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