Practice - Eigenvalues and Eigenfunctions
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Practice Questions
Test your understanding with targeted questions
Define eigenvalue and give an example.
💡 Hint: Think about the formula mentioned in class.
Explain the relationship between eigenvalues and eigenfunctions.
💡 Hint: Consider the definitions you learned.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the formula for the eigenvalue α?
💡 Hint: Look for the formula mentioned in class.
True or False: Eigenfunctions describe the boundary conditions of the system.
💡 Hint: Think about what each term represents.
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Challenge Problems
Push your limits with advanced challenges
A rectangular membrane has a length of 2m and a width of 1m. Calculate the first three eigenvalues.
💡 Hint: Use the formulas for α and β.
If the initial displacement of a vibrating membrane is given by the function f(x,y) = sin(πx/2)sin(πy), identify the corresponding eigenvalue pairs.
💡 Hint: What values of n and m fit the given function?
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Reference links
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