Practice Examples - 10.1.4 | 10. Fourier Cosine and Sine Transforms | Mathematics (Civil Engineering -1)
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10.1.4 - Examples

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Practice Questions

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Question 1 Easy

Define the Fourier Cosine Transform.

💡 Hint: Consider its utility in boundary value problems.

Question 2 Easy

Write the formula for the Fourier Cosine Transform of f(x) = e^(-ax).

💡 Hint: Remember the integral setup you saw in class.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the primary use of the Fourier Cosine Transform?

To transform functions defined on (-∞
∞)
To analyze functions on semi-infinite domains
To express periodic functions only

💡 Hint: Think about where these functions are applicable in engineering.

Question 2

Is the Fourier Cosine Transform linear?

True
False

💡 Hint: Consider the linearity property discussed in class.

1 more question available

Challenge Problems

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Challenge 1 Hard

Given the function f(x) = e^(−3x), derive the Fourier Cosine Transform and explain the meaning of your result in a context of heat transfer.

💡 Hint: Apply the definition of the Fourier Cosine Transform.

Challenge 2 Hard

Consider the beam deflection problem. How would you set up the Fourier Cosine Transform of the beam equation? Explain your steps.

💡 Hint: Start with the Euler-Bernoulli beam equation and think about boundary conditions.

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