Practice Fourier Cosine Transform (FCT) - 15.3.1 | 15. Fourier Integral to Laplace Transforms | Mathematics (Civil Engineering -1)
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Fourier Cosine Transform (FCT)

15.3.1 - Fourier Cosine Transform (FCT)

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.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the formula for the Fourier Cosine Transform?

💡 Hint: Recall the relation to cosine functions.

Question 2 Easy

Is the Fourier Cosine Transform used for functions defined over finite domains?

💡 Hint: Consider the limits of integration.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Fourier Cosine Transform primarily analyze?

Periodic Functions
Semi-infinite Functions
Random Functions

💡 Hint: Think about the limits of integration.

Question 2

True or False: The inverse Fourier Cosine Transform uses sine functions.

True
False

💡 Hint: Recall the definition of the FCT.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a function f(x) = x^2 for x in [0, ∞), calculate and interpret the Fourier Cosine Transform F(ω). Discuss its application.

💡 Hint: Remember to integrate by parts and look up integral tables.

Challenge 2 Hard

Analyze a scenario where a thermal pulse is introduced to a long metal rod. Use the Fourier Cosine Transform to derive heat distribution over time.

💡 Hint: Consider the heat equation while applying the FCT.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.