Practice Examples (10.2.4) - Fourier Cosine and Sine Transforms

Practise this section

8 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the formula for the Fourier Cosine Transform?
Show hintHide hint
Think about how we integrate using cosine.
Question 2.
What is the condition for a function to be transformed using Fourier methods?
Show hintHide hint
Focus on the properties of the function required.
3Question 3.
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
Show hintHide hint
Think about the integral setup.
4Question 4.
True or False: The Fourier Cosine Transform is used when the function is odd.
- True
- False
Show hintHide hint
Consider the behavior of sine and cosine functions.
Question 5.
Given the function f(x) = e^{-5x}, derive the Fourier Cosine Transform and explain its significance in boundary value problems.
Show hintHide hint
Follow the integration method discussed in class.
Question 6.
Apply the Fourier Sine Transform to f(x) = e^{-2x} and interpret the result. Why is the sine transform particularly useful?
Show hintHide hint
Set the integral as per our previous examples.

4 more questions in this section. Enroll free to practise them all.