Math 441 Schedule

Date	Sections	Homework	Other readings	Programs	Homework solution
8/27(R)	1.1, 1.2		non-dimensionalization notes
9/1(T)	1.1, 1.2	Homework 1			HW1: p1 p2 p3 p4
9/3(R)	1.3		Scheffer et.al. Nature 2001 Jiang-Shi, 2009	Maple: solve and plot ODE Maple: bifurcation
9/8(T)	1.4	Homework 2 Homework 1 due	Hopf bifurcation, Science, 2000 Bifurcation: Scholarpedia	Matlab: pplane Maple: system of ODEs	HW2: p1 p2 Maple
9/10(R)	1.4		Rosenzweig, Science, 1971 May, Science, 1972
9/15(T)	2.1	Homework 3 Homework 2 due	Lim, Tang et.al. Cell, 2009	Maple: regular perturbation	HW3: p1 p2 p3 p4 p5 Maple
9/17(R)	2.1		CDC and swine flu
9/22(T)	2.2 (4.2)	Homework 4 Homework 3 due	boundary value problem notes		HW4: p1 p2 p3 p4 p5
9/24(R)	2.2
9/29(T)	2.3	Homework 5 Homework 4 due		Maple: inner-outer solution Maple: solve polynomial	HW5: p1 p2 p3 p4
10/1(R)	2.3			Maple: solve boundary value problem
10/6(T)	multiscale method	Test 1 Homework 5 due	Secular and multiscale		Test 1: p1 p2 p3 p4 p5 Maple
10/8(R)	2.5	Project guide
10/13(T)	Fall Break	no class

Date	Sections	Homework	Other readings	Programs	Homework solutions
10/15(R)	2.5, 2.6	Homework 6			HW6: p1 p2 p3
10/16(F)		Take home Exam 1 due 5pm
10/20(T)	3.1		Dido's problem (who is Dido)  Isoperimetric inequality Geodesic Gradient Descent
10/22(R)	3.2	Homework 7 Homework 6 due	minimal surface Touching Soap Films - An introduction to minimal surfaces minimal surface archive perioidc minimal surface Torus		HW7: p1 p2
10/27(T)	3.3
10/29(R)	3.5	Homework 8 Homework 7 due	cycloid Brachistochrone curve tautochrone problem a science project about cylcoid	Maple: cycloid Econ problem	HW8: p1 p2 p3
11/3(T)	3.5		n-body problem 3-body problem A new solution to the three body problem - and more
11/5(R)	3.6	Homework 9: 3.6 (2,5) Homework 8 due			HW9: p1 p2
11/10(T)	3.5		2-body problem Kepler problem Kepler's laws Kepler's problem with general relativity Perihelion
11/12(R)	5.1	Homework 9 due	Logistic map May's 1976 nature paper Li-Yorke's "period 3 implies chaos" Chaos Theory	Matlab: time series (Malthus logistic) cobweb (Malthus logistic Bellows) bifurcation (logistic Bellows)
11/17(T)	5.2		Notes for univariant discrete model in biology	Matlab: wildebeest.m us_pop.m
11/19(R)	5.2		Notes of  matrix model in biology world population Fibonacci why population decreases in history	Matlab: matrixcalculation.m graphing.m moving.m stage.m eigen1.m loggerhead.m loggerhead_1.m
11/24(T)	no class	Test 2
11/26(R)	Thanksgiving	no class
12/1(T)	presentation		Tess, Kristina, Ben
12/3(R)	presentation		Will, Michael, Olivia
12/7(M)		Project paper due 5pm
12/11 (F)		Take home Exam 2 due 5pm

Project Ideas:

1. The quasi-steady state assumption: a case study in perturbation, SIAM Review, by Segel (1989).
2. Asymptotic Analysis of a Buckling Problem for an Embedded Spherical Shell, G. W. Jones, S. J. Chapman, and D. J. Allwright,  SIAM J. Appl. Math. Volume 70, Issue 3, pp. 901-922 (2009).
3. Catenoid in an Electric Field, D. E. Moulton and J. A. Pelesko, SIAM J. Appl. Math. Volume 70, Issue 1, pp. 212-230 (2009)
4. The Strongly Confined Schrödinger–Poisson System for the Transport of Electrons in a Nanowire , Naoufel Ben Abdallah, Francois Castella, Fanny Delebecque-Fendt, and Florian Méhats, SIAM J. Appl. Math. Volume 69, Issue 4, pp. 1162-1173 (2009)
5.