Practice Common Integral Forms For Reference (9.14)

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9 questions

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6 sample questions

Question 1.
What is the formula for the Fourier Sine Transform of a piecewise constant function?
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Think about what the sine function represents in your problem.
Question 2.
Provide the Fourier Cosine Transform for the function e^{-ax}.
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Consider the implications for decay processes.
3Question 3.
What does the Fourier Sine Transform apply to?
- Even Functions
- Odd Functions
- Periodic Functions
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Recall what type of symmetry each transform addresses.
4Question 4.
The formula for the Fourier Cosine Transform of e^{-ax} is...
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Focus on what this transform helps characterize.
Question 5.
Derive the general forms of the Fourier sine and cosine transforms for an arbitrary function f(x).
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Reference integration by parts and boundary conditions.
Question 6.
Evaluate the convolution of two Fourier transforms for functions defined by the sine and cosine transforms.
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Refer back to linearity and translation properties of the Fourier Transform.

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