This screencast shows a simple example of the solution of a first order differential equation using the integration factors method.

Explains the integrating factor method and gives a quick proof.

This screencast illustrates the method of separation of variables for a medium-level first order differential equation: dv/dpsi=v(tan(psi)-mu sec(psi)).

Starting with the equation for a family of curves, this screencast shows how to differentiate both sides of the equation to produce a differential equation which can be solved to find the grandient of this family of curves. It is then shown how the general form of the gradient for the orthogonal family of curves can be obtained and hence the equation of the orthogonal curves.

This screencast demonstrates how to solve a first-order linear differential equation by using an integrating factor.

This screencast illustrates the method of separation of variables for a medium-level first order differential equation: dy/dx=(2-y)/(1+x). Different ways of displaying the solution are discussed.

Shows how to find a particular form of the chain rule that is needed, depending on the type of problem that is posed. Uses a tree diagram to develop the rule.

Example where equation of a plane and scalar parametric equations of a line are given. To find the angle between the line and the plane, the equations of the line are converted to vector form, the angle between the line and the normal vector to the plane are found, and the angle between the line and plane is then calculated.

An example where the gradient of a surface is found depending on the angle alpha, and then the maximum gradient is calculated.

Applies the multivariate chain rule to an example where z(x,y), x(t), y(t), to find dz/dt.