Courses

 

Multivariable Calculus - Math 2500

 

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Fall 2016 Final Exam Schdule

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).  

 

Syllabus

Lecture Notes

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 RegionNotes on Integration of General Region (Cont.)

 

 

 

Solution to Quiz1

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

 

Solution to Quiz2

Solution to Quiz3-part1, Solution to Quiz3-part2

Midterm-1-Solution-part1Midterm-1-Solution-part2

Solution to Quiz 4

Solution to Quiz 5

Solution to Quiz 6

Solution to Quiz 7-part1Quiz07-part2

Midterm 2 Solution-part1 Midterm 2 Solution-part2