Introduction to Differential Equations

AP Calculus · Axiom Academy

Intro Introduction to Differential Equations What are differential equations and why do they matter? Equations That Involve Derivatives A differential equation (DE) is an equation that involves an unknown function and its derivatives. Instead of solving for a number, you solve for a function . DEs model nearly every dynamic process in science: population growth, radioactive decay, cooling, circuits, and epidemics. Slope fields — visualizing solutions to DEs Euler s method (BC) — numerical approximation of solutions Separation of variables — the primary solving technique Exponential growth & decay — the most famous DE Logistic growth (BC) — bounded population models Why DEs Are Central to Calculus In Calculus AB/BC, differential equations bring together everything: derivatives tell you the rate of change, and solving the DE recovers the original function. The AP exam regularly includes slope fields, separation of variables, and growth/decay problems. Let s dive into the world of differential equations!

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