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

EGM6321 - Principles of Engineering Analysis 1, Fall 2009Edit

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  

ReferencesEdit