MATH 215APROBLEM SET I
JUN LI
Problem set due Wednesday, Oct. 3, 5pm, delivered to oce 383Z.
Textbook:
1.4(Page 24). 7, 8, 12.
2.6. 4, 6, 8, 9, 12.
a. Let be a connected region that is divided into tw
Complex Analysis, Autumn 2009
Stanford University course 215A
HW 3: (due by October 22 at 3:30pm either in class or in Jose Pereas mailbox)
Please write-up your own solutions to problems in an organiz
Solutions Homework 3
Wednesday, October 28 2009
Math 215A
Grading Scheme: In this homework questions 1,2.2, 2.9, 4,5,6 were graded. The
mapping from questions to points worth is as follows : p(1) = 2,
Solutions Homework 2
Wednesday, October 14 2009
Math 215A
Grading Scheme:In this homework questions 2,4,5,6,9,10 were graded. The mapping
from questions to points worth is as follows : p(2) = 2, p(4)
Solutions Homework 1
Wednesday, October 7 2009
Math 215A
Grading Scheme: In this homework questions 1,4,6,9,10,11 were graded. The mapping from questions to points worth is as follows : p(1) = 2, p(4)
Solutions Homework 5
Monday, November 9 2009
Math 215A
Grading Scheme: In this homework questions 1.10, 2.3, 2.4,2.5,2.6 were graded. The
mapping from questions to points worth is constant and equal t
Complex Analysis, Autumn 2009
Stanford University course 215A
HW 6: (due by November 12 at 3:30pm either in class or in Jose Pereas mailbox)
Please write-up your own solutions to problems in an organi
Solutions Homework 7
Wednesday, November 30 2009
Math 215A
Grading Scheme: In this homework questions 1 and 2 were graded. The mapping
from questions to points worth is constant and equal to 5.
1. Sol
Solutions Homework 6
Wednesday, November 18 2009
Math 215A
Grading Scheme: In this homework questions 1, 2, 3, 4 and 5 were graded. The
mapping from questions to points worth is constant and equal to
Complex Analysis, Autumn 2009
Stanford University course 215A
HW 2: (due by October 8 at 3:30pm either in class or in Jose Pereas mailbox)
Please write-up your own solutions to problems in an organize
Complex Analysis, Autumn 2009
Stanford University, Department of Mathematics course 215A
HW 1: (due by October 1, 3:30pm, either in class or in Jose Pereas mailbox)
Please write-up your own solutions
MATH 215 SOLUTION TWO
2.6-15. Suppose f is a non-vanishing continuous function on D that is holomorphic
in D. Prove that if |f (z )| = 1 whenever |z | = 1 then f is constant.
Proof. By maximum module
MATH 215APROBLEM SET II
JUN LI
Problem set due Wednesday, Oct. 10, 5pm, delivered to oce 383Z.
Textbook:
2.6. 15;
2.7. 4;
3.8. 2, 4, 9*, 12, 13, 14;
3.9. 3;
a. Let f be holomorphic on = cfw_z | 1 < Re
MATH 215 SOLUTION THREE
3.8-10. Show that if a > 0, then
0
log x
dx =
log a.
2
+a
2a
x2
Proof. Fix the branch of a translate of log given by log(i) = 0 on C i(, 0]. The
residue of f (z ) = log(z )/(z
MATH 215APROBLEM SET III
JUN LI
Problem set due Wednesday, Oct. 17, 5pm, delivered to oce 383Z.
Textbook:
3.8. 10, 12, 15, 16 , 17;
3.9. 5*.
a . Show that any meromorphic function on C (= P1 ) is a ra
MATH 215A SOLUTION FOUR
JUN LI
5.7-1. Prove that if f is holomorphic in the unit disc, bounded and not identically
zero, and z1 , z2 , ., zn , . are its zeroes, (|zk | < 1), then
(1 |zn |) < .
n
n
Pro
MATH 215APROBLEM SET VI
JUN LI
Problem set due Wednesday, Oct. 24, 5pm, delivered to oce 383Z.
Textbook:
5.6. 10a, 11, 13, 15 .
5.7. 1, 2*.
a. Show that a bounded harmonic function u on the upper-half
MATH 215APROBLEM SET V
JUN LI
Problem set due Wed., Oct. 31, 5pm, delivered to oce 383Z.
Textbook:
6.3, 3, 10, 13, 17.
a. Prove the partial fraction formula
1
2
=
2
sin a n= (n + a)2
by evaluating the
MATH215APROBLEM SET VI
JUN LI
This set is due 5PM Wednesday, Nov. 14.
8.5. 5, 11, 16.
a. Assuming Riemann hypothesis and following the techniques developed in Chapter 7, discuss how to derive an optim
Solutions Homework 4
Monday, November 2 2009
Math 215A
Grading Scheme: In this homework questions 1, 2, 4.6 and 6 were graded. The
mapping from questions to points worth is as follows : p(1) = 2, p(2)