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455 Diary |
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Class Date |
Class # |
HW |
Topics explored |
Source |
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due |
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Tue, Jan 18, 05 |
1 |
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Nonoverlapping generations, Malthusian (geometric) growth, struggle for existence, logistic map |
JR handout |
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Thu, Jan 20, 05 |
2 |
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Maple Orientation I (in computer lab, Hochstetter 139). Numerical exploration of logistic map dynamics. |
JR handout |
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Tue, Jan 25, 05 |
3 |
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Fixed points, attracting and repelling, conjugacy of maps, Hartman-Grobman theorem, slope criterion for attraction/repulsion, range of existence & stability of positive f.p. in logistic map |
JR handout |
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Thu, Jan 27, 05 |
4 |
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Periodic points, analysis of period-2 in logistic map, conjugacy of logistic (r=4) map with tent map, sensitive dependence on ICs / butterfly effect, cannibalism model |
JR handout |
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Tue, Feb 1, 05 |
5 |
HW1 |
Small-group development of discrete-time models of age-structured populations. |
Own brains, Haberman Section 35. |
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Thu, Feb 3, 05 |
6 |
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Regular non-negative matrices. Perron-Frobenius theorems. Dominant eigenvalue, stable age distributions. |
JR lecture. Haberman Ex 35.2. |
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Tue, Feb 8, 05 |
7 |
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Further discussion of discrete-time age-structured models. Deterministic vs. random or stochastic models. Basics of probability. Modelling radioactive decay. |
JR Probability pdf |
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Thu, Feb 10, 05 |
8 |
HW2 |
Comments about Exam #1. Distribution of wait-times in radioactive decay. Generating random numbers with a specified distribution. |
JR Probability pdf |
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Tue, Feb 15, 05 |
9 |
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EXAM#1 |
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Thu, Feb 17, 05 |
10 |
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Evolution of ensemble mean and variance in radioactive decay. Large-numbers limits. |
JR&KK: Text 1d |
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Tue, Feb 22, 05 |
11 |
HW3 |
SIR model of epidemic: deterministic and stochastic versions, and their comparison. |
JR&KK: Text 1d |
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Thu, Feb 24, 05 |
12 |
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Small-group development of better epidemic models. |
Own intuition and experience. |
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Tue, Mar 1, 05 |
13 |
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Basics of heat transfer, and derivation of the heat equation. |
JR: Text 2a |
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Thu, Mar 3, 05 |
14 |
HW4 |
Heat equation in 1D, simplest steady state solution. Diffusion, diffusion of perfume experiment. Fundamental plane source solution: spreading gaussian. |
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Tue, Mar 8, 05 |
15 |
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Time to max temp in briefly heated rod. Method of images for finite slab. Hottest day of the year. |
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Thu, Mar 10, 05 |
16 |
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Chemistry. Principle of mass action as a truncated Taylor (MacLaurin) series. |
JR: Text 3a |
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Tue, Mar 22, 05 |
17 |
HW5 |
Exam #2 review. |
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Thu, Mar 24, 05 |
18 |
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EXAM#2 |
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Tue, Mar 29, 05 |
19 |
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ODEs of chemical dynamics. Equilibrium, bistability in Shlogl model. Brusselator. |
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Thu, Mar 31, 05 |
20 |
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Brusselator, uniform steady state, small perturbations of USS, linearizing, linear stability analysis, Fourier synthesis. |
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Tue, Apr 5, 05 |
21 |
HW6 |
Linear stability analysis of brusselator (real roots case): stability boundary in parameter space. Numerical corroboration (java applet). |
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Thu, Apr 7, 05 |
22 |
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Numerical methods for reaction-diffusion PDEs: finite difference approximations to 1st & 2nd derivatives, Euler's method. |
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Tue, Apr 12, 05 |
23 |
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Qualitative analysis of roots of w^2 + Gamma w + Delta, root types in the n,B plane of Brusselator. Pure modes of the linearized model: animations for various kinds of real and complex w, and mode combinations. Group work: finite difference formulas for derivatives. |
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Thu, Apr 14, 05 |
24 |
HW7 |
Gray-Scott model: Pearson's experiment. Stripes in nature. Group activity: Euler finite difference solution of heat equation. |
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Tue, Apr 19, 05 |
25 |
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Euler finite-difference solution of 2D heat equation as automaton. Conway's 23/3 cellular automaton. Waves: wave equation. |
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Thu, Apr 21, 05 |
26 |
HW8 |
Excitable dynamics. |
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Tue, Apr 26, 05 |
27 |
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Review of semester, and of exam material. |
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Thu, Apr 28, 05 |
28 |
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EXAM#3 |
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