Practice Fourier Series In Solving Pdes (15.2) - Fourier Series Solutions to PDEs

Practice: Fourier Series in Solving PDEs

Lesson 15.2Fourier Series Solutions to PDEs

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9 questions

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4 cards from this section. Quick, good the night before a test.
Exercise
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is a Fourier series?
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Think about how periodic functions can be constructed.
Question 2.
Which PDE describes heat distribution?
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Consider where heat flow is occurring.
3Question 3.
What is a primary feature of Fourier series?
- They can only represent linear functions
- They convert functions to polynomial form
- They express periodic functions as sums of sines and cosines
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Recall what defines a periodic function.
4Question 4.
True or False: The Heat Equation is used to model wave propagation.
- True
- False
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Think about what each equation describes.
Question 5.
Prove that the method of separation of variables applies to the Heat Equation. Derive the series solution explicitly for a given initial function.
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Pay attention to boundary conditions while separating.
Question 6.
Given the boundary conditions for the Wave Equation, derive the complete solution for the wave motion based on initial displacements and velocities.
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Make sure to correctly use the initial displacement and derivative conditions.

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