M408D, Integral and Multivariable Calculus

**Unique numbers**: 53088, 53089
**Lectures** MWF 9-10, CPE 2.208
**Discussion Sections**:

53088: TuTh 1-2, NOA 1.126

53089: TuTh 8:30-9:30, NOA 1.102
**Web page**:
http://www.ma.utexas.edu/users/sadun/S16/M408D
**Professor**: Lorenzo Sadun, RLM 9.114, x1-7121,
sadun@math.utexas.edu
**Teaching Assistant:** Robin Neumayer rneumayer@math.utexas.edu
**Sadun office hours**: Tu10-11, Th2-3. I generally keep an open
door and welcome
visitors at all times.

**TA 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 M408C with a grade of C- or better, or have tested out of
M408C.
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 7 (methods of integration), 9 (differential equations), 10 (parametric equations), 11 (power series),
part of Chapter 14 (partial derivatives) and the first half of
Chapter 15 (multiple integrals), with some sections skipped.
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.

M408C was mostly about the first three pillars, with a little bit about
pillars 4
and 5 at the end. M408D is about pillars 1, 4, and 5, with a little
bit about pillar 6 at the end.

**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.
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 I circulate and talk with you about them. After lecture, and
in discussion section, you will have online homework to do.

**Discussion sections:**
Much of the time you'll be working in groups on worksheets. This is where you
get to explore topics in more depth than in lecture.
**Homework (15% 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
homework).

**No late work** will be accepted for any reason other than
religious holidays.
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.

**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 $30 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 4 scores of each will be dropped.

**Preclass/Learning Modules (5%)**: 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 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 (10%)**: Quest postclass assignments will
summarize the material discussed during class, and will be due at 6pm
the day before the subsequent class (Sunday, Tuesday and Thursday).
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 submit 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
Friday February 19, Friday April 1,
and Monday, May 2, plus a final exam on Saturday
May 14, 7-10 PM. 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__.
**Grading:** Each midterm counts 20%. The final exam counts 25%.
The homework, taken together, counts 15%.
There will not be any makeup exams.
However,
the final exam may substitute for **one** midterm if that improves your
average. That is,
if you do worse on a midterm than on the final,
or miss a midterm **for any reason**, then I
will substitute the final exam in its place. (E.g., if you bomb one
midterm, or if you are sick for a midterm,
then your grade will based 20% on each of the other midterms
and 45% for the final.) If you do badly on (or miss) two or more midterms,
you're out of luck. The final exam **will not substitute**
for the homework grades, so do your homework and rack up points the easy way!

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 M408D 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 11. After that date, a "Q" will
appear on your record. The deadline for dropping, period, is November 3.
**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. This is the **only**
exception to the ``no late work'' rule.