# Courses

## Multivariable Calculus - Math 2500

**>>If you have any questions regarding a problem on webWork, send me email through the webWork system! This way I can see your screen.<<**

## Fall 2016 Final Exam Schdule

**Review Sheet for Final exam**

**Review Sheet for Final exam**

* For those who are curious about the final bonus problem:* You learned from the second last problem that the Lagrange multiplier (min/max for f(x,y) with constraint g(x,y)=0) problem is equivalent to finding min/max with NO constraint for the function E_{aug}(x,y,\lambda)=f-\lambda*g. The stochastic gradient descent method is used to find min/max for no constraints. So you apply the same pseudocode for E_{aug}=Q(w)-\lambda*R(w), i.e., the last line of pseudocode should be (w,\lambda):=(w,\lambda)-\eta*(Q_i(w)-\lambda*R(w)). (All these methods come with technical constraints that have been omitted).

Source of problem: Constraint Optimization Using Lagrange Multipliers, Stochastic gradient descent (and many other sources you could find online for these topics).

Additional Exercises: This list provides a list of additional exercises from the textbook. **However, any information other than the exercise numbers does not have direct connection to our current class.** I might not post much solutions on these exercises, and they will not be directly related to your quiz/exam problems, but you are welcome to try them and direct questions about them to me during office hours or through emails.

Online Exercise on polar coordinates. You should **at the very least** try problem 1-7.

Reading the following online notes will **DEFINITELY **help you understand materials coming later in the semester.

Notes on cylindrical coordinates.

Notes on spherical coordinates.

Notes on Integration of General Region; Notes on Integration of General Region (Cont.)

Effective 09/05/2016, the Friday office hour will be cancelled and moved to Monday 10:00-11:00am.

Solution to Quiz3-part1, Solution to Quiz3-part2

Midterm-1-Solution-part1, Midterm-1-Solution-part2.

Solution to Quiz 7-part1, Quiz07-part2

Midterm 2 Solution-part1 Midterm 2 Solution-part2