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 FridayÕs 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) |
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4 W
1/28 |
Convergence
of Functions: uniform (Ch 17). Mathematica animation of
sequence of functions. |
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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) |
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7 |
Lebesque
Integral, Dominated Convergence Theorem, Bounded Convergence Theorem. |
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8
F
2/06 |
Interchanging:
limit and integral; derivative and integral; order of integration. |
HW 3: due (Wed, Friday). |
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9 M
2/08 |
Taylor
Polynomials, Mathematica Notebook.
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10 W
2/10 |
Taylor
Remainder Theorem, convergence of sequence of Taylor polynomials |
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11 F
2/12 |
Infinite
series. |
Hw 4: due Wed,
Friday |
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12 M
2/16 |
Infinite
Series. Harmonic series. Project Descriptions (return
Choices sheet by Friday). |
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13 W
2/18 |
Geometric
Series, Alternating Series, P-test |
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14 F
2/20 |
Comparison
Test, Absolutely and Conditionally convergent. |
Hw 5: due Wed, Friday |
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15 M
2/23 |
More
absolutely vs conditionally convergent; |
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16 W
2/25 |
Proof
of Ratio Test. Series of Functions |
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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. |
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20 F
3/06 |
No
class |
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21 M
3/16 |
Derived
series works nicely J Answer
key to Midterm Part 1 (Available after Friday) |
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22 W
3/18 |
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23 F
3/20 |
Iteration
using Excel. Intro to 2 dimensional dynamical systems. |
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24 M
3/23 |
Metric
Spaces (Ch. 27) |
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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 |
Banach
Fixed Point Theorem. |
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28 W
4/1 |
Space
Filling Curves; NewtonÕs Method |
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29 F
4/3 |
Now
where differentiable curves. Dynamical systems. |
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30 W
4/ 7 |
Examples
of metric spaces involving function spaces. |
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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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32 |
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33 |
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34 |
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35 |
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36 |
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37 |
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38 |
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39 |
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