Last modified 16 May 2001 by

Math 234, Sections 301, 302, 311, 312

  1. News
  2. Introduction
  3. Course Requirements
  4. Contact Information
  5. Quiz and Exam Results
  6. Friendly Advice
  7. Extra Stuff
  8. Homework Assignments



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.

Course Requirements

Grades for this course will be based on the following components:
  1. Three 50-minute quizzes, given in lecture during the semester (26 February, 2 April, and 27 April), each worth 20% of the course grade.
  2. 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.

Contact Information

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.

Quiz and Exam Results

Here are the results. Come talk to me if you're looking for ways to improve your grade on the coming exams.

GradeQuiz 1 (26 Feb)Quiz 2 (2 Apr)Quiz 3 (27 Apr)
Score RangeNum. StudentsScore RangeNum. StudentsScore RangeNum. Students

Friendly Advice

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:

  1. First, discuss the material with your classmates, me, or the professor.
  2. 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.
  3. 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.
  4. 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.
  5. 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.

Extra Stuff

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.
  1. For every person P, there exists a person M such that M is P's mother.
  2. There exists a person M such that for every person P, M is P's mother.
  3. For every (living) American A, there exists an American P such that P is A's president.
  4. There exists an American P such that for every (living) American A, P is A's president.
  5. For every number X, there exists a number Y such that Y2 = X.
  6. For every number X > 0, there exists a number Y such that Y2 = X.
  7. For every number X, there exists an integer N such that if Y > N then Y > X.
  8. 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.)
  9. 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.)
Here are the answers and explanations:
  1. This says that every person has a mother. That's true. Isn't calculus easy?
  2. 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.
  3. 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.
  4. 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.
  5. This says that every number has a (real) square root. Unfortunately, this is not true of negative numbers. So the statement is false.
  6. This repairs the previous statement to make it true.
  7. 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.
  8. 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?)
  9. 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...
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.

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.