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 DidoIsoperimetric 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)