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

Jan 12-14: Rate Equations and Euler's Method

  • Complete the worksheet on unconstrained population growth. This will serve as an introduction to the idea of a ``continuous model'', that is, a differential equation. Your hand computations illustrate the basic idea behind all techniques of numerical and graphical solution of such an equation.
  • Read Edelstein-Keshet sections 4.1, pp 115-121, and/or Hastings 1.1, 2.1 (just pp 9-12, and box 2.1), 4.1-4.2 on the basic exponential and logistic continuous models. Understand what a DE is, and the various ways that it can be ``solved'' (formula by integration, numerically, graphically).
  • Understand the various ingredients in a mathematical model: DE, initial condition(s), independent variable, dependent variable(s), parameters.
  • Do E-K page 152 problems 1, 2, 3, 5a-f
  • Work through the introductory Maple worksheet intro.mws
  • Work through the Maple worksheet on Euler's method growth.mws
  • Take a look at what else is available Index
  • For next Tuesday (Jan 19), begin reading Cohen 1995 Science 269:341-346 and E-K sections 4.2-4.4, pp 121-128.