6760, Math 21a, Fall 2009
Homework page of Math 21a, Multivariable Calculus
Homework
Course head: Oliver Knill
Office: SciCtr 434

WeekLecture NumberAssignmentSolutions
Week 1 1. Class 9.1: 8,14,18,32,42 9-1-3.pdf
Week 1 2. Class 9.2: 30,44 9.3: 22,44,46 9-1-3.pdf
Week 2 1. Class 9.4: 14,20,26,36,42 9-4.pdf
Week 2 2. Class 9.5: 10,20,30,50,62 9-5.pdf
Week 2 3. Class 9.6: 2,8 (and sketch graph), (15 and 27 together),28,32 9-6.pdf
Week 3 1. Class 10.1: 19-24,38,44, 10.2: 20, 10.4: 28 10-1-4.pdf
Week 3 2. Class 10.3: 2,6,8,12,24 10-2.pdf
Week 3 3. Class 9.7: (6 and 10 together),16,18,20,24 9-7.pdf
Week 4 1. Class 10.5: 6,13-18,26,34,Problem A 10-5-6.pdf
Week 4 2. Class 11.1: 15-18, 35-40 11.2: 8,34,38 11-1.pdf
Week 4 3. Class 11.2: 22 (no computer needed) 11.3: 6,28,36,66 11-2-3.pdf
Week 5 1. Class: midterm
Week 5 2. Class 11.3: 70,72,76,88 Problem B 11-3.pdf
Week 5 3. Class 11.4: 4,14,16,18 Problem C 11-4.pdf
Week 6 1. Class: No homework due to Columbus
Week 6 2. Class 11.5: 4,28,32,36, Problem D Sol 11-5.pdf
Week 6 3. Class 11.6: 20,28,44,50, Problem E Sol 11-6.pdf
Week 7 1. Class 11.7: 4,10,12,44,50 11-7.pdf
Week 7 2. Class 11.8: 6,12,16,20,40 11-8.pdf
Week 7 3. Class 11.8: 18,24,26. Review: 56,60 11-8r.pdf
Week 8 1. Class 12.2: 4,8,28,36, Problem F Sol 12-2.pdf
Week 8 2. Class 12.2: 18,38. 12.3: 36,50,52 12-3.pdf
Week 8 3. Class 12.4: 8,22,28,34. 12.5: 2 12-4.pdf
Week 9 1. Class No homework due to second hourly
Week 9 2. Class 12.6: 2,8,12,22,26 12-6.pdf
Week 9 3. Class 12.7: 8,14,32,44,52 12-7.pdf
Week 10 1. Class 12.8: 4,10,16,36,40 12-8.pdf
Week 10 2. Class no homework due to Veteransday
Week 10 3. Class 13.1:22,36 13.2:18,20,48 13-1-2.pdf
Week 11 1. Class 13.3: 10,18,22,24,31-34 13-3.pdf
Week 11 2. Class 13.4: 8,10,12,14,20 13-4.pdf
Week 11 3. Class 13.5: 6,10,12,29,38a)c) 13-5.pdf
Week 12 1. Class 13.6: 22,24,28,42,47 13-6.pdf
Week 12 2. Class 13.7: 6,8,10,14,18 13-7.pdf
Week 12 3. Class No homework due Thanksgiving
Week 13 1. Class 13.8: 2,10,18 13.9: 32,34 13-8.pdf
Week 13 2. Class Mathematica project due Wed/Thu
  • Homework is due at the beginning of class. We do not accept electronic HW submission. If you do the homework with a word processor like LateX, print it out and submit the paper.
  • Please staple your homework.
  • No late homework accepted but will delete the least 3 scores for MWF sections and 2 for TTh sections. Reserve these 3 "Joker" cards for emergencies.
  • Collaborations are welcome however you must turn in your own copy and list on it the names of your collaborators.
  • Similarly, acknowledge the use of Mathematica. If you use Mathematica, nevertheless, write down all steps of your computation or print out the Mathematica notebook, you authored.
  • If you can not turn in your homework because of a religious holiday like Yom Kipur, turn it in earlier or give it to a friend to turn it in.
  • Please write legibly and indicate clearly, where a new problem starts.
  • Try to keep the problems in order.
  • Use words to explain your work, if necessary. Show your work. Answers without explanations are given zero points.
  • If unable to finish a problem, indicate where you are stuck. This will help us to give partial credit.
  • Please inform about typos, misprints. We state here corrections to the in class distributed texts as well as to the posted solutions. Each hint gives you a bonus point. The texts posted here are corrected.
  • (+Sol) means solutions have been posted.
  • Homework scores from individual sections will be adjusted in the end because different graders grade each section.

MQC information Sunday through Thursday nights, 8:30-10:30 PM in SC 309a

Grading: Each of the 5 problems assigned per unit is worth 10 points. Course assistants are encouraged to grade interpolating the following rubric:
  • 10 Points. Work is completely accurate and essentially perfect. Work is thoroughly developed, neat, and easy to read. Complete sentences are used where appropriate.
  • 5-9 Points. Work is good, but incompletely developed, hard to read or unexplained. Answers that are not explained may received 2 points even if correct. The work contains the right idea but is flawed.
  • 3-5 Point. Work is sketchy. There is some correct work, but most of the work is incorrect.
  • 0-3 Points. Work is minimal or non-existent. Solution is completely incorrect. Only the answer is given.


Problems 28 in 9.6 asks you to plot something with a computer. You can use any software for that. If you should want to give Mathematica a try, here is an example on how to plot
Plot3D[Exp[Cos[x] - Sin[y]],{x,-4,4},{y,-4,4},PlotRange-> All]
You can also use the Wolfram Alpha, an online version of Mathematica. Just enter something like
Plot  Exp[ Cos[x] - Sin[y] ]
into the search field. You still have the task to figure out how to tweak things so that it looks well.
Updated homework policy in case of Swine flu: If you should fall ill from swine flu and not able to attend classes. please do the following:
  1. please get a confirmation from your doctor or Harvard university health services indicating from when to when you were ill.
  2. either use a joker for the homework (they are for such cases and not for boosting homework grades) or
  3. do the homework late and grade the homework yourself with the help of the solutions you find on the website. Turn this homework to your CA at the usual time at the beginning of class together with a note confirming that you could not come to class due to a H1N1 flu case. Your CA can give credit for such late if the paperwork is done and the paper is self-graded. If you prefer not to attach the doctors note to the paper, drop the note in Oliver's office 434 (leave under door if Oliver is not in).
Questions and comments to knill@math.harvard.edu
Math21b | Math 21a | Fall 2009 | Department of Mathematics | Faculty of Art and Sciences | Harvard University