Multivariable Calculus Introduction

DRAFT

Here is a typical function of one variable (x):

f(x) = x²

And its graph:

And here is a function of two variables (x and y):

f(x, y) = x² + y³

And its graph:

Multivariable Calculus is all about functions that have more than one variable. It uses many of the techniques of ordinary calculus, just expanded to cover more than one variable.

Derivatives

In Calculus we can find derivatives (basically the slope of a function).

For single variables it looks like this:

For two variables it looks like this:

(You can read the page on Partial Derivatives if you like)

Integration

In Calculus we can also do integration (basically finding area or volume).

For single variables it looks like this:

For two variables it looks like this:

Differential Equations

And in Calculus we handle differential equations, which are equations that have differentials in them.

Such as:

Once again they have only one variable and are called Ordinary Differential Equations (ODEs for short).

But when there is more than one variable we have the subject of Partial Differential Equations (PDEs for short)