Math 321
practice problems for first prelim
Fall 2006
There are more problems here than many of you can do in fifty minutes, but they are representative of the type of problems you might expect on the exam. On the exam you may use a one-sided lett
Math 3210
Practice problems for rst prelim
Some hints and solutions
Fall 2012
This is not a detailed solution sheet, but rather a collection of hints and summary answers
intended to help you along in preparation for the exam.
1. dg = 2 f (x) cos( f (x)2 )
Math 3210
First prelim
Friday 28 September 2012
10:1011:00 am
Please ll out and sign the front page of your exam booklet.
You may use anything that has been given in class, in the homework, or in the lecture
notes, as long as you show clearly what you are
Math 3210
Second prelim
Wednesday 31 October 2012
10:1011:00 am
Please ll out and sign the front page of your exam booklet.
You may use anything that has been given in class, in the homework, or in the lecture
notes, as long as you show clearly what you a
Math 3210
1.
Second prelim
Wednesday 31 October 2012
Solutions
10:1011:00 am
(a) 1 = ;
(b) = (n 2, n, n 1, n 3, n 4, . . . , 3, 2, 1);
(c) = (n, n 1, n 2, n 3, . . . , 6, 5, 4, 2, 1, 3);
(d) 1 = (1, 2, 3, . . . , n 4, n 3, n 1, n, n 2).
2.
(b)
n
i
n
i
n
i
Math 3210 1.
nal exam
Friday 11 December 2009 Solutions
2:00-4:30 pm
(a) M is the portion of the paraboloid z = x2 + y2 sitting over the disc D. (b) Let f : D R be the function f ( x, y) = x2 + y2 . By a theorem in the notes, ( x, y) = ( x, y, f ( x, y) i
Math 3210 1.
second prelim
Wednesday 28 October 2009 Solutions
10:10-11:00 am
(a) 1 = ; (b) = (n 2, n, n 1, n 3, n 4, . . . , 3, 2, 1); (c) = (n, n 1, n 2, n 3, . . . , 6, 5, 4, 2, 1, 3); (d) 1 = (1, 2, 3, . . . , n 4, n 3, n 1, n, n 2).
n i n i n i (a) i
Math 3210
practice problems for rst prelim Some hints and solutions
Fall 2009
This is not a detailed solution sheet, but rather a collection of hints and summary answers intended to help you along in preparation for the exam. 1. dg = 2 f (x) cos( f (x)2 )
Math 3210
nal exam practice problems
December 2009
On the nal exam you may use anything that has been given in class, in the homework, or in the lecture notes, as long as you show clearly what you are using. You may bring a two-sided letter-size cheat she
Math 3210
practice problems for rst prelim
Fall 2009
There are more problems here than many of you can do in fty minutes, but they are representative of the type of problems you might expect on the exam. On the exam you may use a one-sided letter-size cri
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Math 3210
Practice problems for rst prelim
Fall 2012
There are more problems here than many of you can do in fty minutes, but they are
representative of the type of problems you might expect on the exam. On the exam you
may use a one-sided letter-size cri