Boas 12.1, 12.2
Caveat that this doesn't always work (e.g. if y=log(x))
Example of simple equation (y'=2yx) solved directly, and then as a series
Legendre's equation - discussion of where it comes from
(1-x^2)y'' - 2x y' +l(l+1)y=0, with l any constant (usually a postive integer)
Power series solution, calculated general solution, found particular solution when l is an integer, and which is 1 at x=1 => "The Legendre polynomials". (Mentioned Legendre function of the second kind, which are not polynomials, and which diverge at x=1)
Qualitative discussion of these polynomials, and how they are vaguely reminiscent of sin's and cos's.
Here is the Next lecture
Back to the list of lectures