textbook-theory · English
Difference Equations to Differential Equations — Section 6.1: The Exponential Function
This 12-page chapter section from Dan Sloughter's open calculus text defines the exponential function exp(x) via its power series and derives its key properties: self-differentiation, the addition law exp(a+b)=exp(a)exp(b), and the identification exp(x)=e^x for all real x including irrationals. Differentiation and integration techniques are developed through worked examples, and the section closes with an uninhibited-population-growth application modeled by the differential equation x'(t)=λx(t) with solution x(t)=x0·e^(λt).
exponential functioncalculusdifferential equationspopulation growth