On Mar 15, 8:58 am, [email protected] wrote:
> Hi everyone,I have a function f=f(eta, bx, bt), in which diff(eta,x)=k(bx,bt)
> and diff(eta,t)=-omega(bx,bt) withbx=delta*x and bt=delta^2*t. I want to
> calculate the second order derivative diff(diff(f,x)). Theresult should be
> k^2*D[0,0](f)+2*delta*k*D[0,1](f)+delta*D[0](k)*D[0](f)+delta^2*D[1,1](f).but
> when I did as
> follows:var('x,t,bx,bt,delta')bx=function('bx',x)bx=delta*xbt=function('bt',t)bt=delta^2*tk=function('k',bx,bt)omega=function('omega',bx,bt)eta=function('eta',x,t)f=function('f',eta,bx,bt)it
> does not work. could anyone help me with that?Tanks in advanced!regards,YC
That can be done as
var('x t delta')
map(function,('eta','f','k','omega'))
bx,bt = delta*x,delta^2*t
eq=diff(eta(x,t),x)==k(bx,bt)
f(eta(x,t),bx,bt).diff(x,2).expand().subs(eq).subs(diff(eq,x))
delta^2*D[1, 1](f)(eta(x, t), delta*x, delta^2*t) + 2*delta*k(delta*x,
delta^2*t)*D[0, 1](f)(eta(x, t), delta*x, delta^2*t) +
delta*D[0](f)(eta(x, t), delta*x, delta^2*t)*D[0](k)(delta*x,
delta^2*t)
+ k(delta*x, delta^2*t)^2*D[0, 0](f)(eta(x, t), delta*x, delta^2*t)
Alec Mihailovs
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