Another service from Omega


Functions of Several Variables

What is a function of several variables?
Functions of several variables, Level Curves, plot3d in Maple.
Limits and Continuity
Definitions of limit and continuity.
An Epsilon-Delta Proof of a Limit
The nitty griddy of an epsilon-delta proof of a limit.
Computing limits with maple
Exercises of limits of functions of several variables.
Partial Derivatives
Definition of partial derivatives.
Computing partials with Maple
Maple tricks and notations.
Mixed Partials are NOT always equal
Example where the order in which you take the partials is important.
Tangent planes
The equation of the tangent plane to a surface at a point.
Tangent planes with Maple
Two problems with solutions and pictures are here...
The differential of a function of several variables.
The Chain Rule
Examples of chain rules with maple.
Rates of change
Using the Chain Rule to compute rates of change.
Directional derivatives and the gradient
What is a directional derivative? The definition of the gradient is also here...
Computing directional derivatives
Examples of directional derivatives from their definition and from the grad formula. The fast climber is here...
Some review exercies
Review exercises and their solutions with maple.
Max, Mins and Saddle points
Definition of local and global maxs and mins.
The test of second partials
After you know that the partial derivatives are zero you need to check for the 'sign' of the second derivatives.. Here is how and why.
Finding Extrema with Maple
Two problems with solutions.
Lagrange Multipliers
The method of Lagrange multipliers.

Carlos Rodriguez <>
Last modified: Tue Mar 27 10:58:33 EST 2001