y = mx + c varying the gradient or varying the intercept

y = ax² + bx + c varying a or varying b.

The graph of   y = ax³ + bx² + cx + d   varying  a or varying  b or varying c.

Showing the gradient of a variable tangent to a cubic curve.
There are two versions of the animation: a smaller, faster one and a larger, slower one.

Parabola: illustrating the fact that tangents at opposite ends of a focal chord meet on the directrix.
There are two versions of the animation: a smaller, faster one and a larger, slower one.

Hyperbola: illustrating the fact that tangents at opposite ends of a chord through the centre are parallel.
There are two versions of the animation: a smaller, faster one and a larger, slower one.

Ellipse: again, illustrating the fact that tangents at opposite ends of a chord through the centre are parallel.
There are two versions of the animation: a smaller, faster one and a larger, slower one.

An example of a function  f  of two variables which is not differentiable at the origin but both the partial derivatives ¶ f/¶ x and ¶ f/¶ y exist (and are zero) at the origin.

Constructing a torus by glueing opposite edges of a rectangle.
There are two animations to choose from: a smaller, faster one and a larger, slower one

Constructing a Möbius band by glueing a pair ofopposite edges of a rectangle with a half twist.
Again there are two animations: a smaller, faster one and a larger, slower one.

Klein bottle. Not an animation, this time, just the static image.