10.2.4 - Examples
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Practice Questions
Test your understanding with targeted questions
What is the formula for the Fourier Cosine Transform?
💡 Hint: Think about how we integrate using cosine.
What is the condition for a function to be transformed using Fourier methods?
💡 Hint: Focus on the properties of the function required.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the Fourier Sine Transform of f(x)=e^{-ax}?
💡 Hint: Think about the integral setup.
True or False: The Fourier Cosine Transform is used when the function is odd.
💡 Hint: Consider the behavior of sine and cosine functions.
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Challenge Problems
Push your limits with advanced challenges
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.
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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Reference links
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