Calculus III, Spring 2016 

Instructor: Andrew Obus
email: obus [at] virginia [dot] edu
office: Kerchof Hall 208
phone: 434-424-4930



TuTh 12:30-1:45, Gibson Hall 211.  Please ask questions if anything in lecture is unclear. Lectures will run the entire 75 minutes. Please show up on time!

Schedule of Lectures


You will be assigned to a recitation meeting either Monday 5:00-5:50 in Monroe Hall 124, or Tuesday 5:00-5:50 in New Cabell Hall 389.  The recitation leader for both recitations is Gonzalo Bley (gb3kd [at] virginia [dot] edu).  His office hours are Mondays and Tuesdays from 6:15-7:00, after recitation. Recitations will be highly useful for review and help!


Multivariable Calculus, by James Stewart, edition 7E.  If you have the full Calculus book by Stewart, that is also OK.


This course takes the ideas you have seen in single variable calculus and generalizes them to the cases of two and three (and sometimes more) variables.  This will have many applications: computing surface areas, volumes, and fluxes; finding minima and maxima of functions of several variables; and calculating trajectories of bodies in space.  The book contains a great variety of other applications --- we will cover a few, and I encourage you to read about whatever else piques your interest!
The material here is immensely useful in physics, probability, and higher math. One theme that will run through the second part of the course will be the fundamental theorem of calculus --- we will see some far-reaching generalizations of this, applicable to regions in space, curves, surfaces, and vector fields. 

In particular, we will cover most of Chapters 12 - 16 in Stewart's book.  The beginning material on the properties of three-dimensional space has little calculus content.  We will go through this material rather quickly, so as to have more time for the more difficult material later in the course.

Expected Background: Calculus II or a 5 on the BC Calculus AP.

WARNING!!! This is a very fast-paced class, significantly faster than Calculus II.  It may be the case that you find yourself not having fully understood everything at the end of a lecture.  This is totally normal and nothing to be worried about, but please go over your notes as soon as possible to get up to date (certainly before the next class)!  If you need further help, do not be shy about asking questions at recitation and office hours.  If you fall too far behind in this course, it will be very difficult to catch up --- you do not want to fall into a pattern where each lecture starts to become less understandable than the last.  Please see me promptly if things stop making sense!  Note also the tutoring center below.

Office Hours

Tu 11-12, W 10-11. Kerchof Hall 208 (my office). If these times do not work for you, please make an  appointment with me.


Homework will be given in two parts: a written part due in class on Thursdays, and a WeBWorK portion due at 11:59 PM on Thursdays.  If you are going to miss class for whatever reason, you must either submit the written homework to my mailbox in the mailroom of Kerchof Hall before the beginning of class, or have a friend submit your homework in class. Late or improperly submitted homework will not be accepted. If you know in advance you will be unable to turn in homework when it is due, you should plan to turn it in ahead of time.  I will drop your lowest homework score to allow for missed assignments or for assignments that pose special difficulty.

Homework should be neat, well-organized, and legible. In addition, it must be stapled or paper clipped (no folding over the top-left corner or anything like that). Please write in paragraphs, sentences, and English words (oh my!) when they are called for.  Some problems will require you to write an explanation.  The grader should not have to decipher what you are doing--you should be clear and unambiguous about your methods on a homework problem.

You are encouraged to work together on homework!  But you must write up your own solutions.  I have found that it is helpful if I think about the problems myself first, and then discuss the more difficult questions with others.  It is very important that you truly understand the homework solutions you hand in.  In previous classes I have taught, the students who were the most unpleasantly surprised with their exam grades have been the ones who have "phoned in" their homework.

If you work together on homework, please write the names of your collaborators on the front.

Homework will be graded and every effort will be made to hand it back promptly.  Grades will be posted on UVaCollab.


Midterms will be held at 7 PM on Monday, February 22nd and Monday, March 28th.  The midterms will be 75 minutes long.  If you have a conflict with one of these times, please let me know now.  Things become much more difficult if you delay.  The rooms are TBA.  We should be able to reserve some class time for review the days of the midterms.

The final exam is on Tuesday, May 10th, from 2:00PM-5:00PM in the usual classroom, Gibson 211.

Calculators are not permitted on exams.

Final Course Grades

20% Homework
20% Each Midterm
40% Final Exam

It is possible for exceptional class participation to be factored into the homework grade.


The University of Virginia Honor Code applies in this class.  You will be asked to sign a statement before each exam acknowledging that you understand this.


All students with special needs requiring accommodations should present the appropriate paperwork from the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.

Some Useful Links

University of Virginia Undergraduate Math Page

University of Virginia Math Department

Extra Help


If you have (anonymous) comments for me about teaching style or anything related to the course, you can make them on the Collab page for the course.