M408M, Multivariable Calculus

**Unique numbers**: 56620, 56625, 56630
**Lectures** TuTh 9:30-11:00, CPE 2.208
**Discussion Sections**:

56620: MW 8-9, RLM 5.116

56625: MW 1-2, RLM 5.120

56630: MW 3-4, RLM 5.118
**Web page**:
http://www.ma.utexas.edu/users/sadun/F13/M408M
**Professor**: Lorenzo Sadun, RLM 9.114, x1-7121,
sadun@math.utexas.edu
**Teaching Assistant:** Iordan Ganev iganev@math.utexas.edu
**Sadun office hours**: MW2-3. I generally keep an open
door and welcome
visitors at all times.

**Iordan's office hours:** (Thanks to a truly idiotic interpretation
of federal privacy rules, UT says I'm not allowed to list this yet.)
**Textbook (required):** Calculus, Early Transcendentals,
by Stewart, 7th edition
**Prerequisites**: This class is restricted to students
who have passed M408L or M408S (or equivalent)
with a grade of C- or better.
If you do not meet these conditions, you will be dropped
from the class.
**Calculators and computers**: A basic scientific calculator
may be useful for checking your homework, but you don't need a fancy
programmable graphing calculator. (You can also check your work with
Wolfram Alpha or something similar.) However, calculators and other
electronic aids are **not allowed on exams**, so get
used to doing most of your work by hand! (You'll learn a lot more
doing things yourself than relying on technology.)
**Syllabus:** Chapters 10 (parametric equations), 12 (vectors),
13 (vector-valued functions), 14 (partial derivatives) and the first half of
15 (multiple integrals), with occasional sections skipped.
Some of the material in chapters 14 and 15 is review from M408L/S.
You can find an online day-by-day
schedule here. This course carries the
Quantitative Reasoning flag.
**One variable at a time!** Calculus has a reputation of being a
hard class
that features a million different equations to be memorized. There **are**
a lot of formulas and techniques, but almost everything boils down to
six simple ideas, which I call the **six pillars of calculus**:

1. Close is good enough (limits)

2. Track the changes (derivatives)

3. What goes up has to stop before is can come down (max/min)

4. The whole is the sum of the parts (integrals)

5. The whole change is the sum of the partial changes (fundamental theorem)

6. **One variable at a time.**

M408K/N was mostly about the first three pillars, with a little bit about
pillars 4
and 5 at the end. M408L/S was about pillars 1, 4, and 5, with a little
bit about pillar 6 at the end. **M408M is all about pillar 6.**
Almost everything
in this course can be done by isolating one input variable and one output
variable and applying what you learning in the first two semesters of
calculus.

**Three questions:**
There are three questions associated with every mathematical topic you
ever will see.

1. What is it?

2. How do you
compute it?

3. What is it good for?

Most of high school
calculus is about "how do you compute it?"
This class will put a much greater emphasis on conceptual understanding
and applications than you're probably used to.

**Classroom procedure:**
We will provide you with a variety
of online learning resources, all on Quest, keyed to sections of the book.
These learning modules were prepared by
yours truly, borrowing heavily from John Gilbert's online text for M427L.
The book is also an essential resource.
You are expected to study the material and
complete a fairly easy preclass assignment *before* lecture.
Then, in a typical lecture session, we will discuss what you've studied
(bring questions!) and
you will work in teams on harder and more thought-provoking problems,
while the learning assistants
and I circulate and talk with you about them. After lecture, and
in discussion section, you will have both
written and online homework to do.

**Discussion sections:**
This is where you'll get the written homework, start working on it,
and (the following week) turn it in. Attendance *is* required, and
part of your grade is based on participation.
**Homework (13% of course grade)**:
You should expect to spend 8-10 hours/week outside of class
on calculus. Of that, roughly half is pre-class preparation (reading, watching
videos, and doing the pre-class assignments) and half is post-class (online
and written homework).

**No late work** will be accepted for any reason.
As noted below, we will
drop some of the assignment scores to allow for legitimate reasons for
not turning in an assignment (left it at home, computer crashed the
night the Quest was due, Quest crashed at the last minute, ill with
the flu, didn't get the assignment in time, didn't know the due date,
did the wrong assignment, family emergency, etc.) Please do not ask
if we will accept a late assignment. We will not.

**Written work (5%)**: At the beginning of each discussion section,
you will be given a written assignment consisting of several interesting and
challenging problems. You will work in class on one or more of these
problems, as directed by the TA, during the discussion. You will
continue to work outside of class on these problems, and then your
carefully written solutions will be collected at the beginning of the
first discussion on Monday of the following week. Some of the
problems will be graded. In order to receive credit, you must put
your name and unique number and time of your discussion section at the
top of the page and show all of your work. Your exercises must be
well-labeled, neat, and in order, and the work must be stapled.
Above all, your assignment must be turned in *before*
the discussion begins.
There will be approximately a dozen such weekly assignments; we will drop
the lowest two.

**Online work**: Our online content delivery system is called Quest, which
can be accessed by going to the page at https://quest.cns.utexas.edu/,
logging in, and selecting this class. You will be charged a
one-time $25 fee to use this service, which is mandatory for this
class. There are approximately 25 of each of two types of online
assignments for this class; the lowest 5 scores of each will be dropped.

**Preclass/Learning Modules (3%)**: There will be online
homework assignments due
at midnight the night before each class,
except for exam days and the first day of the semester. (The learning
module for the first day is due the afternoon of the first day.)
The problems in the preclass assignment are intended to be easy, and to get
you ready to learn the material in more depth in lecture.

**Postclass (5%)**: Quest postclass assignments will
summarize the material discussed during class, and will be due at 6pm
the day before the subsequent class (Monday and Wednesday). These will typically
be longer and harder than the preclass assignments.
**Academic honesty**: The University is a place of honor and mutual
respect, and students deserve to be treated with courtesy and trust.
However, betraying that trust is dishonorable and unforgivable.
On an evolutionary scale,
cheaters belong somewhere between tapeworms and cockroaches.
If you are caught cheating, you will be
penalized as harshly as possible under the rules of UT.
Most students are honest, honest students do not like cheaters, and
they do report what they see.

On homework, there is a fine line between collaboration
(which is *encouraged*) and cheating.
The more you explain your reasoning to others, the clearer it will be to you!
In the end, however, you are expected to only turn in what you personally
worked and checked.
Learning from your friends is fine; blindly copying their answers,
or getting Wolfram Alpha to do your homework, is not. When in doubt,
consult your conscience.

**Exams:** There will be three in-class midterm exams, on
Thursday September 26, Tuesday October 29 (shortly before drop day),
and Thursday, November 21, plus a final exam on Saturday evening,
December 14, 7-10. These exams will all
be closed book and calculators will **not** be allowed.
However, each student will be allowed to bring a single
letter-sized
``crib sheet'' (2-sided) to each midterm, and 2 crib sheets to the
final.
These notes must be __HANDWRITTEN ORIGINALS - NO XEROXING ALLOWED__.
**Participation: (7%)** Part of your grade will be based on participation
in lecture and discussion. A few times during the semester you may be called
upon, by name, to answer a question or present a solution to a problem.
You will be graded on a 4-point scale:
- 4 points for answering well or giving a good presentation.
- 3 points for a so-so response.
- 2 points for choosing not to answer or present, or for doing a
very poor job, and
- 0 points for being absent.

If you need to miss class for an excused reason (e.g., a religious holiday),
let me or Iordan know in advance and we won't call on you.
**Grading:** Each midterm counts 20%. The final exam counts 20%.
The homework, taken together, counts 13%. Participation counts 7%.
If you do badly on a midterm,
or miss a midterm for any reason, then I
will substitute the final exam in its place. (E.g., if you bomb one
midterm, then your grade will based on 20% each for the other midterms
and 40% for the final.) If you do badly on (or miss) both midterms,
you're out of luck. The final exam **will not substitute**
for the homework and participation grades.

The final grade distribution is neither a straight
scale nor a fixed curve. The cutoffs will be set at the
end of the semester, based on overall class performance, with the
following qualitative standard for the major grades (with obvious
adjustments for plusses and minuses):
An "A" means that you understand the ideas of the course well enough
that you can use them even in unusual settings.
A "B" means that you can do the standard problems we have done during
the semester, but struggle with novel applications.
A "C" means that you understand the techniques of the class well enough
to handle a class that has M408M as a prerequisite.
A "D" means that you have learned a substantial amount, but that you are
not prepared to take that successor course.
An "F" means that you have failed to grasp the essential
concepts of the course.

Grading isn't an exact science, and with one exception
I'm only going to adjust
cutoffs. (The exception is that, if you are close to the C-/D cutoff, and
if you demonstrate on the final
that you know enough to handle a successor course, then I will give you a
C- for the class. This exception
will affect at most a couple of people.)
Aside from that exception, nobody will leapfrog anybody else;
if you have more points
than your buddy, then your grade will be at least as good as your
buddy's.
Furthermore, a 90% average **will** guarantee you at least an A-, an 80%
average a B-, and a 70% average a C-.

My cutoffs are usually
more generous than that, but each semester is unique.
**Disabilities: **
The University of Texas at Austin provides upon request appropriate
academic accommodations for qualified students with disabilities. For
more information, contact the Office of the Dean of Students at
471-6259, 471-4641 TTY
**Drop dates:** The deadline for dropping the class without the course
appearing on your transcript is September 13. After that date, a "Q" will
appear on your record. The deadline for dropping, period, is November 5.
**Religious Holidays:** I have tried to schedule major class
events to avoid religious holidays, and I apologize if I overlooked
something. If you expect to miss class
or miss an assignment because of a religious holiday, please let me
know 14 days in advance, and you will be given the opportunity to make
up the missed work within a reasonable time.