Math 52 - Integral Calculus of Several Variables - Fall '04

| General Info | Syllabus & Homework | Announcements & Dates | Additional Help | Solutions & Handouts |

General Information

Meeting Time Mon., Tue., Wed., Thu., Fri., 2:15 - 3:05
Location Building 380 (Math), room 380-X
Professor Ben Brubaker (
Office: 382-F (2nd floor, Math building 380)
Office Phone: 3-4507
Office Hours: We'll discuss best times in class
Robin Oliver-Jones - Room 380-H
Office Hours: Mon. 9-11 a.m., Tue., Thu. 3:05-5 p.m.

Yu-jong Tzeng - Room 380-L
Office Hours: Mon. 3:30-5 p.m., Tue. 9-10:30 a.m.

Textbook Multivariable Calculus (With Matrices), by Edwards and Penney, 6th edition.
Required and available at the bookstore.
Homework: 1/8
Midterm I: 3/16
Integration Quiz: 1/16
Midterm II: 1/4
Final Exam: 3/8
We will investigate several generalizations of the one-variable integration taught in first calculus courses. These include iterated integrals, line and surface integrals, and vector analysis. The goal will be a unified picture of integration theory as expressed in the theorems of Green, Gauss, and ultimately Stokes.
Prerequisites Math 51 or its equivalent
A brief list of topics you should be comfortable with (but will be briefly reviewed throughout the course as necessary): (partial) derivatives, single variable integration techniques, vector operations, matrices and basic linear algebra.

Syllabus & Homework

A detailed syllabus together with homework assignments will be available at this link soon.

Announcements & Dates

  • Important Dates and Class Holidays
    • Monday, September 27th: First day of class
    • Sunday, October 17th: Add deadline
    • Wednesday, October 20th: MIDTERM I, 7-9 pm
    • Wednesday, October 27th: In-Class QUIZ
    • Sunday, October 24th: Drop deadline
    • Thursday, November 18th: MIDTERM II, 7-9 pm
    • Thursday-Friday November 25-26th: Thanksgiving Recess -- No Class
    • Monday, December 6, 7-10 pm: FINAL EXAM
  • Important announcements will be posted here throughout the quarter, such as changes to problem sets or due dates, or updates on office hours. These will also ALWAYS be announced in class, so if you attend the course, you need not worry about missing anything.

Additional Help

If you are having trouble with the homework or have questions about the material, the best way to get help is to attend the office hours offered by me and the two teaching assistants. If you can't make the scheduled times, then email us and we'll set up an appointment.

Additional help is given by

  • The Stanford University Mathematics Organization (SUMO) provides free walk-in tutoring for math students in the 51, 52, and 53 classes. Tutoring is held Monday and Wednesday, 6-10 pm, in room 381T of the math building (that's Building 380). Tutoring begins on Monday, October 4.
  • Free tutoring is also available through the Undergraduate Advising Center.
  • Solutions and Handouts

  • The following sample final includes worked solutions. Try not to look at the solutions until you've solved the problems:
  • The 2003 final exam
  • Another sample exam without solutions
  • Here's a sample midterm: Sample Midterm II
  • And here are solutions: Solutions to Sample Midterm II
  • I was having a hard time drawing figures for the Planimeter hand-out, so I searched the web and found lots of nice stuff instead. Here are the two sites that I found the most useful. I think that this is worthwhile, since it helps to understand Green's theorem a bit better.
      A module containing exercises on line integrals and Green's theorem and planimeters you can work through by yourself (made by my friend Dale Winter)
  • Midterm I Solutions Now only missing Question 4, to be added tonight.
  • Sample Midterm I (NOW with hints) Solutions appear inside the pdf file. I am still working on a few of them.
  • Last Year's Midterm (with solutions. I think it is very short and probably far too easy for students of your caliber, but I like the idea of just setting up the integration without evaluating, so I may do some of this too to spare you some time on the integration.)
  • A proof that the double integral over a rectanle is equal to the iterated integral.
    • Additional solutions to problem sets and midterms (written by me and the CAs) will appear here after the assignments are completed. Solutions to the homework problems can be found by following the links to the homework page.