Problems are from Brown and Churchill,
"Complex Variables and Applications," 7th
ed. unless otherwise indicated.

If I write S2, p. 4-5: 3, 4, 10 :
it means do problems 3, 4 and 10 at the end of
Section 2 on pages 4-5 of the book.

**Homework #0: **(Due 9/26/03 in Section)

S2, p. 4-5: 3, 4, 10

S3, p.7 : 1

S4, p. 11: 3, 4.

These problems on basic properties of complex
numbers will not be collected but they will be covered in Section.

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**Homework #1: **(Due 10/3/03 In Section.)

S5, p. 13: 2, 8, 14

S37, p.115-116: 2, 3, 4,

S7, p. 21: 1, 6cd,
10

S9, p. 28-29: 1, 2,
6, 7

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**Homework #2: ** (Due 10/10/03 In Section.)

S10, p. 31: 1 -- 3

S11, p. 35: 1 -- 3

S13, p. 42: 2, 3, 7

S17, p. 53-54: 5,
10, 11

S19, p. 59-60: 1, 3, 4, 9 (Do not hand in
#9.)

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**
****Homework #3: **
(Not to be collected but to be done before the
test.)

S17, p. 53-54: 3b

S28, p.89: 1, 6, 10, 11

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TEST #1: Friday October 17, 2003.
This test covers the material from Homeworks 0 - 3.

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**
****Homework #4: **
(Due 10/24/03 In Section.)

S22, p. 68-69: 1, 2, 6

S24, p. 73-74:
1ab, 2, 4, 7a

S25, p. 78-79: 1, 4, 8 (Do #7 In class.)

S28, p.89: 3, 8

S30, p. 94-95: 2, 3, 7*, 9

S31, p. 96: 1, 2, 5

S32, p. 99-100: 1, 2, 6, 8cd

*You are asked to find z so that log(z) contains i^{.}pi/2.

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**
****Homework #5: **
(Due 10/31/03 In Section.)

S33, p. 103-105: 2, 4, 17, 18

S34, p. 107-108: 4, 5, 8, 14, 15

S35, p. 110: ~~2~~, 3

S38, p. 120-121: 1 (do not turn in)

~~S40, p. 128-130: 1, ~~ ~~2~~~~, 3, 6, 7, 10, 11~~
(Fire delayed until next week.)

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**
****Homework #6: **
(Due 11/7/03 In Section.)

S40, p. 128-130: 1, 3, 6, 7, 11

S41, p. 133-134: 1, 2, 4, 6

S43, p. 141-142: 1, 2, 4, 5 (do not turn in 5.)

S46, p. 153-156: 1acf, 2, 6

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**
TEST #2:
**Monday November 10 at 9:00
AM.

This test covers the material from Homeworks 4 - 6.

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**
****Homework #7: **
(Due 11/14/03 In Section.)

S48, p. 162-164: 1, 2, 3, 8 (do not turn in 8.)

S50, p. 171-173: 2 (Look at but do not turn in.)

S52, p. 181: 4, 6

( **Hint for S52 #4**: Take Eq. (10) on p. 180
and multiply it by z, then set z=re^(i\theta) and take the real and imaginary
parts of the result to get the answers.)

Also compute the following integral

where *a*>0 and *b*>0 and
*a* is** not **equal to *b*.** **

(**Hint:** Use the Residue theorem method from class where we computed the integrals of *(1+x*^{2})^{-1}
and *(1+x*^{4})^{-1}.)

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**
****Homework #8: **
(Due 11/21/03 In Section.)

S72, p. 257-259: 4, 8

S74, p. 265-267: 1, 5, 7

S54, p. 188-190: 1, 2, 3, 4, 7, 11

S60, p. 212-215: 1, 2, 3, 6

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**
****Homework #9: **
(Due Friday, December 5, 2003.) (Thanksgiving Holliday Includes Friday November 28, 2003)

If you think that you need this homework to study for the test please **make a
copy** before you turn it in.

S56, p. 198-200: 1, 2, 6 (use Partial fractions)

S61, p. 218-220: 1, 2, 3

S64, p. 230: 1, 2

S67, p. 238-239: 2, 3, 4

S69, p. 245-246: 2

S74, p. 257-259: 3

Hints on the last problem:

1) Use the fact that the integrand is even so as
the integral is 1/2 of the integral over the whole real line.

2) Replace cos(ax) by e^(iax) and take the real part at the end.

3) Now extend the contour in the usual way and use the residue theorem to
compute the integral.

4) Notice that the integrand has a pole of order 2 at z=ib, so you will need to
use Laurent Series methods to find the residue there.

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**Final Exam:
**Monday
December 8 from 8:00 - 11:00AM.