Chapter 18 · Partial Differential Equations
18.05
The Heat Equation
The heat equation u_t = ku_xx comes from conservation of energy and Fourier's law. Its solutions smooth out, forget their starting shape, and settle to a steady state set by the boundaries.
About 16 minutes
You'll learn to
- →Derive the heat equation
- →Solve it with fixed-temperature or insulated ends
- →Find steady states and handle nonzero boundary temperatures
- →Describe how solutions behave over time