Building on ES_APPM 420-1, this course covers advanced perturbation and asymptotic methods. They may include methods for ordinary differential equations (e.g. WKB method), for integrals (e.g.

time-dependent perturbation theory, tight binding method, variational method and the use of finite basis set. In each case, a specific example is given to clearly show how the method works. Use ...

Perturbation Analysis: A technique used to study how small changes in input data affect the output of a mathematical problem. Tikhonov Regularization: A method used to stabilize the solution of ...

FEP calculations have had a revolutionary effect on computational chemistry. In conjunction with molecular dynamics and Monte Carlo simulations, they have enabled the calculation of free energy ...

Most mathematical models do not admit exact solutions. Asymptotic and perturbation methods provide powerful techniques for obtaining approximate solutions, which allow one to draw physical conclusions ...