10 - Fourier Cosine and Sine Transforms
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Define the Fourier Cosine Transform.
💡 Hint: Recall the definition mentioned in class.
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
What does the Fourier Cosine Transform primarily utilize?
💡 Hint: Remember the definition of the FCT.
True or False: The FST is used for functions that are even.
💡 Hint: Consider the characteristics of even and odd functions.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
Evaluate the integral ∫[0,∞] (x sin(ax))/(x² + b²) dx using Fourier Sine Transform.
💡 Hint: Use known integral results and properties of Fourier transforms.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.