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Taylor series of two variable ?

  • Thread starter rclakmal
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  • #1
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Homework Statement




I want to know that how to calculate the required number of terms to obtain a given decimal accuracy in two variable Taylor series .
In one variable case i know there is an error term R(n)=[ f(e)^(n+1)* (x-c)^(n+1)] / (n+1)! where 'e' is between x and c (c is the center value ) so if we want a 3 decimal place accuracy we can have the inequality below

R(n)<=5*10^(-4) then we can obtain particular ' n ' to have that accuracy

But i don't know how to use this in two variable case .please give some explanation or a good tutorial where i can learn it .
 

Answers and Replies

  • #2
HallsofIvy
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The corresponding formula for two variables is
[tex]R(n)= \sum_{i=0}^{n+1} \frac{\frac{\partial^{n+1} f(e)}{\partial x^{i}\partial y^{n+1-i}}(x-c)^{n+1}}{(n+1)!}[/tex]
 

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