ch11 - Theorem 11.3.1: Existence and Uniqueness of...

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Chapter Review Sheets for Elementary Differential Equations and Boundary Value Problems, 8e Chapter 11: Boundary Value Problems and Sturm-Liouville Theory Definitions: Eigenvalues and Eigenfunctions Separated Boundary Conditions Lagrange's Identity Othogonality of Eigenfunctions Normalized, Orthonormal Set Self-Adjoint boundary value problem Periodic Boundary Conditions Singular Sturm-Liouville Problem Continuous Spectrum Bessel Equation Method of Collocation Mean Square sense Mean Square Error Complete set of functions Square Integrable Theorems: Theorem 11.2.1: Eigenvalues of Sturm-Liouville Problems are Real Theorem 11.2.2: Orthogonality of Sturm-Liouville Eigenfunctions Theorem 11.2.3: Eigenvalues of Sturm-Liouville Problems are Simple, and Ordered Theorem 11.2.4: Convergence of Infinite Sum of Normalized Sturm-Liouville Eigenfunctions
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Unformatted text preview: Theorem 11.3.1: Existence and Uniqueness of Solutions to Nonhomogeneous Sturm-Liouville problems Theorem 11.3.2: Fredholm Alternative Theorem Theorem 11.6.1: Completeness of Sturni-Liouville Eigenfunctions Important Skills: Be able to compute eigenvalues and eigenfunctions. (Example 1, p.660) Know how to normalize a set of eigenfunctions. (Example1 & 2, p.670) Expand a given function in terms of normalized eigenfunctions. (Example 3, p.673) Solve nonhomogeneous PDE's with mixed boundary conditions. (Example 1, p.683) Know circular vibration problems, Bessel functions, and how they relate to singular Sturm-Liouville problems. p.696 and Section 11.5. Discuss the mean convergence of series representations. (Example 1, p.7133) Relevant Applications: Any problems where separation of variables leads to a two point boundary value problem....
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This note was uploaded on 02/22/2010 for the course MATH 23 taught by Professor Dorothywallace during the Spring '10 term at Dartmouth.

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