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.