Multivariable Calculus, M408M, Fall 2015, Unique #s: 53010, 53015

  • Professor: Lorenzo Sadun, sadun@math.utexas.edu
  • Teaching Assistant: Yanlin Cheng, yanlinch@math.utexas.edu
  • Learning Assistant: TBD TBD@utexas.edu
  • Learning Assistant: TBD TBD
  • Lectures: TuTh 11:00-12:30, CPE 2.214
  • Discussion sections by unique number:
    53010: MW 8-9, WRW 113
    53015: MW 2-3, CPE 2.220
  • Website: http://www.ma.utexas.edu/users/sadun/F15/M408M
  • Office: RLM 9.114
  • Sadun Office Hours: M3-4, W10-11, RLM 9.114
  • Yanlin Cheng's Office Hours: TBD, RLM XX.XXX
  • LA's Office Hours: TBD
  • LA's Office Hours: TBD
  • Phone: 471-7121
  • Text: Calculus, Early Transcendentals, 7th Edition, by Stewart.
  • Prerequisites: This class is restricted to students who have passed M408S or M408L or M408D with a grade of C- or better. If you do not meet these conditions, you will be dropped from the class.

  • One variable at a time: Calculus has a reputation of being a hard class that features a million different equations to be memorized. There are a lot of formulas and techniques, but almost everything boils down to six simple ideas, which I call the six pillars of calculus:
    1. Close is good enough (limits)
    2. Track the changes (derivatives)
    3. What goes up has to stop before is can come down (max/min)
    4. The whole is the sum of the parts (integrals)
    5. The whole change is the sum of the partial changes (fundamental theorem)
    6. One variable at a time.
    M408C/K/N was mostly about the first three pillars, with a little bit about pillars 4 and 5 at the end. M408D/L/S was about pillars 1, 4, and 5, with a little bit about pillar 6 at the end. M408M is all about pillar 6. Almost everything in this course can be done by isolating one input variable and one output variable and applying what you learning in the first two semesters of calculus.
  • Three questions: There are three questions associated with every mathematical topic you ever will see.
    1. What is it?
    2. How do you compute it?
    3. What is it good for?
    Most of high school calculus is about "how do you compute it?" This class will put a much greater emphasis on conceptual understanding and applications than you're probably used to.

  • There will be in-class midterm exams on October 8 and November 12. Exams are closed book and calculators are not allowed. However, you are allowed to bring an 8.5" x 11" crib sheet with whatever you want written on it. Outlines, useful formulas, worked problems, calming advice -- you name it. The only restriction is that the crib sheet must be handwritten by you.

  • The final exam will be on Wednesday afternoon, December 9, 2-5 PM. The ground rules are the same as for the midterms, except that you are allowed two crib sheets instead of one. Calculators are not allowed.

  • The homework and grading scheme are explained in the First Day Handout
    •

    *Handouts and Other Course Information

  • First Day Handout
  • Course Schedule
  • Written HW assignments
  • The Quest server. That's where you get learning modules and do the online portion of your homework.
  • My Youtube channel with over 300 calculus videos, including all the videos that appear in the Quest learning modules for M408M.
  • The Calculus Lab website. CalcLab is where you get get TA help 5 days per week, typically 5 hours/day. It won't always be our TA and LAs staffing CalcLab, but there will always be somebody there to answer M408M questions.
  • The Sanger Center, a great source of (mostly) free help.


  • Practice first midterm from 2006, available with and without solutions.
  • Practice first midterm from 2013, available with and without solutions. This was given on September 26, and so doesn't cover as much ground as our first midterm.
  • Actual first midterm from 2015, available with and without solutions.

  • Practice second midterm from 2006, available with and without solutions.
  • Practice second midterm from 2013, available with and without solutions.
  • Actual second midterm from 2015, available with and without solutions.


  • Practice third midterm from 2013, available with and without solutions.

  • Practice final exam from 2006, available with and without solutions.
  • Practice final exam from 2013, available with and without solutions.
  • Actual final exam from 2015, available with and without solutions.