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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define the inner product of two functions.
💡 Hint: Think about the integral of the product of the functions over the given interval.
Question 2
Easy
What does orthogonality mean for two functions?
💡 Hint: Recall the definition of inner product in relation to zero.
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 definition of the inner product of two functions?
💡 Hint: Recap the definition we talked about.
Question 2
Are sin(x) and cos(x) orthogonal over the interval [0, 2π]?
- True
- False
💡 Hint: Think about their integral product.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation