Math 21a Fall 2019
Multivariable Calculus
Final Exam
Final exam and Solution draft |
cos^{2}(t) = (1+ cos(2t))/2 | sin^{2}(t) = (1- cos(2t))/2 |
Practice I, [Solutions] |
Practice II, [Solutions] |
Practice III, [Solutions] |
Practice IV, [Solutions] |
Practice V, [Solutions] |
Practice VI, [Solutions] |
Second hourly
The second midterm took place November 5 at 6-7:30 PM in Hall C. We had a global review on Sunday, November 3, 6-7:30 PM in Hall C. The first midterm had an average 83 with a standard deviation 9.Second midterm and Solution |
Practice 1, [Solutions] |
Practice 2, [Solutions] |
Practice 3, [Solutions] |
If you need more practice about some topics: here are some other practice exams. Also these are adapted old exams.
Practice 4, [Solutions] |
Practice 5, [Solutions] |
Practice 6, [Solutions] |
First hourly
The first midterm took place on Tuesday October 1, from 6-7:30 PM in Hall C. We had a global review on Sunday, September 29, 2019 from 6-7:30 PM in Hall C. The first midterm had an average 85 with a standard deviation 9.First midterm and Solution |
Practice 1, [Solutions] |
Practice 2, [Solutions] |
Practice 3, [Solutions] |
If you need more practice about some topics: here are some other practice exams. Also these are adapted old exams.
Practice 4, [Solutions] |
Practice 5, [Solutions] |
Practice 6, [Solutions] |
Exam policies
"Out of sequence exams" are offered for students observing religious holidays and students who need out of sequence exam as ordered from the accessible education office. See student handbook. If you have a lab conflict, it is usually possible to rearrange the lab for that exam time. We try to accommodate students with rehearsals, practice or regular classes, seminars or labs as well as possible but with a large number of requests this is not possible and would also compromise the integrity of the exam. In case of a qualifying conflict, contact Oliver knill@math.harvard.edu. Note that we can not offer make-up exam any other day. All requests have to arrive a week before the exam.