Sturm Separation Theorem and Sturm Comparison Theorem.
Computing the Wronskian of two functions is a good way to determine whether or not they are linearly independent. But, two functions are linearly dependent if one is a multiple of the other; otherwise they are linearly independent. It is fairly easy to see by inspection, without computing the Wronskian. Sturm Separation Theorem and Sturm Comparison Theorem are stated and proved. Applications of these theorems are shown. Extended Sturm Comparison Theorem is stated.
Instructor: Dr. Vera Mikyoung Hur, Maths, 18.034: Honors Differential Equations, Spring 2009: 10. Separation and comparison theorems: Massachusetts Institute of Technology: MIT Open Course Ware),http://ocw.mit.edu (Accessed December 14, 2011). License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc
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