Linear Algebra › Section E · Eigenvalues and eigenvectors › Topic E.7
Applications to differential equations
When several quantities change continuously and each rate depends on all of them, the result is a system of differential equations. Eigenvectors split such a system into simple exponential pieces, and the eigenvalues predict whether solutions decay, grow or oscillate.
In this topic
- From one equation to a system
- Eigenvectors give exponential solutions
- The general solution
- Worked example: two compartments
- Decoupling
- Attractors, repellers and saddles
- Worked example: a saddle
- Complex eigenvalues: oscillation
- Worked example: an undamped spring
- Common mistakes to avoid
- Key takeaways
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