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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
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.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation