Differential Equations › Section I · Partial differential equations › Topic I.9
PDEs in science and engineering
The heat, wave and Laplace equations of this section turn up far beyond bars and strings, from microchips and drums to atoms, stock options and medical scanners. This topic surveys where they appear and how engineers solve the many problems that no series formula can reach.
In this topic
- The same equations, everywhere
- Diffusion in three dimensions
- Worked example: how far can oxygen diffuse?
- Waves in two and three dimensions
- Schrödinger's equation
- Biology, finance and fluids
- Finite differences
- Worked example: one step, stable and unstable
- Worked example: choosing a time step
- Finite elements and medical imaging
- Common mistakes to avoid
- Key takeaways
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