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Math 380
Takehome Quiz
Due in class Friday, April 30
Name
Ground rules.
You must do this exam in one sitting by yourself. Do not discuss the problems with anyone
between 10 pm April 18 and 10 am April 30. You may use your notes and textbook only.
1. (2 pts) Calculate
I
j
z
j
=3
z
2
z
2
+ 3
z
4
dz
2. (3 pts) Suppose
f
(
z
) =
X
1
k
=
a
k
z
k
where the series converges on the annulus
0
<
j
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Unformatted text preview: z j < 3 : What is I j z j =1 f ( z ) z 10 dz in terms of the a k ? 3. (2 pts) Find the &rst three nonzero terms of the Maclaurin seris for e z sin z without computing derivatives of e z sin z: 4. (3 pts) Find the annulus of convergence of the following Laurent series: 1 X k =1 1 2 k z k + 1 X k =0 z k 2 k : 1...
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This note was uploaded on 09/16/2011 for the course MATH 380 taught by Professor Staff during the Spring '11 term at S.F. State.
 Spring '11
 Staff
 Math

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