Module EC-3
Differential Equations
What a circuit or a machine actually is once written down. How a first-order equation produces the exponential settling of a charging capacitor, what the two roots of a second-order equation say about whether a system rings on its way to rest, how several equations together become the state model whose eigenvalues decide the behaviour, and the two partial equations that describe a wave travelling and a concentration spreading. The linear algebra the state model leans on is a course of its own, offered beside this one on the area roadmap.
4 topics ~42 h estimated learning time
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- EC-3.1 First-Order Equations, and the Circuits That Obey Them
Foundation · 10 h
- EC-3.2 Second-Order Equations, Damping and Resonance
Foundation · 12 h
- EC-3.3 Systems of Equations, and the State Model
Foundation · 12 h
- EC-3.4 The Wave and the Diffusion Equation
Foundation · 8 h