This review sheet covers the third third of class, this together with the first two are what you should be comfortable with going into the final.

With these terms, as always, give a prose and mathematical interpretation of their meaning.

1.

Level curves

2.

Limits of multivariable functions

3.

Partial derivatives (first, higher order)

4.

Chain Rule (From Linear Transformation point of View!!)

5.

Differentials and Linear approximation

6.

Gradient (make sure you have the prose explanation well understood here!)

7.

Directional Derivaive

8.

Tangent plane, Tangent line

9.

Curves of maximum change

10.

Critical points (local maxima, minima, saddle point) and classification tests.

11.

Lagrange multipliers (as a tool for optimization)

Here are some questions you might want to ponder

1.

When is $\frac{\partial f^2}{\partial x \partial y}=\frac{\partial f^2}{\partial y \partial x}$?

2.

Why do we use linear transformations to represent derivatives of multivariable functions?

3.

Why is the gradient the direction of maximum change of a function?

4.

Why do the following methods work: Lagrange multipliers, test for classifying critical points.

5.

Uh-oh, my critical point came out of the test undetermined. What now?

Here are some book problems for you to work on. As always, feel free to try any book problems and bring them to the review session if you find them interesting/challenging.

1.

p.767: 4,5,7, 10 (and Challenging Problem 3, if the rest of the material leaves you unchallenged)

2.

p.816 2, 5, 10, 14