how to obtain the inverse series for multivariable functions using
- To: mathgroup at smc.vnet.net
- Subject: [mg130587] how to obtain the inverse series for multivariable functions using
- From: Qi Hao <xqi.hao at gmail.com>
- Date: Wed, 24 Apr 2013 07:02:54 -0400 (EDT)
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Hello, everyone: Now, I have a question about how to obtain the inverse series for multivariable functions. The system of nonlinear equations is like this: x = f(p,q) y = g(p,q). The inverse functions are p = h(x,y) q = r(x,y). Now, I have known the taylor expansion of x and y with respect to p and q at point(0,0), that is x = f(0,0) + df/dp(0,0)p + df/dq(0,0)q + ... y = g(0,0) + dg/dp(0,0)p + dg/dq(0,0)q + ... I want to know the taylor expansion of the inverse functions, that is p = h(0,0) + dh/dx(0,0)x + dh/dx(0,0)y + ... q = r(0,0) + dr/dx(0,0)x + dr/dy(0,0)y + ... Could you show me your mathematica codes to solve this problem ? Thank you very much! Qi Hao