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March 5th, 2012, 07:03 AM  #1 
Newbie Joined: Feb 2012 Posts: 5 Thanks: 0  path dependent function with a definite path
This question is about if I have a path dependent function but a deinite path, then can I take partial derivatives? And are the points that are along path A connected to the points that are along path B. If I consider a nonconservative vector field I must specify a path, in this case the path is always: (eq. 1) and integrate along the path to create the field: (eq. 2) and also: (eq. 3) may I now treat t as path independent? In other words, may I now take the total derivative and evaluate at a constant x like this: (eq. 4) (eq. 5) and then evaluate eq. 5 at a fixed x so that dx = 0 It seems to me that I can't do this because I think that I have defined a relationship between dx and dz in equation 1. Since t is path dependent, p must be in the definition of t so setting dx = 0 violates the constraint that p has set on the relationship between dx and dz. Is what I was thinking correct? Or am I allowed to take the total derivative of X and set dx = 0? Is the point t(x,z) connected to t(x,z+dz)? I am posting this question here and in the differentials section because I am not sure if this is a question about disconnected space or conservative fields. 
March 5th, 2012, 04:27 PM  #2 
Newbie Joined: Feb 2012 Posts: 5 Thanks: 0  Re: path dependent function with a definite path
I should have mentioned that all paths go through the origin and x and z can only be positive.

March 5th, 2012, 06:30 PM  #3  
Senior Member Joined: Apr 2010 Posts: 451 Thanks: 1  Re: path dependent function with a definite path Quote:
Is the vector field two dimentional or three dimentional ??  
March 5th, 2012, 06:36 PM  #4 
Newbie Joined: Feb 2012 Posts: 5 Thanks: 0  Re: path dependent function with a definite path
It is 2 dimensional.


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definite, dependent, function, path 
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