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.
- 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.
- 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.
- The method of Lagrange multipliers.