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3 cards from this section. Quick, good the night before a test.
Define the term 'Complementary Function'.
Think about the role of a system without any external influences.
What does a 'Particular Integral' account for in a PDE?
Consider what changes when external forces are introduced.
What does CF stand for in the context of PDEs?
Think about the natural state of a system.
True or False: The PI component is only relevant for homogeneous PDEs.
Consider the role of external influences.
Consider the PDE u_xx + 2u_xy + u_yy = sin(xy). How would you approach finding its CF and PI?
Think about the sine function form you might encounter in trigonometric relationships.
Solve a non-homogeneous PDE like u_xx - u = e^x. First, get the CF, then derive the PI based on the forcing function.
Try a form similar to the e^x when guessing your PI.
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