A differential equation has as its unknown not a number, but a function: the one describing how a coffee cools, how a radioactive substance decays, how a spring oscillates. Whenever a quantity changes over time with a rate that depends on its current value, the equation governing it is a differential equation (ODE). The chapter starts from the definition, tackles the method of separable variables with its physical applications (exponential growth and decay, Newton’s cooling, barometric formula), moves on to first-order and second-order linear equations with constant coefficients through the characteristic equation, and culminates in the guided physical examples of the harmonic oscillator and of RC and RLC circuits, where a single equation describes wildly different phenomena.
Sections
- What is a differential equation
- Separable equations
- First-order linear equations
- Second-order linear equations with constant coefficients