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3 cards from this section. Quick, good the night before a test.
What is a Taylor Series?
Think about series expansion.
What is meant by the step size ℎ in the context of the Taylor Series Method?
It influences how frequently we compute new approximations.
What does the Taylor Series Method primarily approximate?
Consider what the method seeks to find.
True or False: The Taylor Series Method is only applicable for linear ODEs.
Think about the flexibility of derivatives.
Using the ODE dy/dx = e^x + y with y(0) = 1, compute y(0.2) using Taylor series expansion up to third order.
Don’t forget to calculate each step carefully!
Given the initial value problem dy/dx = y^2 + sin(x) with y(0) = 0, approximate y(0.1) using Taylor series.
Consider the initial condition and how non-linear effects the initial derivatives!
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