Math 233 Spring, 2017





Instructor: Steven G. Krantz

Textbook: Calculus Multivariable, by Brian E. Blank and Steven G. Krantz, second edition, John Wiley and Sons, New York, 2011.

Office: 103, Cupples I

Office Hour: Monday, Wednesday, Friday 2:00pm-3:00pm.

Phone: (314) 935-6712


Personal Web Address:

Class Web Page: The class Web page is

You can also just go to my personal Web page (above) and click on the button

for Math 233.

Dept. Office: 100, Cupples I

Dept. Phone: (314) 935-6760


Course Description: The purpose of this course is to introduce you to the calculus of several variables. This is different from calculus of one variable, just because it is very geometric. Learning this material will entail vector language and techniques as well as 2- and 3-dimensional geometry. The culmination of the course will be Green's theorem.

The course will follow the text rather closely. But it is strongly advised to attend class, as the instructor will offer many ideas and insights not to be found in the book. It is also important to keep up with the homework.

Work Required in the Course: There will be weekly homework assignments. These will be done using the OnLine system WebWork. WebWork is handled through wustlkey. The URL is

What is nice about WebWork is that it grades your problems in real time so that you get instant feedback. More information about how to access WebWork will be provided in due course.

Another learning tool for this course is CalcHelper, which is a help room in where you can go for help with your work. Our TA Yifei Li ( will have office hours on Tuesdays and Wednesdays from 2:00pm to 3:30pm Room 6, Cupples I. Yifei will also have an office hour/help session at CalcHelper on Fridays from 10:00am to 12:00noon in Lopata 323. The University has specified that we have three miderm exams (on February 7, March 7, and April 4 from 6:30pm to 8:30pm in rooms to be specified) and a final exam (on May 4 from 3:30pm to 5:30pm in rooms to be specified). If you cannot make one of these exams then you should tell me (the instructor) at least a week in advance so that other arrangements can be made. You find out your room and seat assigment for each exam by logging on, on the morning of the exam, to . The relative weights of the course components are as follows:

Homework: 20%

Midterm I: 15%

Midterm II: 15%

Midterm III: 15%

Final Exam: 35%

TOTAL: 100%

I will conclude here with a variety of useful information:

1. The Math Department mandates that we have three midterms. They are scheduled on February 7, March 7, and April 4 from 6:30pm to 8:30pm in the evening. The Final Exam is on May 4 from 3:30pm to 5:30pm. You can find out what room to go to and what your seat assignment is for each exam by logging on, on the morning of the exam, to

2. To access WebWork, you need to go to and select Math 233. Your username and your password are both the student ID number. The password should be changed as soon as possible.

4. I do not allow calculators during exams.

5. Your exam grades may be found on BlackBoard.

6. Disability Resources: Special accommodations for exams are offered to students who are registered at Disability Resources (DR). Information about DR may be found at Students who desire to take advantage of this service should visit DR early in the semester, well before the first exam.

7. We have Peer-Led Team Learning (PLTL) groups to to assist with calculus learning. Lisa Kuehne ( is in charge of these activities. You should sign up for PLTL by 1:00pm on Thursday of the first week of class. The Web link for PLTL is

8. This Web page is the lifeline of the class. Homework assignments, additional course information, corrigenda, exam information, and other announcements will all be posted here. Bookmark the page and refer to it frequently.

Here is some essential information about the First Midterm for Math 233.

a) The exam is on February 7 from 6:30pm to 8:30pm. On the morning of the exam, go to to find out your room and seat.

b) You can bring one 4" x 6" card with notes to the exam.

c) You cannot bring a calculator or tablet or computer.

d) There are seven multiple choice questions, one TRUE/FALSE, and two written-out questions. For the first eight of these you will be given a ScanTron card to record your answers. The last two you will write out on the exam.

e) I will be out of town on February 6 and 7. So no class on Monday, February 6. Professors Chris Cox, Brian Blank, and Jimin Ding will be available during the exam to answer your questions.

f) Exam grades will be recorded on BlackBoard. *************************************************

Solutions to First Midterm

Solutions to Second Midterm

Practice Exam for Second Midterm

No class on Monday, March 6. Instead I will have office hours from 11:00am to 2:00pm.

Solutions to Practice Exam for Second Midterm

Solutions to Third Midterm

Practice Exam for Third Midterm

Solutions to Practice Exam for Third Midterm

Solutions to Final Exam

For your reading (and singing) pleasure, here are the lyrics
to the Quotient Rule Song:

If the quotient rule you wish to know,
It's low d-high less high d-low.
Then draw the line and down below
Denominator squared will go.

Practice Final Exam

Solutions to Practice Final Exam