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 xn?

b.        What topics from Real Analysis 1 are related to dynamical systems.

Please fill in Background Information survey before Friday’s class; Click here to take survey

Pre-Course 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, P-test

 

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 in-class 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

Answer key to HW 6

Answer key to Closed book midterm

 

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 3rd.

26

F 3/27

Laura: Fourier Series. Handouts on Blackboard.

HW Assignment #2 from her handouts due Friday April 3.

27

M 3/31

Midterm Take Home Scoring Key

Banach Fixed Point Theorem.

 

 

 

 

28

W 4/1

Space Filling Curves; Newton’s 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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33

 

 

34

 

 

 

 

 

 

 

 

35

 

 

36

 

 

37

 

 

38

 

 

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