Overview
Differentiation is a central notion of the calculus. It began simply as a method to find the tangent to a curve in the plane. The notion was then extended to include tangent planes to surfaces and was developed into numerous definitions and types of mathematical objects.
Example
A graph of the function {% y = x^2 %} with the tangent line drawn.
Moving the slider moves the tangency point.
Definition
The definition of differention relies on the notion of a limit. The derivative of a function {% f(x) %} is a new function , here denoted by {% f'(x) %} where
{% f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} %}
if it exists.
Topics
- Analytic Techniques : a set of analytic techniques for computing the derivative
- Abstract Definition (Total Derivative)
- Multi-Variable
- Differential Forms: are used to extend calculus to be used on curved surfaces and manifolds.
- Directional Derivative
- Functional Differentiation - gives a notion of differentiating a functional by a function.
- Theorems
- Numeric Implementation