Multivariable Calculus

Spring 2016

Instructor: Matt Kerr
Office: Cupples I, Room 114
e-mail: matkerr [at]
Office Hours: 4:30-5:30 Monday, 3-4 Tuesday, 3-4 Friday

TA: Philip Benge
e-mail: benge [at]
Calc help room hours: 4-5 Tuesday (in Lopata 323)
Review session hours: 3-4 Monday (in Eads 215), 4-5 Thursday (in Cupples I Room 113)

Prerequisites: Math 132 (Calculus II), or a score of 4-5 on the AP Exam (Calculus BC)

Class Schedule:

Lectures are on Monday, Wednesday, and Friday in Rebstock 215, from 11-12 (section 1) and 1-2 (section 2). Class begins on Wednesday Jan. 20th and ends with a final exam review class on Friday April 29th. Spring break is the week of March 14th.

Midterm Exam 1: Tuesday, February 9, 7-9 PM
Review packet  + solutions / Exam 1 solutions
Midterm Exam 2: Tuesday, March 8, 7-9 PM
Review packet  + solutions / Exam 2 solutions
Midterm Exam 3: Tuesday, April 12, 7-9 PM
Review packet + solutions  / Exam 3 solutions
Final Exam: Thursday, May 5, 3:30-5:30 PM
Practice Final Exam + Solutions, Review suggestions  / Final Exam solutions

Regarding missed exams, see the Grading Policy section below. Neither notes nor calculators are allowed, but the exams will not be computationally heavy. The final is cumulative, i.e. covering up through section 16.6.

To find your room and seat assignment for an exam, click here on exam day, or go to

For exam score lookup (on the day after the exam), use this link. (Note that for exam 1, this will not reflect the correction to the Crow 201 exam scoring. Instead see blackboard.)

Copies of old exams are maintained at this link.


James Stewart, Calculus (8th Ed., looseleaf, w/Webassign access), Cengage Learning, 2015.

We will cover most of Chapters 12-16. The publisher maintains a webpage for Stewart's Calculus with lots of helpful and interesting links.

Course Syllabus:

This is an introductory course in multivariable calculus. You can expect a mild amount of abstraction, but the emphasis is on topics which are useful in science and engineering. My goal is for each of you to come away in 15 weeks with a good understanding of:

  • vector-valued functions, and derivatives and integrals of these;
  • functions of several variables: partial and directional derivatives, tangent planes, maxima and minima, and Lagrange multipliers;
  • multiple integrals and change of variable formula;
  • vector calculus, including line integrals and Green's theorem.

  • Assignments:

    We will use Webassign for the weekly homework, which is usually due each Tuesday (at 11:59 PM!), covering the previous week's lectures. The exception is (midterm) exam weeks, on which HW is due Monday (at 11:59 PM), and the exam is Tuesday evening.

    My office hours and the TA's review sessions are chosen with this schedule in mind, and we are there to help.

    If you are new to Webassign, see this student support webpage. At the beginning of the course, you will need to enter the class key here. For routine Webassign login (to work on homework), click here.

    The first assignment is due Tuesday January 26.


    In the calendar below I will post brief summaries of each lecture, containing the key ideas and formulas, which should help when reading the text or preparing for exams. They are not meant to substitute for the lectures, which will not be posted in their entirety.

    The section(s) I plan to cover in each lecture are displayed in the table. Not all the sections indicated will be covered in full.


    Week of ... Mon Tue Wed Thu Fri
    Jan. 18 (week 1) MLK HOLIDAY Lec 1 [12.1-2] Lec 2 [12.3-4]
    Jan. 25 (week 2) Lec 3 [12.4-5] HW 1 Lec 4 [12.5] Lec 5 [12.5-6]
    Feb. 1 (week 3) Lec 6 [Ch. 10] HW 2 Lec 7 [13.1] Lec 8 [13.2]
    Feb. 8 (week 4) Lec 9 [13.3]
    HW 3
    EXAM 1 Lec 10 [13.3] Lec 11 [13.4]
    Feb. 15 (week 5) Lec 12 [14.1] HW 4 Lec 13 [14.2] Lec 14 [14.3]
    Feb. 22 (week 6) Lec 15 [14.4] HW 5 Lec 16 [14.5] Lec 17 [14.6]
    Feb. 29 (week 7) Lec 18 [14.6] HW 6 Lec 19 [14.7] Lec 20 [14.7]
    Mar. 7 (week 8) Lec 21 [14.8]
    HW 7
    EXAM 2 Lec 22 [14.8] Lec 23 [14.8]
    Mar. 14 (week 9)
    Mar. 21 (week 10) Lec 24 [15.1] HW 8 Lec 25 [15.1] Lec 26 [15.1]
    Mar. 28 (week 11) Lec 27 [15.2] HW 9 Lec 28 [15.2-3] Lec 29 [15.3]
    Apr. 4 (week 12) Lec 30 [15.4] HW 10 Lec 31 [15.9] Lec 32 [16.1]
    Apr. 11 (week 13) Lec 33 [16.2]
    HW 11
    EXAM 3 Lec 34 [16.3] Lec 35 [16.3]
    Apr. 18 (week 14) Lec 36 [16.4] HW 12 Lec 37 [16.4-5] Lec 38 [16.5]
    Apr. 25 (week 15) Lec 39 [16.6] Lec 40 [16.7-9] Lec 41 [REVIEW]
    HW 13

    Additional Resources:

    Here is a list of resources for help with calculus:

  • Instructor's office hours (see top of page)
  • TA's office hours in Calculus Help Room and review sessions (see top of page)
  • Cornerstone Math Help, available in Cornerstone and on the South 40
  • PLTL (Peer-Led team Learning): students who wish to participate must sign up at the beginning of the semester
  • Engineering student services (tutoring for EN students)
  • There is a list of math tutors available in the main office of the Mathematics Department (Cupples I Room 100): 935-6760
  • Link to old Math 233 exams
  • Stewart Calculus website
  • Link to RPM (Residential Peer Mentoring) calendar

  • Grading Policy:

    Webwork and Midterm Exams 1, 2, and 3 are worth 15% each; the Final Exam is worth 40%. I will drop your lowest 2 HW scores. Grades will be kept track of on blackboard, with the exception of Webassign which will be entered as a block score at the end of the course. (In the meantime, Webassign will keep track of your WW scores.)

    If you have to miss a midterm exam for a legitimate reason, you will be given an excused absence for that exam, and your grade will be calculated from the homework and other taken exams. Of course verified illness and serious family emergency are legitimate reasons. Regarding other conflicts, e-mail me as soon as you know about them.

    Verified illness and serious family emergency are in general the only acceptable reasons for missing the final exam. In this event, you will be given a makeup exam.

    To have any excused absence approved, please contact Blake Thornton (blake [at] and cc me in the e-mail.

    In general, credit will be given for late homework only in the event of illness or emergency.

    You are encouraged to discuss homework problems with other students (calculators are of course also allowed).

    This link takes you to the standard university policies on academic integrity.