Practice Sturm–Liouville Problems and Eigenfunctions - 18.2 | 18. Eigenfunction Expansion Method | Mathematics - iii (Differential Calculus) - Vol 2
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Sturm–Liouville Problems and Eigenfunctions

18.2 - Sturm–Liouville Problems and Eigenfunctions

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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