Harvard University,FAS
Fall 2006

Mathematics Math21a
Fall 2006

Multivariable Calculus

Course Head: Oliver Knill
Office: SciCtr 434
Email: knill@math.harvard.edu
Harvard Mathematics

Weekly checklists: "Somewhere, over the rainbow ..."
Week1 Week2 Week3 Week4 Week5 Week6 Week7 Week8 Week9 Week10 Week11 Week12


The final:

The final exam took place January 22 at 9:15 AM. Students with names A-M were in Hall C, students with names N-Z were in Hall D. Here was the exam schedule [PDF]. As usual, we recommended to do at least one of the practice exams before looking at the solutions. Watching solutions before attempting to solve it, is both frustrating and unefficient. There are often many ways to solve a problem and the provided solution might not be the one which is natural to the student. We had 5 practice episodes, the sixth "came to a theater near you" on January 22nd.
The final average was 77 with a standard deviation of 15. The graph shows the difference between final grade and average grade Here is the correlation between final grade and average grade

    Episode I
    Practice exam 1

    Episode II
    Practice exam 2

    Episode III
    Practice exam 3

    Episode IV
    Practice exam 4

    Episode V
    Practice exam 5

    Episode VI
    Final Exam
    Corrected Errata:
    • January 20 in Episode 1, TF problem 4, "smaller" should read "smaller or equal". The two vectors could be parallel.
    • January 18 in Episode 5, TF problem 20, the explanation mentioned that (0,0,1) is a maximum. The maxima occur on the circle r2=2, the boundary where sqrt(f(x,y)) is defined. The picture to the left shows the rz-plane.
    • January 18 in Episode 5, problem 14: delete the info that the amputated surface has volume 5 is not needed, Nor is it consistent with the info the full brezel has volume 3.
    • January 18 in Episode 4, problem 4a), the answer is -14x+2y-12z=0 not -14x-2y-12z.
    • January 18 in Episode 4, problem 7) the final answer is 20 not -4.
    • January 16: in Episode 2, problem 11, there were typos in the cylindrical and spherical coordinate solutions. In problem 12 the solution is 2/3 + pi not 2/3 - pi.
    • January 13 in Episode 4, problem 3, the picture of the 3D vector field and the one-sheeted hyperboloid are corrected (there were wrong pictures there).
    Final review times: (sorry about the conflict on Wednesday with the life science review, we will make slides available)
    1. Wed 1/10 2-3:30PM Hall C, (Start until Lagrange if time permits start with 2D integrals) Review Episode I slides
    2. Thu 1/11 2-3:30PM Hall C, (From 2D integrals to Stokes theorem) Review Episode II slides
    3. Fri 1/12 4-5:30PM Hall B, (From Stokes to Divergence, Q&A, TF problems) Review Episode III slides
  • FAS archive of old exams
Our final exam is a three-hour final exam administered by the Exams Office for all enrolled students. As such the exam is subject to the following criteria:
  • All students enrolled in the course are required without exception to attend the exam administered by the FAS Exams Office. Students not present at this exam will receive a grade of ABS for the course.
  • Instructors may not approve or administer a makeup exam to any student absent from the exam. Makeup exams may only be approved by the Administrative Board for undergraduates or the Deputy Registrar for graduate students, Special Students, or cross-registered students and will be administered by the FAS Exams Office during the scheduled makeup exam period.
The second hourly:

took place Tuesday, Nov 14, 2006, Hall B, 7-8:30 PM We had a course wide review on Sunday, November 12 from 7-8:30 PM in Lecture Hall C. The mean of the second midterm exam was 80, the standard deviation was 9.
Official policy at Havard is that "out of sequence exams" are only offered for students observing religious holidays. We sometimes can accomodate students who happen to have an important sports event at the same time (it must be an actual game or tournament) or a concert or theater event (regular practice or rehearsals of course do not qualify to miss the exam). In case of a qualifying conflict, contact the course head to see whether it is possible to arrange the exam earlier at the same day. We will need a letter from your coach or director. The request has to come at least a week before the exam.
The first hourly, took place on Wednesday, Oct 18. 2006, Hall C, 7-8:30 PM.

The average of the first midterm exam was 75, the standard deviation 14.

Please send comments to math21a@fas.harvard.edu

Math21a, Multivariable Calculus, Fall 2006, Department of Mathematics, Faculty of Art and Sciences, Harvard University

Thu Jan 25 21:36:37 EST 2007