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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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