MATH 2220, SPRING 2011
Multivariable Calculus

Prelim 1 Problems Spring 2011

FINAL EXAM: Please double check with the website

MATH 2220   Fri, May 13   9:00 AM   IVS105: Ives Hall 105

News!: Practice Problem Term 3 Solutions

News!: Prelim 2 Solutions

News!: Matsumura's office hour changed: Wed 3:00 to 5:00pm (Effective from March 2nd)

News!: Practice Problems Week1-4 Solutions (Typo fixed Monday 2/21)

News!: Prelim I, 2/22 (Tue), 7:30PM - 9:00 PM (90 minutes), GSH132 University Exam Schedule

News! (2/10): Solution to HW2 is uploaded.

News! (2/4): Solution to HW1 is uploaded.

News! (2/4): Due to the cancellation of a class on Monday, we have decided not to cover Section 3.2 Taylor's theorem in detail. As a consequence, the problems from Section 3.2 are no more HW problems.

News! (1/28): After one week of class, we decided not to give quizzes during the semester. Although it is the tentative percentage, we changed that HW scores give 15% of the final grade.


  • Lec 1, MWF 10:10am - 11:00am, MLT406, Xiaodong Cao
  • Lec 2, MWF 12:20pm - 01:10pm, MLT406, Tomoo Matsumura
  • Discussions:

  • DIS 201, Wed 01:25PM - 02:15PM, MLT 203 Chor Hang Lam
  • DIS 202, Wed 02:30PM - 03:20PM, MLT 224 Chor Hang Lam
  • DIS 203, Thu 02:30PM - 03:20PM, MRL 111 Jennifer Biermann
  • DIS 204, Thu 03:35PM - 04:25PM, RCK 110 Jennifer Biermann
  • Office hours: Other than the following fixed hours, please contact the instructors by email to ask their availability.

  • Xiaodong Cao: W 1:25-2:25pm, F 1:25-2:25pm
  • Tomoo Matsumura: W 3-5pm
  • Chor Hang Lam: M 2:45-4:45pm
  • Jennifer Biermann: M,W 1:30-2:30pm

  • Prerequisites: Besides single-variable calculus, we will be assuming some linear algebra. Math 2210 is officially listed as a prerequisite for 2220, and it contains more than enough linear algebra for 2220. Students who haven't had 2210 and who are willing to learn the necessary linear algebra on their own should be able to manage in 2220. The textbook begins with a chapter on vectors that includes most of the linear algebra we will need. This chapter is not part of the course syllabus, but topics from it will be reviewed briefly in class as they come up. However, keep in mind that this is only a review of things you are already supposed to know.

    Text: Vector Calculus by Jerrold Marsden and Anthony Tromba, Fifth Edition. We will not always be doing topics in the same order as in the book. Some students may wish to use the textbook more as a reference, relying more on what happens in class for learning the material.

    Course Schedule (follow the link). The course breaks up into three parts:

    I. Multivariable Differentiation. (Chapters 2 and 3 of the book)

    II. Multivariable Integration. (Chapters 5 and 6)

    III. Vector Analysis, combining parts I and II. (Chapters 4, 7 and 8)

    This fits well with the exam schedule of two prelims and a final, as the first prelim will cover topic I and the second prelim will cover topic II. The final will be cumulative, but with some emphasis on topic III (which uses both I and II).

    Homework: There will be problem sets due on Wednesday/Thursday of each week in your discussion section, starting with the second week. Students may work alone or in groups on the homework, but the solutions you hand in should be your own write-up. The list of problems can be found on the Course Schedule. We won't grade all problems, instead, we give the completion points. So please check the solutions after solutions are posted a few days after the problem sets are due. Two lowest scores will dropped. No late homework.

    Grading: Prelim 1 (20%), Prelim 2 (25%), Final (40%), HW (15%)

    Exams: Students with special needs should contact their lecturers well in advance of the exams. Same in the case of conflict exams, although it is the student's responsibility to check the University Exam Schedule before registering classes.

  • Prelim I, Tue 22-Feb-11, 7:30PM - 9:00 PM, GSH132: Goldwin Smith Hall 132-HEC Aud
  • Prelim II, Thu 31-Mar-11, 7:30PM - 9:00 PM, GSH132: Goldwin Smith Hall 132-HEC Aud
  • Final, Fri 13-May-11 9:00 AM-11:30 AM, Place TBA
  • Find the place for the final exam in

    University official website:

    Practice Problems for exams:

  • Prelim 1: Spring 2008/ Solutions, Spring 2009/ Solutions, Spring 2010/ Solutions, Fall 2010/ Solutions
  • Prelim 2: Spring 2008/ Solutions, Spring 2009/ Solutions, Spring 2010/ Solutions, Fall 2010/ Solutions
  • Final: Spring 2008/ Solutions, Spring 2009/ Solutions, Spring 2010/ Solutions, Fall 2010/ Solutions(not available)

  • Graphing: It can be very helpful to visualize some of the content of the course by using computer graphing software. This is not officially part of the course (and won't be part of the exams or homework sets), but you may find it worthwhile to explore this on your own. There is probably lots of software available for this, but if you happen to have a Mac that isn't too ancient, you will already have a little application called Grapher that can create some amazing pictures -- just try it!

    Academic Integrity: Each student in this course is expected to abide by the Cornell University Code of Academic Integrity.

    Extra Help is available in the Math Support Center.