Study of equations involving derivatives and their applications.
Partial differential equations (PDEs) describe how things change with respect to more than one variable—think time and space together!
PDEs are generally trickier than ODEs. Common methods include separation of variables, Fourier series, and numerical approximations.
Many processes in physics, engineering, and finance are governed by PDEs—like weather prediction and stock pricing.
Using the heat equation to model how a metal bar cools down.
Predicting vibrations on a drumhead with the wave equation.
PDEs help us understand how things like heat or sound travel and change in space and time.