A tentative course schedule is below. Recommended eadings are
in "Population Biology" by Hastings, on reserve. The book
"Mathematical Models in Biology" by EdelsteinKeshet will also
be on reserve for the course. I will also try and get out via email
notes for some of the lectures (perhaps scanned versions or perhaps retyped
versions). Grading will be based on homework assignments (70%) and
a take home final (30%). The lecture schedule is tentative because my goal here
is to teach and not to lecture. Class is 1:403:00 P.M. in 1020 Wickson.
Below the syllabus is a description of
various tools for computing numerical solutions. I will do in class demos
with some of them, in particular xpp.
Instructor: Alan Hastings,
3136AWickson 28116 email:amhastings@ucdavis.edu
These will be sent via email using the class email list.
DATE 
TOPIC 
READING IN EDELSTEINKESHET 
READING IN HASTINGS 

9/24 
introduction, model
formulation 
pages 311 
Pages 15 

9/29 
qualitative behavior of
difference equations using linear algebrapart 1 
pages 1221 
Pages 938 

10/1 
qualitative behavior of
difference equations using linear algebrapart 2 

10/6 
Complex eigenvalues, steady
states, stability of difference equations< 
Pages 2225, 3944 
Pages 4160 

10/8 
more on steady states and
stability of difference equations 
pages 5560 
Pages 181188 

10/13 
chaos and all that 
pages 4655 
Pages 96101 

10/15 
NicholsonBailey dynamics 

10/20 
model formulation and dimensional
analysis 
pages 113128 
Pages 8187 

10/22 
steady states and stability
of differential equations 
pp. 128145 
Pages 8792;119128 

10/27 
linearization and linear
systems for differential equations 

10/29 
linear systems of
differential equations and stability criteria 

11/3 
phase plane methods 
pages 164186 
Pages 129180; 189200 for both lectures 

11/5 
qualitative behavior of
differential equations 
pages 186199 

11/10 
review of functions of
several variables & the diffusion equation 
pp. 385395 

11/12 
the diffusion equationpart
2 
pages 406410, 437
441,447452 

11/17 
Diffusion equationspart 3 

11/19 
Diffusion equationspart 4 

11/24 
TBA 

12/1 
TBA 



Solving
ODE's and other dynamical systems numerically is an important first step,
especailly for nonlinear systems.
This table is a summary of easily available solutions.
 
Program 
COST 
Handles ODES 
progamming needed 
installation 
graphics 
handles PDE's 
includes continuation package and bifruaction diagrams 
other 
free 
Y 
very minimal 
easy except on windows, possible on windows 
yes 
no 
yes 
runs on ipad and iphone, very good tutorials and texts 

free 
Y 
moderate 
moderate 
yes 
yes 
no 
very good tutorials and texts 

$ + free 
Y 
very minimal 
moderate 
yes 
no 
yes 
good tutorials 

$$$ 
Y 
very minimal 
easy 
yes 
yes 
no 
symbolic as well 

do it yourself 
free 
Y 
lots 
depends 
depends 
yes 
no 