1 / 14

D. R. Wilton ECE Dept.

ECE 6382. Fall 2008. Second Order Linear Differential Equations. D. R. Wilton ECE Dept. Separation of Variables. Separation of Variables (cont.). Separation of Variables (cont.). Standard Form of Legendre’s Eq.

olivia-gomez
Download Presentation

D. R. Wilton ECE Dept.

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. ECE 6382 Fall 2008 Second Order Linear Differential Equations D. R. Wilton ECE Dept.

  2. Separation of Variables

  3. Separation of Variables (cont.)

  4. Separation of Variables (cont.)

  5. Standard Form of Legendre’s Eq.

  6. Most equations of mathematical physics are linear(ized) second order partial differential equations: • Wave equation • Heat equation • Navier-Stokes equation • Dirac equation • As above, when applicable, the separation of variables method then leads to second order linear differential eqs. (SOLDEs) • Harmonic eq. • Bessel’s eq. (cylindrical and spherical) • Jacobi, Chebyshev, Legendre, Laguerre, Hermite eqs. • Laplace’s, Poisson’s equation • Klein-Gordon equation • Schrödinger equation Separation of Variables

  7. Second Order Linear Differential Equations (SOLDE)

  8. Second Order Linear Differential Eqs. (SOLDEs)

  9. Series Solutions – Ordinary Point

  10. Series Solutions – Regular Singular Point

  11. nearest singularity Im z x = Re z a R Series Solutions – Irregular Singular Point

  12. Classification of Singular Points - Example

  13. Classification of the Point at Infinity

  14. The End

More Related