University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg41

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EGM6321 - Principles of Engineering Analysis 1, Fall 2009[edit]

Mtg 41: Tues, 1Dec09


Page 41-1

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Review for exam 2

- Historical development - Legendre functions
Question: How to obtain based on known  ? - 2 recurring relationships. Same technique in power series.
Solution: Frobenius method
Question: Find a differential equation governing all  ? - Legendre differential equations
2 families of homogeneous solutions:
- Legendre functions= +

or

Newtonian potential is solution of Laplace equation

i.e.,


Page 41-2

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, where

, where


Where this argument is based on the power series
Laplace equations in a sphere
axisymmetrical case P.29-1
separation of variables P.30-1
General solution of axisymmetrical Laplace equations in a sphere



Where can be found on P.31-2

and can be found on P.32-1

and

References[edit]