Errata for practice exams: the above files were corrected at the time indicated
 5. January, 3 PM: Practice I Problem 8, clarified UFO situation with a second picture.
 5. January, 4 PM: Practice 7,Problem 2, curve picture 4 had appeared twice.
 7. January, 3 PM: Practice 2,Problem 14c, explanation not clear. Thanks to Leslie Beh
 7. January, 11 PM: Practice 5, Problem 5, replace inclusive by inconclusive. Practice 6,Problem 6c, at the end of the solution (0,1), not (0,0). Thanks to Jenny Xia
 8. January, 0:30 AM: Practice 6, TF 3, replace cylinder by paraboloid, answer stays. Thanks to Kenric Tam.
 9. January, 4 PM: Practice 6, Problem 8, gradient <4x,4y>, not <<8x,8y>, answer stays. Thanks to Dominik Nieszporowski
 9. January, 6 PM: Practice 7, Problem 2, order III,I,II,IV, Thanks to Connie Lee and Samir Patel and Ben Li
 10. January 6 PM: Practice 4, Problem 8 b) sign error in the result. Thanks to Jenny Xia.
 10. January 6 PM, Practice 7, Problem 9 b). In the integration computation, the part F(r(t)).r'(t) had been evaluated already. The result is the same. Thanks to Jason Varnell.
 11. January 1 AM, Practice 5, Problem 6, two typos in gradient and discriminant. Result stays. Thanks to Corinne Tu.
 11. January 1 AM, Practice 1, Problem TF15, divergence is 3, not 1, result stays. Thanks to James Danz.
 11. January 1 AM, Practice 2, Problem 14a, the parametrization must be r(phi,theta), not r(theta,phi) to have the orientation outwards. The result stays. Thanks go Hanna Retallack.
 11. January 1:30 AM, Practice 4, Problem 6, typo with one 6 too much. Thanks to Jenny Xia
 11. January 5 PM, Practice 3, Problem 4, discriminant is 12y. Thanks to Jenny Xia
 11. January 11 PM, Practice 7, Problem 3, vector field mixup (and error introduced early January when rerunning some graphics in mathematica 7), Thanks to Justin Koh.
 11. January 11 PM, Practice 5, Problem 8, typo pi3/ instead of pi/3. Thanks to Daniel Norris
 11. January 11:30 PM, Practice 2, TF4, correction of L(x,y,z) at (1,1,1). Result does not change. Thanks to Jim Danz.
 12. January 7 PM, Practice 6, TF20, the region under considering is an octant intersected with a solid sphere. Result stays. Thanks to Sanjay Misra.
 12. January 4 PM, Practice 1, 14), instead of f_{xx}, it should rather be f_{aa}. Thanks to Taylor Shimberg.
 12. January 8 PM, Practice 3, TF 16, div (F) = 2x + 2y + 2z, Problem 14, differentials in wrong order. Thanks to James Danz.

The final exam in exam group 1 is a threehour 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 crossregistered students and will be
administered by the FAS Exams Office during the scheduled makeup exam period.

Second hourly

The second hourly took place on Tuesday November 18 at 7 PM in
Hall B.
It covers week 58. There was a global review on Sunday 11/16 from 78:30pm in
Science center lecture hall C.
Review slides. Here is the exam and practice exams
The average score of the class for the second midterm was 81 points, the standard deviation was 10.

Errata for practice exams: since many problems were rewritten or added newly, there quite a few typos and errors:
thanks for everybody for hunting them down. (The name indicates the first person noticing the error,
the date and time indicates, when a corrected version has been posted on the website).
 11/13/08, 11:59 PM, Denise Xu, I 3), typo in final boxed result, in b), typo in 3y^{2}, does not affect answer
 11/13/08, 11:59 PM, Edward Li, III 8) , typo 2st changes answer.
 11/14/08, 12:05 AM, Adam Lee Purvis, I 2), solution had been missing
 11/14/08, 12:15 AM, Anirudh Penumaka, III 2a), a(y) and b(y) for type II integral
 11/15/08, 7:15 AM, Adam Lee Purvis, I TF4) direction <0,1> in explanation. Result remains,
I6 (2,1) > (1,2) Result remains, I 7) x=y=1, result remains
 11/15/08: 7:25 AM, Denise Xu, I4), exponent 2/3, not 2/3, result remains.
 11/15/08: 7:30 AM, Denise Xu and Dominik Nieszporowski, I 5bc) were false, the result changed.
 11/14/08: 7:30 AM, Edward Li, I 10), incorrect upper bound. The result changed.
 11/14/08: 6:25 PM, Nan Du, I 4), Typo (0,90) should be (0,3). Result unchanged.
 11/14/08: 6:40 PM, Dominik Nieszporowski, II 10a), the answer changed

 11/14/08: 6:45 PM, Christopher Madl, I 10a), still a bug in the final result
 11/15/08: 1:20 PM, Jacob Weatherly, II 4a) factor of r missing in computation. Result unchanged.
 11/15/08: 6:30 PM, Samantha Keyser, II 2,10) missing or incomplete solutions.
 11/16/08: 2:00 AM, Denise Xu, III 9) integral goes to pi^2, the final result changes
 11/17/08: 3:20 PM, Hanzi Zhang, III 6) typos in computation, final result remains
 11/17/08: 8:00 PM, William Hawley, I 3), clean out typo 6y result remains
 11/17/08: 11:00 PM, Lakshmi Parthasarthy, Sean Singh, Jeremy Cushman III 4), typos after changing order of integration, result unchanged
 11/17/08: 11:30 PM, Sean Singh and Kevin McNamara IV TF1, wrong answer. The condition implies that it is a local minimum


First hourly

The first hourly took place Tuesday October 21 at 7 PM in Hall B.
It covered the material from week 14.
There was a global review on Sunday October 19'th from 78:30 PM in
lecture hall B. slides [PDF].
Here are the practice exams:
The average score of the class for the first hourly was 75 points, the standard deviation was 13.5.

Errata for practice exams:
(the name indicates the first person noticing the error,
the date and time indicates, when a corrected version has been posted on the website).
 10/16/08, 7 AM: Sean Singh: Practice 1, TF12 "in" missing, TF11/TF16 had been identical.
 10/18/08, 9 AM, Edward Li: Practice 4, Problem 9), sign error for z= ...
 10/18/08, 9 AM, Edward Li, Practice 4, TF 19, is true, not false
 10/18/08 12:30 PM, Jacob Weatherly, Practice 4, TF 4, is false, not true
 10/18/08 23 PM, Jeremy Feng, Practice 3, TF 1, the answer is false
 10/19/08 7:30 AM, Denise Xu, Practice 3, 7b), typo in zpart of acceleration
 10/19/08/ 11:30 AM, Tom Yu , Practice 2, 9b), parametrization of ellipsoid.
 10/20/08 20:00 PM, Ezgi Bereketli, Practice 4, 5), <5,0,2> instead of <5,2,0>, result stays

Official policy at Harvard is that "out of sequence exams" are
only offered for students observing religious holidays and students who
need out of sequence exam as ordered from the accessible education office.
We sometimes can accommodate 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) or a political election event (for which you
are a major candidate). 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.

