Higher Education · Differential Equations
Partial Differential Equations
What is it
A partial differential equation (PDE) involves partial derivatives of a function of several variables — undergraduate study covers classic examples like the heat equation, wave equation, and Laplace's equation, and basic solution techniques like separation of variables.
Why it matters
PDEs are how physics describes anything that varies continuously across space and time — heat diffusing through a material, sound waves travelling through air, the shape of a stretched membrane — making this genuinely foundational for physics and engineering.
Exam tip
When using separation of variables on a PDE, assume the solution can be written as a product of functions each depending on only one variable — this assumption, while not obviously justified at first, is what allows the PDE to be broken into simpler ODEs.
Related topics
Want help mastering Partial Differential Equations?
Tell us about the student's goals and confidence — we'll design a personalised plan.