Math Question: Three variable Taylor series expansion?

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Trying to linearize a very complex differential eq, general form for a two variable expansion is:

F(a+h,b+k)=F(a,b)+d/dh(F(a,b))h + d/dk(F(a,b))k + .... That's not quite 100% correct cause it's hard to write it out on here. However, does such an expansion exist for a three variable Taylor expansion?

 

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[RossGr]

If you have got the 2d version simply extend that idea for the 3d or nd version. If all you want are the linear terms it should be easy if you need any higher order terms it will be nasty. Be carefull double check your results, a good check is to get an estimate for the size of the first term you ditch. If it is large wrt to your answer you may be throwing out the baby with the bath.