## Math 4 Log

Week 1 (January 7-11) :

Read chapter 1-3 of the text and carefully read the article on HIV-1 Dynamics by Perelson et al on pages 15-22 of your text. The first assignment is based on the ideas and equations in this reading. The assignment will be due on Friday January 18th. On Wednesday we developed our first method to construct the solution of a differential equation as well as stating our fundamental theorem concerning these solutions.

Week 2 :

X-Session in Starr 274 Thursday Jan. 17 Please read carefully chapter 4 and skim chapter 5. The first assignment is due Friday. On Thursday we will have our first Maple help session in Berry Starr 274 . The first group assignment is due Monday February 11th.

In lecture we are busy exploring basic differential equations like modifications of the logistic equation. The following theorem is very useful for understanding the logistic equation, especially when we apply it to more complicated phenomena.

Week 3 :

No X-session. Please read carefully chapter 5 and skim chapter 6. In class we have been busy exploring systems of equations like the Lokta-Voltera system.

Week 4 :

X-Session in Starr 274 Thursday Jan. 31 (must ends by 1 rather than 1:15 on this particular day). Please read carefully chapter 6. In class we have been busy exploring phase portraits.

Week 5 :

X-Session in Starr 274 Thursday Feb. 7 Please read carefully chapter 7. In class we have been begun exploring the notion of bifurcation, and have begun motivating linear systems and their relations to non-linear systems and equilibrium point exploration. In particular we have begun to explore uses and meaning of the Linearization theorem.

Week 6 :

No X-session. Please read carefully chapter 8, and the three reading at the end of chapter 7. The second individual assignment is due next Friday (February 22nd). In class we have begun to explore the 2 by two systems arise in the Big Theorem as well as this theorem's meaning and use.

Week 7 :

X-Session in Starr 274 Thursday Feb. 21 Please read carefully chapter 11 and skim chapters 9 and 10. The version of these chapters which you will need of is summed up by our our Big Theorem . In class we have been exploring how to use the big theorem via the eigenvalues and the detection theorem. The final group project is due Wednesday March 6.

Week 8 :

X-Session in Starr 274 Thursday Feb. 28 (This is a come if you want help session) In class we are going through some specific epidemic models from the literate. In particular your group will produce some variations of the De Leo and Dobson models (it may be useful to look over how to decouple the birth and death rates). Below is a plot of a model from the De Leo and Dobson paper on on Allometry and Simple Epidemic Models for Microparasites. and here our some solutions to the variation explore above: the article , variation 1 , variation 2 , and variation 3 .

Week 9 :

On Monday we took a look at some less vicious epidemics, that may help you clear up some last minute issues arising in your final projects (Due Wednesday). I will hold extra office hours on Tuesday and Wednesday day from 1:00-3:00. Wednesday March 6 is the last day of class

On Wednesday day we will introduce the van der Pole equation, whose phase portrait is displayed below. Tomorrow there is a Colloquium at 4:00 in 102 Bradley Hall on the "Mathematical Modeling of the Portion of the Brain that Governs Circadian Rhythm" where Clyde Martin will use the van der Pol equation in order to explore some interesting sounding biological phenomena.