Last modified 16 May 2001 by email@example.com
Math 234, Sections 301, 302, 311, 312
- Course Requirements
- Contact Information
- Quiz and Exam Results
- Friendly Advice
- Extra Stuff
- Homework Assignments
- 16 May: The final grades have been determined. E-mail me if you want to know yours. Have a good summer!
- 12 May: Just a reminder: The final is on Monday 14 May 2001, from 2:45 to 4:45 PM, in room B102 of Van Vleck Hall.
- 9 May: The review session will be on Sunday from 12:25 to 2:25 in Sterling 3335. (Sterling is the physics building, next to Van Vleck.)
- 7 May: This week in discussion I will be reviewing the most important definitions and theorems of the semester. My office hours this week will be very unusual: Tue 11:00-11:50 and 2:25-3:15, Wed 11:00-11:50, Thu 12:05-12:55, Fri 10:00-12:00, Sat 10:00-12:00. I will be holding a review session, in which you can once again barrage me with questions, on Sunday from 12:25 to 2:25. The place will be announced later. The final exam is on Monday (see below).
- 2 May: I have posted the quiz grades below.
- 30 Apr: This week in discussion I will hand back the quizzes and we will discuss Section 14.9.
- 23 Apr: I will be hosting a review session on Thursday, from 6:00 to 8:00 PM, in B239 Van Vleck. Bring many questions. Note that this Friday's quiz covers Sections 14.1-14.8. Also, I will be holding extended office hours this week in preparation for the quiz: Tue 11:00-12:55, Wed 11:00-11:50 and 1:20-2:10, and Thu 11:00-12:55. On the other hand, I will be cancelling my usual Friday office hour this week.
- 23 Apr: This week in discussion we will wrap up 14.6 and cover 14.7 and 14.8.
- 16 Apr: This week in discussion we will cover 14.4, 14.5, and some of 14.6. Note that the next quiz is on Friday 27 April in class.
- 9 Apr: This week in discussion we will cover 14.2 and 14.3.
- 3 Apr: The grade distributions for the second quiz have been posted below.
- 2 Apr: This week in discussion we will be reviewing the quiz and writing TA evaluations. If time permits, we might actually learn some new math (that is, 14.1).
- 27 Mar: The review session will be Saturday 31 March, 1:00-3:00 PM, in B239 Van Vleck. We will begin by discussing Section 13.9. Then we will discuss miscellaneous questions. Bring your questions!
- 27 Mar: I will be holding extended office hours this week in preparation for the second quiz: Tue 11:00-12:55, Wed 11:00-11:50, Thu 11:00-12:55, Fri 11:00-11:50 and 2:25-3:15, Sat after the review session, and Sun 1:00-3:00.
- 26 Mar: This week in discussion section we will cover 13.6, 13.7, and 13.8. I suspect that we will have to delay discussion of 13.9 until the review session on Saturday.
- 23 Mar: The second quiz (on April 2 in class) will cover Sections 12.8-13.9. News on the review session and extended office hours will come later.
- 19 Mar: This week in discussion section we will wrap up 13.3 and discuss 13.4 and 13.5. If time permits, we could also cover 13.6, which is very short.
- 27 Feb: Grades for the first quiz have been announced. There were many high grades. See below.
- 15 Feb: I do not plan to hold a group review session for the 26 February quiz, but I am announcing extensive office hours leading up to it. Although I may leave the office temporarily, I should be available to talk during the following times, beginning Monday 19 February: Mon 11:00-11:50, Tue 11:00-12:55, Wed 11:00-11:50, Thu 11:00-12:55 and 4:00-4:50, Fri 11:00-11:50 and 2:25-3:15, Sat 1:00-3:00, Sun 1:00-3:00.
- 8 Feb: I have posted the questions from our little logical game below. Next week I intend to spend the entire time answering homework questions from students.
- 5 Feb: An extra Math Lab hour in the Red Gym has been noted below.
- 2 Feb: The second quiz is set for 2 April. The quiz/exam policy is outlined below.
- 26 Jan: Today it was announced that the first quiz will be on 26 February, in lecture.
- 25 Jan: My office hours have been determined; see below.
- 23 Jan: For next week, you should have questions prepared from the homework in Sections 11.7, 11.8, and 11.9.
Mathematics 234 is third-semester calculus. In this course, vectors are used to extend the basic concepts of calculus (limit, continuity, derivative, integral) to higher-dimensional settings, where they form the underlying geometric language for diverse mathematical disciplines including physics, engineering, and economics. Our textbook is Stewart's Calculus: Early Transcendentals, Third Edition. We will draw material from Chapters 11, 12, 13, and 14.
This web page will be updated occasionally with the results of quizzes, extra explanations of problems, and other important news.
Grades for this course will be based on the following components:
- Three 50-minute quizzes, given in lecture during the semester (26 February, 2 April, and 27 April), each worth 20% of the course grade.
- One 2-hour final exam, to be given on Monday 14 May 2001 from 2:45-4:45 PM, worth 40% of the course grade.
On the quizzes and the exam, any kind of calculator is allowed. On the other hand, "cheat sheets" with formulas, etc. will not be allowed.
If for some reason you are unable to take the final exam at the appointed time, you must notify me as soon as possible. "I want to leave early for vacation" is not a valid reason.
Note that homework and attendance are not counted in the grading process. On the other hand, you will find the homework useful in learning the course material. Furthermore, I expect students to come to every discussion section ready to discuss mathematics, so you will have to work consistently. Review your lecture notes, read the relevant book sections, and then do the homework problems. Homework is assigned at Prof. Slemrod's 234 web page.
The professor is Marshall Slemrod. Here's how to reach him:
I am your teaching assistant, Joshua Davis. (Call me Josh.) I am a third-year graduate student in mathematics. Here's how to reach me:
If you want to make an appointment with me, check out my weekly schedule, pick a free slot, and e-mail me.
Here are the results. Come talk to me if you're looking for ways to improve your grade on the coming exams.
|Grade||Quiz 1 (26 Feb)||Quiz 2 (2 Apr)||Quiz 3 (27 Apr)
|Score Range||Num. Students||Score Range||Num. Students||Score Range||Num. Students
In Math 234, students are expected to exhibit a higher level of maturity, both personal and mathematical, than in lower math courses.
You have been given freedom over homework and attendance because it is recognized that you sometimes have other things to do (illness, dental appointments, vacations, washing the dog) that cause you to miss a day or two, and because you know your learning style better than the teachers do. The lack of daily course requirements means that you will have to be self-motivated. Review your lecture notes, read the textbook, and complete the homework diligently.
If you do fall behind, try to catch up as quickly as possible. Whereas Math 222 is an assortment of widely varying topics, Math 234 is very cohesive. Concepts build on each other, and rapidly. Don't wait around for the topic to change; when it does, it will probably refer back to the old topic extensively.
Speaking of old topics: If you can't explain terms like limit and derivative off the top of your head, then go back to the beginning of the book and review. When we start moving into two, three, and more dimensions, you'll want to be very comfortable with the old 1-dimensional case.
The course material is very geometric. When you read your notes and your textbook, try to visualize what is going on. Explain each concept to yourself in English (or your native language). Then ask a classmate to explain it. Your explanations could be quite different; try to reconcile them. In doing so, draw pictures and gesture wildly with your hands.
If you find yourself wanting help in this course, there are various options:
- First, discuss the material with your classmates, me, or the professor.
- The Department of Mathematics runs a "Math Lab" in B227 Van Vleck, Monday through Thursday, 3:30-5:10 and 6:30-8:10 PM. There is also a Math Lab session on Wednesdays, 6:30-8:10 PM in the Multicultural Students Center (on the second floor of the Red Gym.) Math 234 students can drop in for help from miscellaneous math teaching assistants.
- The Greater University Tutoring Service (GUTS) provides volunteer tutors for a variety of classes, and can also help with study skills and English speaking skills.
- Apparently, tutoring is available through the College of Engineering; I don't know much about that. Maybe it's the stuff mentioned on Prof. Slemrod's page.
- The Department of Mathematics maintains a list of tutors that you can hire for one-on-one tutoring sessions. See the department receptionist on the second floor of Van Vleck Hall.
Limit Logic Game
The following exercise is intended to help students understand complicated logical sentences like the one involved in the definition of limit. For each statement below, evaluate whether it is true or false. "Number" is always taken to mean "real number", and "<=" means "less than or equal to". Answers follow.
Here are the answers and explanations:
- For every person P, there exists a person M such that M is P's mother.
- There exists a person M such that for every person P, M is P's mother.
- For every (living) American A, there exists an American P such that P is A's president.
- There exists an American P such that for every (living) American A, P is A's president.
- For every number X, there exists a number Y such that Y2 = X.
- For every number X > 0, there exists a number Y such that Y2 = X.
- For every number X, there exists an integer N such that if Y > N then Y > X.
- There exist numbers C and D in the closed interval [A, B] such that for all X in [A, B], F(D) <= F(X) <= F(C). (Warning: This statement will be true for some functions F and false for some others.)
- For every number E > 0, there exists a number D > 0 such that if 0 < distance(X, C) < D then distance(F(X), L) < E. (Hint: Usually E is called epsilon and D is called delta.)
Note that Statement 9 is similar in form to Statement 7 (and, to a lesser degree, Statements 1, 3, 5, and 6). In Statement 7, we are given an X, and we must find an N based on that X. For X = 3.14, we could choose N = 4, 5, 1734, etc. But for X = 20500.327, N = 4, 5, and 1734 won't work; we must choose a bigger N, such as N = 20501. Valid values of N depend on the value of X given, just as the mother M in Statement 1 depends on the person P we're talking about.
- This says that every person has a mother. That's true. Isn't calculus easy?
- This says that there is a person M who is a mother to everyone; that is, everyone has the same mother. That's false. In Statement 1, the mother M depended on the person P we were discussing; in Statement 2, there is a fixed mother, not dependent on the person P. This is the key difference.
- This says that every American has a president. Ignoring for the moment any doubts you might have about the 2000 election, this is true. It's very much like Statement 1.
- This says that every American has the same president. It's very much like Statement 2, but unlike Statement 2 it's true, because the president is unique.
- This says that every number has a (real) square root. Unfortunately, this is not true of negative numbers. So the statement is false.
- This repairs the previous statement to make it true.
- No matter where you are on the real number line, there is always some integer to the right of you; any number greater than this integer must be greater than you as well. The statement is true.
- First we must understand what the statement is trying to say about F. It is saying that there exist X-values C and D where F achieves a maximum and a minimum, respectively. So we must ask ourselves: Is it always true that a function F achieves a maximum and a minimum on [A, B]? Check out the Extreme Value Theorem on page 255 of our textbook. It tells us that Statement 8 is only guaranteed to be true when F is continuous. Note also that it is crucial that the interval be closed. (Why?)
- You should recognize this as the definition of limit. To be precise, this statement says exactly, "The limit as X goes to C of F(X) is L." Discussion follows...
Similary, to show that the limit of F(X) is L (at X = C), we must be able to produce a suitable D for any given E. In practice, we do this by analyzing the particular function F in question, to understand how a change of size D in the input produces a change of size E in the output. If the limit really does equal L, then we should be able to express D as a function of E, so that, whenever someone gives us an E, we can spit out a D that makes the statement work.
On the other hand, if the limit does not equal L, then there will be values of E for which there are no corresponding D values to make the statement work. That is, we will not be able to make a change in the output small just by making a change in the input small.
If you have suggestions for improving this exercise (such as good new statements), please e-mail me.