Recall that the solution of the initial-value problem \(y^\prime=ky\text{,}\) \(y(0)=A\text{,}\) is given by \(\ds y=Ae^{kx}\text{.}\) Solve the following problems ...

Definite and indefinite integrals and the Fundamental Theorem of Calculus. Simple differential equations (separable ODE, linear ODE). ODE models leading to exponential growth and decay.

Two basic principles are involved, the idea of exponential growth and its ultimate control. The basics of population ecology emerge from some of the most elementary considerations of biological facts.