Homepage for Math205
AnalysisII
Winter2009
This page will provide updated information about the course.
Please check it regularly.
Please check changes
to solutions HW5: Problem 5, chapter 6
Enrollment:
For problems with and questions about enrollment please contact Andrea
Gilovich(gilovich@math.ucsc.edu) at the Math office (195 Baskin Engineering Bld).
Syllabus: pdf
Instructor:
Maria Schonbek
email: schonbek at math dot ucsc dot edu
phone: 459-4657
Office: Baskin Engineering 353A
Office Hours: T: 12am -1pm, Th 2pm-3pm Th 4-5pm.
Lectures: T-Th 10::-11:45,
Baskin Engineering 379
Textbook: Real and Complex Variables, 3rd edition,
Rudin
First Midterm: February 5, 2009.
Homework:
Homework
problems will be assigned on this webpage each Friday and
will be due
the following Thursday.
(this might be changed)
Homework problems:
HW1:
Page 31: 1, 2, 3, 5.
A.Let (x,M,m) be a measure space. Let A be a dense set
in R. Show that
the function f: X into R is measurable if an only if the set {x
in
X: f(x) \geq a}
is measurable for all a in A.
B.Give an example of a nonmeasurable function.
C. Let f and g be measurable functions then
a. f+g is mesurable functions.
b. f g is measurable functions.
c. |f| and |f|^p are measurable functions .
Answers to HW1
HW2:
Page 32: 7, 8, 9, 10, 12.
Page 58: 1,5,6, 7.
Answers HW2
HW3
Page 58-59: 8, 9, 15, 20
Page 58-60 : 11,12, 21, 25
Answers HW3
HW 4
Due week after exam
Page 60: 24
Page 71: 4, 5
Page 72: 9 (warning:very hard), 10, 11, 12 (hard)
Answers to HW4
Additional Solutions
Problem 4c, Page 71
Problem 9, page 72
Problem 12, Page 72
HW 5
Page 72: 14, 16 ( show just the first part: Egorov Theorem), 20,24.
Page 132-133: 1, 2, 4, 5.
You do not need to hand this in, but you should know how to establish
Prop 6.8.( page 120)
Additional
problems
Solutions
HW5
Chapter3, problem14b
HW6
Page 133: 6, 10 a,b, 13.
Additional
Problems
Hint for Problem 6
HW7 ( due March 13)
Problems HW7
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Final ( Closed Book) Due by
Friday March 20 at 5pm.