Mathematical Biology 1: An Introduction

Change is the nature of things in biology and differential equations are used to model change. The concentrations of some bio-chemicals present in an organism change over time, sometimes dramatically, in response to the changes in the concentrations of other chemicals. Other systems make up a steady-state system, where the concentrations of reactants are damped within fairly rigid bounds. Segments of organisms change due to dynamic feedback with other segments of the same organism, actions in one location can propagate throughout the entire creature. Organisms of one species interact with others of the same species, sometimes in cooperation, and other times in competition. The same thing applies to populations of different species, in some circumstances, all species benefit or suffer and in other circumstances the advantage to one species is based on harm to the other(s). All of these situations are examined in a thorough manner; the models are based on differential equations started from some basic, logical assumptions.