Jan Zijlstra, Math 3120 Fall 2006

 The Use of MAPLE           in Models involving Differential Equations.

MODULE A:  Models involving separable first order DE

Section A.1  A Learning Model

 Model Hypothesis: 'The rate of learning is proportional to the amount left to learn' Corresponding DE: y'(t) = k ( 100 - y(t) ) Symbols: y(t): amount mastered, in % of the learning task, at time t (hours). y'(t): rate of learning, in % of learning task per hour, at time t.   k: rate constant.

Section A.2.  A Model for Exponential Growth
 Model Hypothesis: 'The population growth is proportional to the population size ' Corresponding DE: y'(t) = k y(t) Symbols: y(t) : population size, in millions, at time t (years). y'(t) : population growth, in millions per year, at time t.   k: rate constant.

Section A.3.  A Logistic Growth Model
 Model Hypothesis: 'The relative population growth is proportional to the difference between  the maximum sustainable population, M ,and the population size' Corresponding DE: y'(t)/y(t)= k [M - y(t)]  or  y'(t) = k y(t) [M - y(t)] Symbols: y(t) : population size, in millions, at time t (years) y'(t)/y(t) : relative population growth, in millions per million per year, at time t. k : rate constant.