Math-4210 Spring 2012
Assignment 1: Metric spaces
Due Thursday, February 4 (Either in class, or my mailbox in AE 301, or under my door
AE 405).
As concerns the assigned problems, you are welcome to consult the text and notes and discuss
the problems with
Mathematical Analysis II, MATH4210
Homework #5
Gregor Kovai
cc
Due: Thursday, March 3, 2011
Solve problems 83 through 89, 91, and 93 and on the problems list.
Project: Problem 90, for 20 points for two people.
Project: Problem 92, for 20 points for two pe
Mathematical Analysis II, MATH4210
Homework #7
Gregor Kovai
cc
Due: Thursday, March 24, 2011
Solve problems 103 through 110 on the problems list.
Problem 106 is extra credit. If you know linear algebra well, it is very easy.
SOMEOM 05p 3W Work From.
(a) Problem 9.2.5#11. Let M be a metric space and A1 2 A2 2 be a sequence of
nonempty compact sets (a nested sequence). Prove agglAk is nonempty. Hint:
Complements of sets Ak are open. If the intersection is empty then the comple
2. Find the directional derivative du f (0, 0) of the function
2
$9
7' : A 3 0 =
my) 332+, f( 0) 0
for any u 2 [C036,Si119]. Prove that f is not differentiable at (0, O).
t w e l {[email protected](£gime)l %
04M Q (0)0) w W ?[U ws-6+§1M20 O 3. Let E be a closed subs
Mathematical Analysis II, MATH4210
Homework #10
Gregor Kovai
cc
Due: Thursday, April 14, 2011
Solve problems 131 through 137 on the problems list.
Only indicate the integral for the total length in 133 (ii). It cannot be computed explicitly
in terms of el
Mathematical Analysis II, MATH4210
Homework #8
Gregor Kovai
cc
Due: Thursday, March 31, 2011
Solve problems 111 through 119 on the problems list.
If you did problem 80 as a project, you can add problem 120 to it for 5 points.