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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define 'orthogonal set' in your own words.
π‘ Hint: Think about functions that do not overlap.
Question 2
Easy
What is the inner product of two functions?
π‘ Hint: Consider it as measuring how similar or different two functions are.
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 defines an orthogonal set of functions?
- A collection where all functions are equal.
- A collection where any two functions integrate to zero.
- A collection with infinite elements.
π‘ Hint: Think about integration results over specific intervals.
Question 2
True or False: A complete set of functions can represent every possible function.
- True
- False
π‘ Hint: Consider 'well-behaved' functions.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given two functions sin(t) and cos(t), calculate their inner product over the interval [0, 2Ο]. What conclusion can you draw?
π‘ Hint: Set up the integral and apply the orthogonality condition.
Question 2
Demonstrate how to represent a non-square-integrable function using an incomplete set of Fourier series terms.
π‘ Hint: Consider practical examples where harmonics are missed.
Challenge and get performance evaluation