Differential Equations › Section I · Partial differential equations › Topic I.4
Separation of variables
A partial differential equation is hard; two ordinary ones are familiar. Separation of variables guesses a solution that is a product of one-variable functions, and that guess splits the heat, wave and Laplace equations into ODEs you already know how to handle.
In this topic
- The idea: guess a product
- Separating the heat equation
- Why both sides equal a constant
- Boundary conditions carry over
- Worked example: a bar with both ends at zero
- Separating the wave equation
- Worked example: a string with fixed ends
- Separating Laplace's equation
- Worked example: a bar losing heat through its sides
- When separation fails
- Common mistakes to avoid
- Key takeaways
This topic is part of Wuanberri Pro. Checking your access…