18.02  Multivariable Calculus

Dear 18.02 students:
As explained at the beginning of the course in the information sheet, a numerical average is computed, and the letter grade is a function of that.  Here are the minimum numerical averages needed:
97 A+
90 A
80 A-
78 B+
74 B
70 B-
68 C+
64 C
60 C-
50 D
0 F
For freshmen, who receive Pass/No Record, C- or above counts as Pass.  To find out your grade, visit WebSIS; probably it will be available sometime next week.

In any case, congratulations on all your hard work!  I hope it helps you in your future subjects.  And I hope that you'll come visit me in 2-244 later on during your time at MIT to let me know how you are doing!

Happy holidays,
Bjorn Poonen

The 18.02 final exam will be held Thurs. Dec. 17, 9:00am-12 at the Johnson Athletic Center.  See the online notes from the last two lectures to see what is covered.  Two practice finals with solutions are available on OCW, and another one will be available under Materials soon.

There will be no makeup final for those who score poorly.

If you are sick, contact MIT Medical for medical attention, stay home, email me and your recitation instructor as soon as possible, contact a dean at S^3 to have an excuse notice sent to all your professors; you will then receive a grade of OX for the course and will have to retake an 18.02 final exam sometime in 2010 to change it to a regular grade: contact Galina Lastovkina (galina@math.mit.edu) in 2-108 if you have questions about this.

Please plan to arrive by 8:55am at the latest, and please use the restroom beforehand if possible.

No notes, books, or electronic devices are permitted.  All you need to bring are pencils or pens, and your student ID card.  You will write your answers in the exam booklet provided, and blank paper for scratch work will be attached at the back of the exam.

If you finish more than 5 minutes early, you may hand your exam in early.  But if you finish during the last 5 minutes, please wait in your seat until the end, and then pass your exams to the aisles, and continue to wait silently in your seats until the proctors have collected all exams.  To earn full credit for your exam, you must drop your pencil or pen immediately when the exam ends (do not try to finish the sentence you are in the middle of); this is for the sake of fairness.

Shortly after the exam, solutions will be posted on Stellar (probably within 24 hours).  You may view your graded exam in 2-108.

Good luck everybody,
Bjorn Poonen

Any 18.02 student can go to any of the recitation
instructor's review sessions below (instructors, please
add your review session time and room and your last name under
the appropriate date below, sorted by start time):


Fri Dec 11:

12 pm - 2 pm, 4-231, Hon (review session)
12:30-1:30pm, 2-244, Poonen (office hours)
4 pm - 6 pm, 2-146, Liu


Sat Dec 12

1pm-3pm 2-131 Stoica


Mon Dec 14:

1.30 pm - 3 pm, 2-142, Bernardi
2 pm - 3 pm, 2-400, Balagovic (Q&A session)
3pm - 4pm 2-136, McLean
5 pm - 7 pm, 4-237, Sohinger


Tues Dec 15:

9:30-11:30am, 2-244, Poonen (office hours)
5-6pm, Hon (office hours)
4:30-6:30pm, 2-102 Speh


Wed Dec 16:

10:30-11:30am, 2-244, Poonen (office hours)
10:00 - noon 2-131 Tam

2pm -3pm 4-145 Naber
3pm - 4pm 2-136, McLean
4pm-6pm: 2-093, Speh (office hours)
5 pm - 7 pm, 2-131, Balagovic (Q&A session)

Midterm 4 is Friday Dec. 4 from 2:05 to 2:55pm.  It covers up to and including the lecture on Tues. Dec. 1 (see the notes for the exact cutoff).  The focus will be on material since midterm 3, but math is cumulative so really you need to know everything up to now.  A practice exam with solutions is available under Materials, and other exams can be found at OCW.

Because of MIT regulations about exams during the last week of classes, there will be no makeup midterm for those who score below the minimum passing grade.  So do well the first time!

If you are sick, contact MIT Medical for medical attention, stay home, email me and your recitation instructor as soon as possible, contact a dean at S^3 to have an excuse notice sent to all your professors (this is necessary if you want to receive credit for a makeup), and contact Galina Lastovkina (galina@math.mit.edu) in 2-108 to arrange a makeup on an individual basis.

Your exam location may be different from last time!  Recitations r01-r12 go to 50-340.  Recitations r13-r18 and everyone else go to 10-250.  In determining where to go, use the section that Stellar says you are officially enrolled in.

Please plan to arrive by 2:00pm sharp at the latest, and please use the restroom beforehand if possible.  If in 10-250, sit in every third seat.

No notes, books, or electronic devices are permitted.  All you need to bring are pencils or pens, and your student ID card.  You will write your answers in the exam booklet provided, and blank paper for scratch work will be attached at the back of the exam.

If you finish more than 5 minutes early, you may hand your exam in early.  But if you finish during the last 5 minutes, please wait in your seat until the end, and then pass your exams to the aisles, and continue to wait silently in your seats until the proctors have collected all exams.  To earn full credit for your exam, you must drop your pencil or pen immediately when the exam ends (do not try to finish the sentence you are in the middle of); this is for the sake of fairness.

Shortly after the exam, solutions will be posted on Stellar (probably within 24 hours).  Exams will be returned during your next recitation section.  If your exam needs to be regraded, explain on a separate sheet of paper why your grade should be different, and submit it with your entire exam to your recitation instructor.

Good luck everybody,
Bjorn Poonen

For the second integral in 3A-6, the solution should take the simpler region of integration S to be the upper half of R (or the lower half), not the right half.
The answer in the book to p.968, #41 is off by a factor of 8.
The supplementary notes sometimes write dr dtheta instead of r dr theta when it is not concerned with the integrand.  In any case, the area element dA should always equal r dr dtheta.