1 / 7

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.

osgood
Download Presentation

Fourier Series

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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 = + +

More Related