Matlab - Differential Equations Linear, Nonlinear, Ordinary, Partial.pdf

Differential Equations
Linear, Nonlinear, Ordinary, Partial
. King, J. Billingham and . Otto
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Cambridge University Press
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© Cambridge University Press 2003
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First published in print format 2003
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Contents
Prefacepageix
PartOne:LinearEquations1
1 Variable Coefficient, Second Order, Linear, Ordinary
DifferentialEquations3
The Method of Reduction of Order 5
The Method of Variation of Parameters 7
Solution by Power Series: The Method of Frobenius 11
2LegendreFunctions31
,Pn(x)31
The Generating Function for Pn(x)35
Differential and Recurrence Relations Between Legendre
Polynomials38
’Formula39
Orthogonality of the Legendre Polynomials 41
Physical Applications of the Legendre Polynomials 44
The Associated Legendre Equation 52
3BesselFunctions58
The Gamma Function and the Pockhammer Symbol 58
Series Solutions of Bessel’s Equation 60
The Generating Function for Jn(x), n an