Differential equations

Differential equations serve as mathematical models of physical processes. This course is intended to be an introduction to ordinary differential equations and their solutions. A differential equation (DE) is an equation relating a function to its derivatives. If the function is of only one variable, we call the equation an ordinary differential equation (ODE). Equations relating the partial derivatives (See: Vector calculus) of a function of several variables are called partial differential equations (PDEs). Ordinary differential equations are much easier to solve than partial differential equations, so these will be our main focus.

Syllabus

 * Introduction to ordinary differential equations.
 * /Ordinary Differential Equations/
 * Slope Fields
 * First-order equations
 * /Introduction to First Order Linear Differential Equations/
 * /Separable differential equations/ 50% [[Image:50%25.svg|20px|]]
 * /Exact differential equations/ 25% [[Image:25%25.svg|20px|]]
 * /Homogeneous differential equations/ 25% [[Image:25%25.svg|20px|]]
 * /Integrating factors/ 25% [[Image:25%25.svg|20px|]]
 * /Change of variables/ 25% [[Image:25%25.svg|20px|]]
 * Higher-order linear equations
 * /Linear homogeneous differential equations/ 25% [[Image:25%25.svg|20px|]]
 * /Linear inhomogeneous differential equations/ 25% [[Image:25%25.svg|20px|]]
 * /Laplace transforms/ 25% [[Image:25%25.svg|20px|]]
 * /Power series solutions/ 25% [[Image:25%25.svg|20px|]]
 * Introduction to nonlinear equations
 * Stability problems in 1D/
 * Stability problems in 2D/
 * /Approximate solutions to differential equations/