MATH 618 (SPRING 2010): FINAL EXAM
Instructions: All lemmas, claims, examples, counterexamples, etc. require proof,
except when explicitly stated otherwise.
Closed book: No notes, books, calculators, cell phones, or other electronic devices.
1. (a) (10 po
MATH 618 (SPRING 2013, PHILLIPS): SOLUTIONS TO
SELECTED PROBLEMS IN HOMEWORK 9
Warning: Little proofreading has been done.
1. Rudin Chapter 10 Problem 11
Problem 1.1. Let C satisfy | = 1. Calculate
2
0
1
d
1 2 cos() + 2
by integrating (z )1 (z 1/)1 around
MATH 618 (SPRING 2013, PHILLIPS): SOLUTIONS TO
HOMEWORK 8
Warning: No proofreading has been done.
1. Rudin Chapter 10 Problem 21
Problem 1.1. Let C be an open set which contains the closed unit disk. Let
f be a holomorphic function on such that |f (z )| <
MATH 618 (SPRING 2013, PHILLIPS): SOLUTIONS TO
HOMEWORK 7
Warning: No proofreading has been done.
1. Rudin Chapter 10 Problem 8
Problem 1.1. Let P and Q be polynomials such that deg(Q) deg(P ) + 2. Let
R be the rational function R(z ) = P (z )/Q(z ) for z
MATH 618 (SPRING 2013, PHILLIPS): SOLUTIONS TO
SELECTED PROBLEMS IN HOMEWORK 6
Little proofreading has been done.
For some problems, several solutions are given, usually corresponding to dierent
approaches taken by students in the past.
1. Rudin Chapter 1
MATH 618 (SPRING 2013, PHILLIPS): SOLUTIONS TO
HOMEWORK 5
Little proofreading has been done.
For some problems, several solutions are given, usually corresponding to dierent
approaches taken by students in the past.
1. Rudin Chapter 10 Problem 2
Problem 1
MATH 618 (SPRING 2013, PHILLIPS): SOLUTIONS TO
HOMEWORK 2
Conventions on measures: m is ordinary Lebesgue measure, m = (2 )1/2 m,
and in expressions of the form R f (x) dx, ordinary Lebesgue measure is assumed.
(The choice of notation varies from one solu
MATH 618 (SPRING 2013, PHILLIPS): SOLUTIONS TO
HOMEWORK 1
Conventions on measures: m is ordinary Lebesgue measure, m = (2 )1/2 m,
and in expressions of the form R f (x) dx, ordinary Lebesgue measure is assumed.
Little proofreading has been done.
Some part
MATH 618 (SPRING 2013): FINAL EXAM SOLUTIONS
Instructions: All lemmas, claims, examples, counterexamples, etc. require proof,
except when explicitly stated otherwise.
Closed book. In particular, no notes or books; no calculators, cell phones, or
other ele
MATH 618 (SPRING 2010): FINAL EXAM SOLUTIONS
Instructions: All lemmas, claims, examples, counterexamples, etc. require proof,
except when explicitly stated otherwise.
Closed book: No notes, books, calculators, cell phones, or other electronic devices.
1.
MATH 618 (SPRING 2013): FINAL EXAM
Instructions: All lemmas, claims, examples, counterexamples, etc. require proof,
except when explicitly stated otherwise.
Closed book. In particular, no notes or books; no calculators, cell phones, or
other electronic de
MATH 618 (SPRING 2013, PHILLIPS): SOLUTIONS TO
HOMEWORK 10
Warning: Little proofreading has been done.
1. Rudin Chapter 10 Problem 9
Problem 1.1. For t R, use the method of Problem 8 to compute
eitx
dx.
1 + x2
Check your answer against the inversion theor