[Maxima] taylor series expansion question

Barton Willis willisb at unk.edu
Sat Oct 27 11:43:01 CDT 2007


-----maxima-bounces at math.utexas.edu wrote: -----

>I'm having trouble getting a Taylor series expansion of an expression
>involving the derivative.  I have the equation f(t) = (d/dt)u(t)+a*u(t)
>and I would like to obtain the Taylor series expansion of f(t+dt) (or
>f(t+2dt)) about the point t.


Maybe pdiff will do what you want:

(%i1) load(pdiff)$

(%i2) diff(u(t),t)+a*u(t);
(%o2) u[(1)](t)+a*u(t)

(%i3) subst(t = t+2*dt,%);
(%o3) u[(1)](t+2*dt)+a*u(t+2*dt)

(%i4) taylor(%,dt,0,2);
(%o4)
u[(1)](t)+u(t)*a+(2*u[(1)](t)*a+2*u[(2)](t))*dt+(2*u[(2)](t)*a+2*u[(3)](t))*dt^2+...


BW


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