Syllabus for Math 211: Honors multivariable calculus.
Fall 2009, Prof. Andrew Salch
Office: 412 Krieger
Office hours: 1:00 to 3:00 on Tuesdays
Classroom: Shaffer 303


General notes:



No late work will be accepted and there will be no makeups for any assignments or exams in this course.



Attendance is mandatory. You must come to class (this is what "mandatory" means), but since a professor telling you what you "must" do without mention of your grade is something of a meaningless gesture, I will give five five-minute quizzes in class throughout the course of the term. These will be unannounced and if you miss them, there will be no opportunity to make them up (just like any other assignment in the course). I will make sure that the quiz problems are relatively easy, and I will grade them leniently; the purpose of the quizzes is to give the more grade-oriented students among you some incentive to come to class consistently.



You should do the reading for a lecture before you come to class. You will need to see every idea in this class at least twice: once from the textbook, and once from me, during the in-class lecture. This will help you to absorb the material. If you feel that you are bored by seeing the same material more than once (especially since some of you will have already seen some calculus, in a high school class, for instance), this is not an indication that you already understand the material; in fact, it is an indication that you have an inadequate grasp of the course material, as there is so much depth and useful generalization to be made beyond the simple cases of calculus which we cover in this class that a student who truly understands the course material will not have an opportunity to be bored, because she or he will have so many further avenues to explore. I will give some examples of this during class lectures.



You have a weekly recitation which you will attend on Thursdays or Fridays; your recitation is run by the course TA, Peng Shao.



Each Wednesday, I will assign you a homework assignment, which you will turn in during your recitation of the following week (so you will have eight or nine days to work on each homework assignment). Each homework assignment will consist of a set of problems from your textbook, and possibly supplementary problems not in your textbook. I will mark one problem in each homework assignment as a problem which you should prepare to present at the board during that week's recitation. That problem will generally be a proof problem, rather than a computation. During each week's recitation, your TA will choose students randomly to present their proof for that week's assignment. It is not as important that your proof be correct as it is important that you try to prove it, so if there are problems with your proof, your TA can show you where you've stumbled and how to correct the problem.



No calculators are allowed on any test in the course. You should not use calculators to do the homework assignments, either--they are designed to be done without a calculator, and you will need practice solving them without a calculator, if you're going to do well on the exams. Occasionally you may find it useful, during a class lecture or outside of class, to use a graphing calculator to plot the graph of a function, as this can be faster and more accurate than doing it by hand; this can also be a good way to review what the graphs of some typical functions (y = tan x, y = ln x, etc.) look like. This is not a bad use for a calculator but be careful that you do not become dependent on a calculator even just for graphing functions, because you will need to know how to do that by hand on an exam, also.



Grading for the course is as follows:

Weekly homework	30%
In-class pop quizzes	10%
Midterm 1	15%
Midterm 2	15%
Final exam	30%

If you need help, try the following things, in approximately this order:
1. Read the relevant sections in your textbook. (If you know the phrase "RTFM" from computer science, it applies here.)
2. Did you read the relevant sections in your textbook? Make sure you did that.
3. See your TA. Your TA will have office hours during the week. During his office hours, you can come in and ask him questions about the class material; you don't need an appointment for this.
4. There is a "Math Help Room" at 213 Krieger. Its hours are 9 AM to 9 PM, Monday through Thursday, and 9 AM to 5 PM on Fridays. It is staffed by graduate students in mathematics who can help answer your math questions.
5. You can come to my office hours, but make sure you tried to answer your questions using the textbook first. My office is 412 Krieger, in a niche off of the stairwell at the west end of the fourth floor; I will announce my office hours for the semester during the second or third week of classes. Again, you are free to come in and ask questions during office hours, without making an appointment with me.
6. If you cannot make it to my usual office hours due to a scheduling conflict, you can email me or talk to me in person, and we can find a time to meet when you can ask me any questions about the class material that you may have; just email me and ask when I am free to make an office hours appointment with you.
7. Keep in mind that human beings took thousands of years to develop calculus. If you can't make sense of it in a single semester, this doesn't make you a dunce.



I will try to tell enough bad jokes in class to make up for the dire tone of this syllabus.



Our goal in this course is to cover the majority of the material from all eight chapters in your book, and in particular, section 7.4 on Maxwell's equations, and section 8.3 on the generalized Stokes' theorem; these sections cover some extremely powerful results that very important in pure mathematics, applied mathematics, physics, engineering, ... I will be making up our course schedule as we go along, so that we can fine-tune how much time we spend on each chapter in the book.



Your first midterm exam will be in class on Wednesday, October 7.

Your first homework assignment, due in your recitation on September 10 or 11: section 1.1, problems 3-4, 10, 14. Section 1.2, problems 4-7, 22-23, 33-34. Section 1.3: problems 5-8, 11-14. Proof problem: section 1.3, problem 18.

Homework assignment #2, due in recitation on September 17 or 18: section 1.3, problem 17. Section 1.4, problems 6-8, 10-12, 16-19. Proof problem: section 1.4, problem 22.

Homework assignment #3, due in recitation on September 24 or 25: section 1.7, problems 40,41. Section 2.1, problems 1-4,7,8. Section 2.2, problems 1-8,28,29,42,43. Section 2.3, problems 5-10. Proof problem: let X be a subset of R^n, and let C(X,R) be the set of continuous functions from X to R. Given two functions f,g in C(X,R), let f+g be the function defined by (f+g)(x) = f(x) + g(x), and given a real number r, let rf be the function defined by (rf)(x) = r(f(x)). Prove that these two operations make C(X,R) into a vector space. For next week, read sections 2.1-2.4.

Homework assignment #4, due in recitation on October 1 or 2: section 2.3, problems 30-33. Section 2.4, problems 9-12,20,21 (skip parts where you are asked to graph something). Section 2.5, problems 6-7, 23-24. Section 2.6, problem 14-15. Proof problem: section 2.6, problem 25.

Homework assignment #5, due in recitation on October 8 or 9: no homework this week, just study for your midterm exam.

Homework assignment #6, due in recitation on October 22 or 23: section 3.1, problems 9-10,17-18. Section 3.2, problems 1-4,12,15-16. Section 3.3, problems 18-24. Proof problem: section 3.1, problems 27-28. For next week, read sections 3.1-3.4.

Homework assignment #7, due in recitation on October 29 or 30: section 3.4, problems 3-10. Proof problem: section 3.4, problem 16. For next week, read chapter 4.

Homework assignment #8, due in recitation on November 5 or 6: section 4.1, problems 10-15. Section 4.2, problems 13-16,22,23,32. Section 4.3, problems 3-6,17,19. Section 4.4, problems 1,7-9. Proof problem: section 4.2, problem 46. For next week, read sections 5.1-5.3.

Homework assignment #9, due in recitation on November 12 or 13: section 5.2, problems 12-15,22-23. Section 5.3, problems 14-15. Section 5.4, problems 6-7,11-12. Proof problem: section 5.2, problem 17. For next week, read sections 5.5, 6.1-6.3.

Homework assignment #10, due in recitation on November 19 or 20: section 5.5, problems 9-12. Section 6.1, problems 4-7. Section 6.2, problems 7-8, 14-15. Section 6.3, problems 16-17. Proof problem: section 6.1, problem 23. For next week, study for your second midterm.