Differential Equations › Section E · Systems of differential equations › Topic E.2
Systems of differential equations
Salt moving between connected tanks, current in a two-loop circuit, two masses joined by springs: whenever several quantities drive each other's rates of change, one equation is not enough. This topic sets up systems of equations, shows how any higher-order equation becomes one, and introduces the matrix form used for the rest of the section.
In this topic
- Quantities that change together
- First-order linear systems
- Worked example: two connected tanks
- Higher-order equations become systems
- Worked example: a second-order initial value problem
- Matrix form
- Worked example: a third-order equation with forcing
- Homogeneous systems and initial value problems
- Why the conversion pays off
- Common mistakes to avoid
- Key takeaways
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