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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a Sturm-Liouville problem?
💡 Hint: Think about the components of a differential equation.
Question 2
Easy
Define eigenvalues in the context of Sturm-Liouville problems.
💡 Hint: Consider their role in eigenfunction solutions.
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 form does a Sturm-Liouville problem take?
- d/dx(p(x)dϕ/dx) + [λw(x) - q(x)]ϕ = 0
- d^2ϕ/dx^2 +λϕ = 0
- ∂u/∂x = f(x)
💡 Hint: Look at how the equations are structured.
Question 2
True or False: Eigenfunctions can be non-orthogonal.
- True
- False
💡 Hint: Recall the definition of orthogonality.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a Sturm-Liouville problem with a known weight function w(x) and boundary conditions. How would you derive the eigenfunctions?
💡 Hint: Dive into the boundary conditions to start framing your solutions.
Question 2
If given a set of eigenvalues λ, how would you check for orthogonality among the corresponding eigenfunctions?
💡 Hint: Remember the definition of the orthogonality condition.
Challenge and get performance evaluation