M408M, Multivariable Calculus

Unique numbers: 53010, 53015

Lectures TuTh 11:00-12:30, CPE 2.214

Discussion Sections:
56620: MW 8-9, WRW 113
56630: MW 2-3, CPE 2.220

Web page: http://www.ma.utexas.edu/users/sadun/F15/M408M

Professor: Lorenzo Sadun, RLM 9.114, x1-7121, sadun@math.utexas.edu

Teaching Assistant: Yanlin Cheng yanlinch@math.utexas.edu

Sadun office hours: M3-4, W10-11. I generally keep an open door and welcome visitors at all times.

TA and LA'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 M408D or 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 M408D/L/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.

M408C/K/N was mostly about the first three pillars, with a little bit about pillars 4 and 5 at the end. M408D/L/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: Much of the time you'll be working in groups on worksheets and weekly written homework. Since this is where you'll be turning in all your written work, 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 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.
Written work (10%): There are several kinds of written homework assignments. There will be a weekly list of problems from the text, which you should turn in at the beginning of discussion on Monday (Wednesday if Monday is a holiday). There will also be worksheets distributed in lecture and discussion. Some are meant to be worked in class. Others are meant to be started in class and turned in the next day. Written work is best done in teams of up to four people, all from the same discussion section. Put all four names at the top of the page, and all four of you will get credit. This is supposed to be collaborative, not division of labor. Four people should talk about problem 1 and have somebody write it up, then four people should talk about problem 2, etc. Saying ``I'll work problem #1 while you do #2 and you do #3 and you do #4.'' is not OK. Every member of the team should be prepared to explain every answer that's submitted. At the end of the semester I will drop 10% of your weekly homeworks and 10% of your worksheets, rounded up. (E.g. if there are 11 or more weekly homeworks, I'll drop 2, but if there are 10 or fewer I'll only drop 1.) See hw.html for the latest information on written homework.
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 (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.) 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 (6%): 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 two in-class midterm exams, on Thursday October 8, and Thursday, November 12, plus a final exam on Wednesday December 9, 2-5. 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 based on 25% for the other midterm and 55% 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 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 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 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.