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.