We consider a diffusing particle in one dimension that is subject to a time-dependent drift or potential field. A reflecting barrier constrains the particle's position to the half-line X≥ 0. Such ...

The course begins with an overview of classes of ordinary and partial differential equations (ODEs & PDEs) that are solved by exact methods. Fourier methods for solving linear DEs are extended to ...

The simplest approach to solving PDEs (partial differential equations) is the method of separation of variables. The course discussion will begin from a natural extension of separation that leads to ...

A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables, an unknown function that is dependent on those variables, and partial derivatives of the ...