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Simple taylor expansion of symbolic variables

Posted 9 years ago

Hi all,

I am a first time user of Mathematica. What I am trying to do is quite simple to do by hand, but not so much using Mathematica.

Suppose I have a partial differential equation in u(x,t)

\partial_{t} u + u \partial_{x} u = 0

I want to be able to manipulate this equation as such,

\partial_{t} u = - u \partial_{x} u


\partial_{tt} u = \partial_{xt}(-u^2/2) = \partial{x}(u*\partial_{t}u) = \partial_{x}(u^2*\partial_{x}u)

As you can see, a Taylor expansion of u entirely made of t can be achieved.

u(x,t) ~ u(x0,t0) + t*\partial u_{t} + t^2/2*\partial u_{tt}

I would like some guidance in Mathematica to achieve this process. I would appreciate any help from experienced users.

POSTED BY: Jungyeoul Maeng

Be aware of Mathematica code for nth partial derivative of f[x,y] wrt x


POSTED BY: S M Blinder
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