# Maths - Calculus

## Prerequisites

If you are not familiar with mathematical functions you may like to look at the following pages first:

## Calculus

A mathematical function such as y=f(x) defines a value of y for every x.

Differentiation and Integration defines a whole function for a a given input function.

## Differentiation

Differentiation defines the rate of change of a given function for every point on that function: ## Integration

Integration defines the cumulative area under a given function for every point on that function: ## Leibnitz Notation

The Differential of a function f(x) is denoted by d f(x)/dx.

Even if you don't want to learn any more about calculus it is useful to recognise that:

d f(x)/dx means the rate of change of f(x) with respect to x. To take a more specific example:

d distance / d time

Means the rate of change of distance with respect to time, in other words, as time changes what is the corresponding change in distance. In other words the value of velocity for every value of time.

So you will often see on this site, the form d ... / d ... means the rate of change of something with respect to something else.

Note: d f(x) does not mean d times f(x), instead d is an 'operator' acting on f(x). I guess that 'd' stands for difference.

## Further Topics

 metadata block see also: Correspondence about this page Book Shop - Further reading. Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.       Mathematics for 3D game Programming - Includes introduction to Vectors, Matrices, Transforms and Trigonometry. (But no euler angles or quaternions). Also includes ray tracing and some linear & rotational physics also collision detection (but not collision response). Other Math Books Commercial Software Shop Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.  Mathmatica