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Fourier Series

Fourier Series. Consider a set of eigenfunctions ϕ n that are orthogonal , where orthogonality is defined as. for m ≠ n. An arbitrary function f ( x ) can be expanded as series of these orthogonal eigenfunctions. or. Due to orthogonality , we thus know.

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Fourier Series

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  1. Fourier Series Consider a set of eigenfunctionsϕn that are orthogonal, where orthogonality is defined as for m ≠ n An arbitrary function f(x) can be expanded as series of these orthogonal eigenfunctions or Due to orthogonality, we thus know all other ϕnAmϕmintegrate to zero because m ≠ n Thus, the constants in the Fourier series are

  2. Cartesian Sturm-Liouville Characteristic Value Problem p(x) = 1; q(x) = 0; w(x) = 1 homogeneous B.C. After Applying Final B.C. Typical B.C. Dirichlet Neumann Robin

  3. Cartesian Sturm-Liouville Kakac & Yenner Heat Conduction, 3rd Ed.

  4. Cylindrical Sturm-Liouville Characteristic Value Problem p(r) =r; q(r) = −ν2/r; w(r) = r homogeneous B.C. After Applying Final B.C. Typical B.C. Dirichlet Neumann Robin

  5. Cylindrical Sturm-Liouville Special B.C. case: a = 0, b = r0 homogeneous B.C. After Applying Final B.C. Typical B.C. Dirichlet Neumann Robin

  6. Cylindrical Sturm-Liouville Kakac & Yenner Heat Conduction, 3rd Ed.

  7. Inhomogeneous BC to Homogeneous BC = + +

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