Welcome to this webpage!
<br><br>
<a href="syllabus-MAP4484.html">Syllabus</a>
<br>
<br>
<b>Homework assignments:</b><br>
<b><font color=red> Note that late HW is not accepted!</font></b>
<ul>
HW 1, <b>due Mon 1/23</b>: <a href="hw1.pdf">click</a><p>

HW 2, <b>due Fr 2/10</b>: <a href="hw2.pdf">click</a> (correction/clarification Feb 3; see below)<p>

HW 3, <b>due Mon 2/27</b>: <a href="hw3.pdf">click</a><p>   

HW 4, <b>due Wed 3/29</b>: <a href="hw4.pdf">click</a> 
(<font color=red>Typo in problem 2: a and b should be alpha and beta</font>)<br>
(see below for a Mathematica tutorial and an example of a Mathematica notebook)<p>

Suggested problems for PDE's: All problems in Sec 5.1, 5.2, 5.4 from our text. (These will <b>not</b> be graded!)
  
</ul>

<b>Announcements:</b><br>
<ul>
<li> <b><blink><font color=red> The final exam will be in class on Wednesday April 26, not
  in the final exam week.</font></blink></b> <br>
<li> Apparently our textbook is out of print. We will have it copied in Target
  (376-3824, contact person is Laura).<br> Julia Porchiazzo made the order; please
  contact her for details. Her office is in LIT 358.<br>
  Another option is to call one of the several bookstores in town to see if they still have some copies.<br>
  Here's a partial list:<br> 
Gator Bookstore - 374-4500<br>
Goerings Bookstore - 377-3703<br>
TIS Bookstore - 377-1788<br>
Wild Iris Books - 375-7477<br>
UF Bookstore - 392-0194<br>
You could also try to buy it online. I've used mysimon.com, amazon.com, etc.
<li> <font color=green> Copies of the textbook will be available tomorrow Saturday 1/14 in Target from 8 am on.</font>

<li> I'll be out of town in the week of February 20-24. There will be 2 guest lectures by 
<a href="http://www.math.ufl.edu/~maia/">Professor Martcheva</a> 
(on Monday 2/20 and Wednesday 2/22) and 1 by <a href="http://www.math.ufl.edu/~pilyugin/">Professor Pilyugin</a> 
(on Friday 2/24).

<li> Feb 3:  I corrected a mistake (in problem 1) and clarified problem 2 in HW2.

<li> Feb 8: Here are some notes on the renewal equation: <a href="renewal1.jpg">page 1</a>,
  <a href="renewal2.jpg">page 2</a>.

<li> Feb 8: Here are notes on the simple birth-death process:
  <a href="birth-death1.jpg">page 1</a> (<font color=red>Typo: lambda is birth rate,
  mu is death rate)</font>, 
  <a href="birth-death2.jpg">page 2</a>, <a href="birth-death3.jpg">page 3</a>,
  <a href="birth-death4.jpg">page 4</a>, <a href="birth-death5.jpg">page 5</a> 
(<font color=red>Typo: the variance of N(t) in Case 1 should be 2n_0 lambda t)</font>.

<li> As we agreed in class, <font color=red>Exam I</font> will be on <font color=red>Wed March 1</font> in class.<br>
  It covers everything up to and including the birth-death process.
<li>Feb 13: Solutions to problem 5 in HW2: <a href="hw2-sol5-p1.jpg">page 1</a>, 
  <a href="hw2-sol5-p2.jpg">page 2</a>, <a href="hw2-sol5-p3.jpg">page 3</a>,
  <a href="hw2-sol5-p4.jpg">page 4</a>. 
<li>Feb 20: Topics for exam I: Everything discussed in class (discrete models, density dependence, continuous-time models, Verhulst's equation, chemostat model, meta-population models, delay equations, age structure: Leslie's model including Perron-Frobenius Thm and particularly the concepts of irreducibility and primitivity, Mc Kendrick's model including the renewal equation, method of characteristics for solving PDE's, stochastic models: simple birth-death process, generating function). Best way to prepare: understand class notes, understand solutions to all HW problems. The exam problems will be very similar to what we did in class, or what you did to solve HW.
<li>Mar 10: Here are some <a href="http://www.mpcfaculty.net/ron_rinehart/1B/oscillat.htm">links</a> 
to info on the Belousov-Zhabotinskii reaction.<br>
The first link to the University of Regensburg has the movie we played in class, and also the details of the
reactions involved.<br>
The second link to Regensburg has a load of other reactions and movies of oscillatory reactions.

<li>Mar 14: Go <a href="http://library.wolfram.com/conferences/devconf99/withoff/index2.html"> here </a> for a Mathematica tutorial. And click 
<a href="simulatie-PDL-scaled-ex.nb"> here</a> for a sample 
of a Mathematica notebook which could be helpful when you're doing HW4. (to save, right-click and choose
"Save Link Target As"; after that, load the file in Mathematica which should be available on most campus computers)<br>

<li>Mar 20: Click <a href="hal-cyclicgene.pdf"> here</a> for notes by Hal Smith 
(Department of Mathematics at Arizona State University) 
on the on-off switch for tryptophan synthesis in E-coli.

<li>Mar 22: Near future agenda: Review for Ex II on Fr 3/31. <font color=red> 
Exam II on Mon 4/3</font> will be in class and covers everything we discussed after 
birth-death processes up to and including the genetic network switch in E-coli. The 
format of Ex II is the same as that of Ex I, and the best way to prepare yourself 
is also still the same.

<Li>Mar 24: If you're an undergraduate interested in an REU (Research Experience for Undergraduates),
<a href="http://www.math.ttu.edu/~padhu/reu_ttu06.html">click here</a>.

<li>Mar 27: Target Copy on University Ave has copies of Chapter 5 from our Textbook for sale. 

<li>Mar 29: We will have a review session on Fr Mar 31 discussing the material for Ex II.

<li>Mar 31: Topics for Exam II: Everything discussed in class except for the cell cycle model discussed by Professor
Pilyugin (but the epidemiological model Professor Martcheva discussed IS part of the material).
More precisely the topics are: phase plane analysis (trapping regions, carefully argue why solutions converge to a
steady state), linearization at steady states of nonlinear systems,
classification of  steady states in 2D (stable or unstable node, saddle, stable or unstable spiral),
Lotka-Volterra equations, SIR model, chemical reaction networks (knowing how to write down ODE's for concentrations of
all chemicals involved, assuming mass action kinetics), Brusselator, periodic orbits, Poincare-Bendixson Theorem, 
rescaling of systems (to reduce the number of parameters), tryptophan synthesis model.<br>
The format of the exam is the same as for Exam I (open "everything").

<li>April 14: For the solution to the third problem on Exam II, <a href="ex2-prob3.pdf"> go here</a>.

<li>April 17: The final exam (which will take place in class on April 26) covers all the material of Exam II (see the Mar 31 announcement above), and
the material on PDE's as discussed in class (see also chapter 5 in our text, sections 5.1, 5.2, 5.3, 5.4, 5.6 and provided
we get there in class, also 5.7).<br>
As usual, this will be an open book exam. There will be
2 problems, one on the material of Exam II and another on the material of chapter 5.

</ul>