Practice - Inner Product and Orthogonality in Function Spaces
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 inner product of two functions.
💡 Hint: Think about the integral of the product of the functions over the given interval.
What does orthogonality mean for two functions?
💡 Hint: Recall the definition of inner product in relation to zero.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the definition of the inner product of two functions?
💡 Hint: Recap the definition we talked about.
Are sin(x) and cos(x) orthogonal over the interval [0, 2π]?
💡 Hint: Think about their integral product.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Prove that the functions f(x) = x and g(x) = x^2 are not orthogonal over the interval [-1, 1].
💡 Hint: Remember to use the odd property of the function x^3 over symmetric limits.
Construct the Fourier series for a square wave using orthogonal sine functions over the interval [0, T].
💡 Hint: Think about how coefficients are calculated using the integral of the square wave function multiplied by the sine functions.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.