Advanced Calculus and Linear Algebra I, Fall 2017
Instructor: Andrew Obus
email: obus [at]
virginia [dot] edu
office: Kerchof Hall 208
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 SessionsDiscussion sessions will be held Mondays 5:00-5:50 in
Monroe Hall 116. The discussion leader is Aron Daw (email@example.com),
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
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
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.
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
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
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.
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
we can work problems that you or I select (room TBA). The Wednesday sessions
but you may find them very helpful. If these times do not work for you, please make an appointment
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
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
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
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
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
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
Some Useful Links
Virginia Undergraduate Math Page
University of Virginia Math
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