Math
302
Spring
2009
Prof.
Donnay
Class
Materials and Assignments
Class#, Date 
Class
Material 
Assignment 
1 W
1/21 
Introduction
to Course. Iteration and Dynamical Systems; an application of analysis. Worksheet on dynamical
systems (finish for Friday). Extra
Questions for worksheet: a.
For f(x) = ½ x, can you
find a general formula for x_{n}? b.
What topics from Real Analysis
1 are related to dynamical systems. 
Please
fill in Background Information survey before FridayÕs class; Click
here to take survey PreCourse Assessment
(due Friday). 
2 F
1/23 
Connections
between Dynamical Systems and Analysis. Fixed
Point theorem. (Limit pt of a continuous iteration is a fixed pt) 
HW1 (parts due Monday, Wed, and Friday) 
3
M
1/26 
Convergence
of Functions: pointwise (Ch 17) 

4 W
1/28 
Convergence
of Functions: uniform (Ch 17). Mathematica animation of
sequence of functions. 

5 F
1/30 
Thm: Uniform
limit of continous functions is continuous. Can
bring limit inside integral for limit of functions providing the convergence
is uniform. 
HW 2: (due Wed, Friday) Hints to HW2: use if you get stuck. 
6 
Measure
theory, sets of measure zero. (Ch 18) 

7 
Lebesque
Integral, Dominated Convergence Theorem, Bounded Convergence Theorem. 

8
F
2/06 
Interchanging:
limit and integral; derivative and integral; order of integration. 
HW 3: due (Wed, Friday). 



9 M
2/08 
Taylor
Polynomials, Mathematica Notebook.


10 W
2/10 
Taylor
Remainder Theorem, convergence of sequence of Taylor polynomials 

11 F
2/12 
Infinite
series. 
Hw 4: due Wed,
Friday 



12 M
2/16 
Infinite
Series. Harmonic series. Project Descriptions (return
Choices sheet by Friday). 

13 W
2/18 
Geometric
Series, Alternating Series, Ptest 

14 F
2/20 
Comparison
Test, Absolutely and Conditionally convergent. 
Hw 5: due Wed, Friday 



15 M
2/23 
More
absolutely vs conditionally convergent; 

16 W
2/25 
Proof
of Ratio Test. Series of Functions 

17 F
2/27 
Sequences
of Functions; Examples of Power series that are Geometric Series, Radius of
Convergence of Power Series. Ch 21. List of possible topics for inclass midterm. 
Quiz
6: Due Monday in class Hand
in one problem that could be put on the test. 
18 M/3/02 
Radius
of Convergence, integrating, differentiation of power series 
HW 6: due Wed March 18. Hints for HW 6 
19 W
3/04 
Proof
of Radius of Convergence Theorem. 

20 F
3/06 
No
class 

21 M
3/16 
Derived
series works nicely J Answer
key to Midterm Part 1 (Available after Friday) 

22 W
3/18 


23 F
3/20 
Iteration
using Excel. Intro to 2 dimensional dynamical systems. 

24 M
3/23 
Metric
Spaces (Ch. 27) 

25 W
3/25 
Metric
Spaces (Ch. 27 and Ch. 28) 
Ch.
27 #1; Ch. 28 #1 due Friday April 3^{rd}. 
26 F
3/27 
Laura:
Fourier Series. Handouts on Blackboard. 
HW
Assignment #2 from her handouts due Friday April 3. 
27 M
3/31 
Banach
Fixed Point Theorem. 




28 W
4/1 
Space
Filling Curves; NewtonÕs Method 

29 F
4/3 
Now
where differentiable curves. Dynamical systems. 

30 W
4/ 7 
Examples
of metric spaces involving function spaces. 

31 F
4/9 
Mean
Value Theorem to estimate contraction Mathematica
commands for NestList.

HW wk 11. Due Friday 4/16. 
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