Practice Examples - 10.2.4 | 10. Fourier Cosine and Sine Transforms | Mathematics (Civil Engineering -1)
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10.2.4 - Examples

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Practice Questions

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Question 1 Easy

What is the formula for the Fourier Cosine Transform?

💡 Hint: Think about how we integrate using cosine.

Question 2 Easy

What is the condition for a function to be transformed using Fourier methods?

💡 Hint: Focus on the properties of the function required.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the Fourier Sine Transform of f(x)=e^{-ax}?

\\frac{2s}{\\pi (a^2 + s^2)}
\\frac{2a}{\\pi (a^2 + s^2)}
None of the above

💡 Hint: Think about the integral setup.

Question 2

True or False: The Fourier Cosine Transform is used when the function is odd.

True
False

💡 Hint: Consider the behavior of sine and cosine functions.

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Challenge Problems

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Challenge 1 Hard

Given the function f(x) = e^{-5x}, derive the Fourier Cosine Transform and explain its significance in boundary value problems.

💡 Hint: Follow the integration method discussed in class.

Challenge 2 Hard

Apply the Fourier Sine Transform to f(x) = e^{-2x} and interpret the result. Why is the sine transform particularly useful?

💡 Hint: Set the integral as per our previous examples.

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