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3 cards from this section. Quick, good the night before a test.
What is the definition of an Ordinary Differential Equation (ODE)?
Think about how these equations describe changes over time.
Explain what a Laplace Transform does.
Remember the advantages of using transforms over standard methods.
What does the Laplace Transform do?
Think about what transformations allow us to do more easily.
True or False: Laplace Transforms can only be used for linear ODEs.
Remember that not all ODEs fit neatly into 'linear' categories.
Solve the differential equation d^2y/dt^2 + 3dy/dt + 2y = 0 with specified conditions y(0) = 2 and dy/dt (0) = 3 using Laplace Transforms.
Don't forget to handle both initial conditions carefully during transformation.
Using the Laplace Transform, determine the current i(t) in an RLC circuit satisfying the equation L(d^2i/dt^2) + R(di/dt) + i/C = V(t), with the step function V(t).
Recognize how each component in the circuit interacts as you develop your transformations.
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