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

10 - Fourier Cosine and Sine Transforms

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define the Fourier Cosine Transform.

💡 Hint: Recall the definition mentioned in class.

Question 2 Easy

What property of Fourier transforms allows combining functions?

💡 Hint: Think about how you can factor out constants.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Fourier Cosine Transform primarily utilize?

Sine functions
Cosine functions
Exponential functions

💡 Hint: Remember the definition of the FCT.

Question 2

True or False: The FST is used for functions that are even.

True
False

💡 Hint: Consider the characteristics of even and odd functions.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider a semi-infinite rod initially at zero temperature. If one end is held at a constant temperature T, derive the solution to the heat equation with appropriate boundary conditions using FCT.

💡 Hint: Focus on setting up the heat equation and applying the appropriate boundary conditions.

Challenge 2 Hard

Evaluate the integral ∫[0,∞] (x sin(ax))/(x² + b²) dx using Fourier Sine Transform.

💡 Hint: Use known integral results and properties of Fourier transforms.

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