Math 310, Fall 2012
Homework 10 Solutions
Due: November 16
Be sure to read the homework guidelines before completing this assignment.
(1) Suppose that f is analytic in a domain G, that z0 G and that f
Problem Set 4: Mathematics 310
Instructor: Stanley Chang
1. Let F : R2 R2 be a vector field. We say that the field is incompressible if the divergence
F is zero, and we say that the field is irrotati
Problem Set 3: Mathematics 310
Read pages 196-204 of the Rudin text.
1. Let f : Rn Rm be a function, and let its i-th coordinate be given by fi : Rn R. Prove that
f is continuous at a = (a1 , . . . ,
Problem Set 6: Mathematics 310
Instructor: Stanley Chang
1. Find all removable singularities, zeroes and poles of the given functions. Find the order of the
zeroes and poles. Write down the analytic e
Problem Set 2: Mathematics 310
1. For the following subsets of C, state whether it is (i) open, closed or neither, (ii) connected.
No explanation is required. Then identify (iii) its boundary and (iv)
EASTRIDGE GYM SCHEDULE - DECEMBER
Revised: 12.15.16
Thursday
Gym Closures:
December 16 & 17
Breakfast with Santa
December 24 (close at 5pm)
Christmas Eve
December 25
Christmas Day
December 31 (close a
Math 310, Fall 2012
Homework 1 Solutions
Due: September 7
Be sure to read the homework guidelines before completing this assignment.
(1) For z, w C, show that
|z + w|2 = |z|2 + 2Re(z w) + |w|2
and
|z
Math 310, Fall 2012
Homework 3 Solutions
Due: September 21
Be sure to read the homework guidelines before completing this assignment.
Read sections 16-22 of the text.
1
(1) Use the denition of the de
Math 310, Fall 2012
Homework 5 Solutions
Due: October 5
Be sure to read the homework guidelines before completing this assignment.
Read sections 30-35 of the text.
(1) Suppose that T is a Mobius tran
Math 310, Fall 2012
Homework 2
Due: September 14
Be sure to read the homework guidelines before completing this assignment.
(1) Suppose n > 1. Let n = cos
2
n
+ i sin
2
n
.
0
1
2
n1
(a) Prove n + n +
Math 310, Fall 2012
Homework 6
Due: October 19
Be sure to read the homework guidelines before completing this assignment.
Read sections 35-40 of the text.
(1) Suppose that C is a simple closed contou
Math 310, Fall 2012
Homework 4
Due: September 28
Be sure to read the homework guidelines before completing this assignment.
Read Chapter 3 of the text.
(1) Prove the complex analogs of the usual form
Math 310, Fall 2012
Homework 7
Due: October 26
Be sure to read the homework guidelines before completing this assignment.
Read sections 41-43 of the text.
(1) Calculate the following integrals:
(a)
s
Math 310, Fall 2012
Homework 12
Due: December 11
Be sure to read the homework guidelines before completing this assignment. For all improper integrals, you
are free to assume that these integrals do c
Math 310, Fall 2012
Homework 11
Due: November 30
Be sure to read the homework guidelines before completing this assignment.
Read sections 56-59 in the text.
z
.
1)(ez 2)
Solution. Since the numerato
Math 310, Fall 2012
Homework 9 Solutions
Due: November 9
Be sure to read the homework guidelines before completing this assignment.
Read sections 48-51 of the text.
(1) Give the MacLaurin series for
Math 310, Fall 2012
Homework 8 Solutions
Due: November 2
Be sure to read the homework guidelines before completing this assignment.
Read sections 43-45 of the text.
(1) Suppose that is a simple close
Problem Set 7: Mathematics 310
Instructor: Stanley Chang
1. Use a semicircular contour to compute the following.
Z
x2
(a)
dx
4
1 + x
Z
x2
(b)
dx
4
2
x + 4x + 3
2. Compute the following by changing