. |
Content
- Second order differential equations
- Introduction to 2nd order differential equations
- Solution of homogeneous equations
- Singularities and series solutions
- Frobenius method
- Special functions
- 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
- 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
- General definition
- Separation of variables method
- Wave equation
- Laplace and Poisson equations
- Diffusion equation
- Helmholtz equation
- Continuum eigenvalue spectrum
- Green functions
- For Sturm-Liouville operators
- For 2 dimensions
- For initial value problems
- For boundary value problems
- Solution of higher-order differential equations
- Reduction to canonical form
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