18.2 - Sturm–Liouville Problems and Eigenfunctions
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is a Sturm-Liouville problem?
💡 Hint: Think about the components of a differential equation.
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
What form does a Sturm-Liouville problem take?
💡 Hint: Look at how the equations are structured.
True or False: Eigenfunctions can be non-orthogonal.
💡 Hint: Recall the definition of orthogonality.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.