A tentative course schedule is below. Recommended eadings are
in "Population Biology" by Hastings, on reserve. The book
"Mathematical Models in Biology" by Edelstein-Keshet will also
be on reserve for the course. I will also try and get out via e-mail
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 1:40-3:00 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 2-8116 email:amhastings@ucdavis.edu
These will be sent via e-mail using the class e-mail list.
|
DATE |
TOPIC |
READING IN EDELSTEIN-KESHET |
READING IN HASTINGS |
||||
|
9/24 |
introduction, model
formulation |
pages 3-11 |
Pages 1-5 |
||||
|
9/29 |
qualitative behavior of
difference equations using linear algebra-part 1 |
pages 12-21 |
Pages 9-38 |
||||
|
10/1 |
qualitative behavior of
difference equations using linear algebra-part 2 |
||||||
|
10/6 |
Complex eigenvalues, steady
states, stability of difference equations< |
Pages 22-25, 39-44 |
Pages 41-60 |
||||
|
10/8 |
more on steady states and
stability of difference equations |
pages 55-60 |
Pages 181-188 |
||||
|
10/13 |
chaos and all that |
pages 46-55 |
Pages 96-101 |
||||
|
10/15 |
Nicholson-Bailey dynamics |
||||||
|
10/20 |
model formulation and dimensional
analysis |
pages 113-128 |
Pages 81-87 |
||||
|
10/22 |
steady states and stability
of differential equations |
pp. 128-145 |
Pages 87-92;119-128 |
||||
|
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 164-186 |
Pages 129-180; 189-200 for both lectures |
||||
|
11/5 |
qualitative behavior of
differential equations |
pages 186-199 |
|||||
|
11/10 |
review of functions of
several variables & the diffusion equation |
pp. 385-395 |
|||||
|
11/12 |
the diffusion equation-part
2 |
pages 406-410, 437-
441,447-452 |
|||||
|
11/17 |
Diffusion equations-part 3 |
||||||
|
11/19 |
Diffusion equations-part 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 |