
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 EpsilonDelta Proof of a Limit
 The nitty griddy of an epsilondelta 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...

Differentiability
 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.
