M408S, Integral Calculus for Scientists

**Unique numbers**: 56095, 56100, 56105
**Lectures** TuTh 9:30-11:00, CPE 2.214
**Discussion Sections**:

56095: MW 12-1, RLM 5.122

55645: MW 1-2, RLM 5.118

55650: MW 3-4, RLM 5.116
**Web page**:
http://www.ma.utexas.edu/users/sadun/S13/M408S
**Professor**: Lorenzo Sadun, RLM 9.114, x1-7121,
sadun@math.utexas.edu
**Teaching Assistant:** TBD
**Sadun office hours**: TBD. 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
(The UT custom edition from a couple of years ago is missing chapter 9,
of which we'll be doing a couple of sections)
**Prerequisites**: This class is restricted to students
in the College of Natural Sciences who have passed M408N (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:** Sections 5.3-5.5 (integrals), 6.1 and 6.2 (volumes),
7.1-7.5 and 7.8 (methods of integration), 9.3 and 9.4 (improper integrals),
11.1-11.11 (sequences and series), 14.3 and 14.4 (partial derivatives)
and 15.1-15.3 (multiple integrals). Most of the time will be spent on
chapters 7 and 11.
You can find an online day-by-day
schedule here. This course carries the
Quantitative Reasoning flag. Quantitative Reasoning courses are
designed to equip you with skills that are necessary for understanding
the types of quantitative arguments you will regularly encounter in
your adult and professional life.
**Six pillars:** 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!

M408N was mostly about the first three pillars, with a little bit about #4
and #5 at the end. M408S is about pillars 1, 4, and 5, with a little
bit about #6 at the end. M408M is all about pillar 6.

**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?", and plenty of students
get 5's on the AP exams without ever understanding what they're actually
doing. **College calculus is different!**
We'll study techniques of integration and tests for convergence,
but we'll also study what convergence means, what an integral is, and
what integrals are good for.

When you understand
those ideas, and think about how each new formula or technique
follows from those ideas, then everything will become much, much easier.

**Hybrid classes:** As with M408N, this class will use a variation
on the ``flipped" classroom.
We will provide you with a variety
of online learning resources, all on Quest. Some of these are prepared by
yours truly, and some by Elizabeth Stepp using videos from MIT and elsewhere.
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 work on more traditional homework, both
written and online.

Last semester was the first time that I taught in this manner. In
terms of student outcomes, it was the most successful of my 20+ years
of teaching calculus. The failure rate was tiny, and the combined failure/drop
rate was *less than half* of what used
to be typical of CNS students taking calculus.
In terms of student satisfaction, however, it was a disaster, and my students
gave me the worst student evaluations I have every received for
teaching calculus.

Our job this semester is to find a way to bridge the gap, and to make
learning calculus both effective and pleasant. I am open to suggestions
on ways to make the class better, bearing in mind that

1. There will be a lot of homework.

2. There will be a lot of theory, in addition to ``how do you compute it''
drilling.

3. Lecture will be an active learning environment, not a place to sleep
while I drone on. However, there are many good ways to do active learning.
Please share any ideas that you may have.

4. Exams serve a different purpose from homework, and will not resemble
homework. Homework is to help you learn. Exams are for me to see if you did.

**Discussion sections:** These are not just glorified office hours.
This is where you'll get the written homework, start working on it,
and (the following week) turn it in. Attendance *is* required.
**Homework (20% 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 (8%)**: 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 (4%)**: 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.)
Unlike last semester, these are embedded within the
relevant online learning modules, and may also require reading
the relevent section of the book.
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 (8%)**: 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**:
Cheating is dishonorable and disgusting, and on an evolutionary scale,
cheaters lie somewhere between tapeworms and cockroaches.
Most students are honest, and honest students do not like cheaters, and
they do report what they see. If you are caught cheating, you will be
penalized as harshly as possible under the rules of UT. Do not cheat.

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 two in-class midterm exams, on
Thursday February 21 and Thursday March 21 (shortly before drop day),
plus a final exam on Monday morning, May 13, 9-12.
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 25%. The final exam counts 30%.
The homework, taken together, counts 20%. 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 be 20% homework, 25% the other midterm, and
55% final.) If you do badly on (or miss) both midterms,
you're out of luck. The final exam **will not substitute**
for the homework grade, 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 can't do anything new.
A "C" means that you understand the techniques of the class well enough
to handle a class (such as M408M) that has M408S 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 M408M, 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*
much more lenient than that, but each semester is unique. Last semester
I only gave 2 Fs and 4 Ds, because 94% of the students who took the final
really did know the material at a C- level or better. Let's see if we can
duplicate that success this semester.
**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 January 30. After that date, a "Q" will
appear on your record. The deadline for dropping, period, is April 1.
**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.