textbook-theory · English
Difference Equations to Differential Equations — Section 1.4: Difference Equations
Section 1.4 of Dan Sloughter's open calculus textbook introduces first-order difference equations, covering both the pure geometric form xn+1 = αxn and the general first-order linear form xn+1 = αxn + β. Applications include population growth, radioactive decay half-life calculation, and Newton's law of cooling, with explicit closed-form solutions derived and graphically illustrated. The section closes with sixteen exercises ranging from computing sequence terms to modeling the Fibonacci sequence and two-dimensional heat distribution.
difference equationsfirst-order linear recurrencesexponential growth and decaydiscrete dynamical systems