**Instructor:** Jeffrey
Diller (click for contact info)

**Office hours: **Wednesdays
5(ish)-6:30 PM in the math
bunker and by appointment.
Please take advantage also of the help sessions (also held in the
math library's math bunker) from 7-9 every evening Sunday through
Thursday.

**Official Time and place:** MWF 11:30-12:20 AM in Pasquerilla
116, Th 3:30-4:20 in Pasquerilla 109.

**Textbook: ***Multivariable
Mathematics* by Theodore
Shifrin. I put a few other textbooks on reserve in the math library,
and you might look at these for alternative explanations/more
examples, etc. However, I'd especially like to draw your attention to
two very good online sources: Linear
Algebra Done Wrong by Sergei Treil (deals only with linear
algebra), and some very cool online
vector calculus notes by Frank Jones (which cover roughly the
same material as Shifrin).

**What the course covers:** I'll devote the first week to the
inverse and implicit function theorems, which concern solutions of
non-linear systems of equations. The second week, I'll talk about
determinants. Possibly I'll spend a week on eigenvalues and
eigenvectors, too. After that it's all integration, first on
rectangles and other open subsets of R^n, then on parametrized curves
and surfaces. We'll see the usual classical integral theorems
(Green's, Stokes', Gauss') in dimensions two and three and in
particular the fact that they are all variants on the same much more
general theorem (generalized Stokes' Theorem). This will require us
to become acquainted with the linear algebra and calculus of
`differential forms'. We'll deal with applications as time permits.

**How you will be evaluated:**

**Homework**:
assigned and collected each Friday, together with quizzes worth 40%
of your grade. Homework is the most important part of this course. I
urge you to start each assignment the day after I post it, and to
take a lot of care in writing up your solutions. I strongly encourage
you to work on homework with other students, and you are welcome to
turn in joint homework solutions with up to two other students in the
class. Collaborating with other people is an important skill in
mathematics and also tends to make it all more fun. There is one
exception to this: occasionally I give out extra credit problems. On
these, I expect you to work alone and turn solutions in to me apart
from other homework.

**Two in-class
midterm Exams:** Thursday 2/25 and Thursday 4/7; each worth 15%. of
your grade.

**Final Exam:**
Monday May 2 from 4:15-6:15 PM in TBA, comprehensive and worth 30% of
final grade.