Mathematical Methods in Physics

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/