Advanced Calculus and Linear Algebra I, Fall 2017

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



TuTh 9:30-10:45, New Cabell Hall 323.  Please ask questions if anything in lecture is unclear.  Lectures will start promptly at 9:30 and run the entire 75 minutes.  I know it is early, but it is essential that you show up on time!

Unlike in other math classes you may have taken, we will not cover all details of the necessary material in lecture --- this course requires some independent reading and learning.  Homework will include reading assignments, and material from these reading assignments will show up on problem sets and exams. 

Discussion Sessions

Discussion sessions will be held Mondays 5:00-5:50 in Monroe Hall 116.  The discussion leader is Aron Daw (, who will also be grading your homework.  His office hours are Tu 2:00 - 3:00 and Thu 11:00 - 12:00 in Kerchof 119. 

The primary purpose of these sessions is to review/flesh out material from the previous week, as well as to correct any pervasive misconceptions arising from the homework.  Attendance at discussion sessions will be extremely useful, and is in any case mandatory.  If attendance is low, we reserve the right to take attendance at the discussion sessions (unannounced) and count absences against your participation grade.

I will also be running a problem session most weeks (see "Office Hours" below).


Multivariable Mathematics, 4th ed., by Richard E. Williamson and Hale F. Trotter.  This book will be available at the bookstore and a copy will be placed on reserve at Brown Library.


This is a course in multivariable calculus using the language of linear algebra.  It is meant to be a challenging course for students interested in mathematics and related sciences.  While we cover much of the same material as Math 2310, our pace will be faster, our problems will be more challenging, our presentation will be somewhat more conceptual, and there will be a more serious requirement to write basic proofs and justifications.

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 material here is immensely useful in physics, economics, probability, and higher math. One theme that will run through the last month 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.  The language of linear algebra (matrices, vectors, systems of linear equations) is the natural setting for multivariable calculus, so the first part of the class will cover the basics of linear algebra. 

In particular, we will cover most of Chapters 1 - 9 in Williamson and Trotter's book.  This is all of the material in Math 2310 plus some of the material in Math 3351.  We will also review complex numbers, and discuss some relevant basic principles of set theory and mathematical proof.

Math 3315 is the sequel to this course and will be offered in the Spring, however it is not mandatory to continue this course by taking Math 3315!  The Math 2315-3315 sequence covers more or less all the material in Math 2310, Math 3351, and Math 3250, and will exempt you from any requirements to take these classes.  Taking Math 2315 alone exempts you only from requirements to take Math 2310.

Expected Background: Math 1320 (with a grade of at least B+), a 5 on the BC Calculus AP, or international equivalent.

WARNING!!! This is a very fast-paced class, significantly faster than Math 1320 or Math 2310.  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 11:00-12:00, W 5:00-6:00.  The Tuesday office hour is a standard "drop-in" office hour held in Kerchof 208 (my office).  The Wednesday office hour will sometimes be a standard drop-in office hour in Kerchof 208, and will sometimes be more of a problem session where we can work problems that you or I select (room TBA).  The Wednesday sessions are optional, but you may find them very helpful.  If these times do not work for you, please make an appointment with me.

I will let you know each week whether there is a problem session or a regular office hour that Wednesday.  On Wednesday August 24th (the first week of class), it will be a regular office hour.


Homework will be posted on Collab on Thursdays.  Each homework assignment, in addition to a reading assignment, will consist of two parts:

1) A comprehension quiz that is due in my mailbox in Kerchof by 8:00pm on Mondays.  This will consist of straightforward problems meant to check your basic understanding of the material.  If you find the comprehension quizzes difficult/confusing, that is a sign that you should be coming to office hours/problem sessions/making an appointment with me to discuss!

2) The regular assignment that will be due Thursdays by 5:00pm in Aron's mailbox in Kerchof (you can also hand it to me in class if you wish).   Some of these problems are meant to be difficult --- don't be alarmed if you find them so!

Late homework will never 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, you must 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 Collab.


There will be a take-home midterm in lieu of a homework assignment due on October 12th at 5:00pm. 

The final exam will also be a take-home exam.  It will be posted on Collab on Friday, December 1st and will be due on Saturday, December 9th (the day the final exam for our class is scheduled) at 6:00pm.

For both exams, you may use your textbook, course notes, and old homework assignments, but no other sources (including people and internet)!  In particular, you may not work with classmates.

Final Course Grades

10% Comprehension quizzes
20% Homework
25% Midterm
40% Final Exam
5% Class participation


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.