Population Biology
BIOL 763/599 / SCCC 411B / MATH 599
Spring 1999
University of South Carolina

Professor Matt Miller
miller@math.sc.edu
Department of Mathematics
 Professor Dave Wethey
wethey@biol.sc.edu
Department of Biological Sciences

Feb 2-4: Dimensional analysis, systems (beginning)

  • Walk through of the Maple worksheets lead.mws and volterra.mws and answer the questions that you find in them. The main thing here is to understand the difference between the phase plane plot (phase portrait) for a system and the time plot. How would you recognize equilibria in each of these, for example?
  • Study the handout on vectors, matrices, transformations, systems of DE's, and linearization, working out the problems that are scattered throughout the text
  • Augment this by stepping through matrix.mws and eigen.mws
  • You'll find the various calculus and DE texts present this material in all sorts of different ways, and to find the one that suits you best it might pay to do a little preliminary browsing.
  • You will probably find it is easier to read EK, chapter 5 (on the phase plane and the various phenomena there) before the technical material of chapter 4. Section 5.1 gives a "phase line" analysis of the equations that we have been working with; this is nice, but not essential. Sections 5.2, 5.3, 5.4, and 5.7 give the main points of the analysis of systems in the plane (skipping for the time being the connection to nonlinear systems: nullcline analysis and linearization at equilibrium points). If you really want details read sections 4.8 and 4.9 (but if you just understand the time plots on page 137, that should be enough). The really important pages are 185 and 187: what local behavior goes with what eigenvalues?