My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 5th, 2012, 08:03 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 non-conservative 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.
aise5668 is offline  
 
March 5th, 2012, 05:27 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.
aise5668 is offline  
March 5th, 2012, 07:30 PM   #3
Senior Member
 
Joined: Apr 2010

Posts: 451
Thanks: 1

Re: path dependent function with a definite path

Quote:
Originally Posted by aise5668
I should have mentioned that all paths go through the origin and x and z can only be positive.

Is the vector field two dimentional or three dimentional ??
outsos is offline  
March 5th, 2012, 07:36 PM   #4
Newbie
 
Joined: Feb 2012

Posts: 5
Thanks: 0

Re: path dependent function with a definite path

It is 2 dimensional.
aise5668 is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
definite, dependent, function, path



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
path integral shayanh Calculus 3 January 17th, 2014 03:50 PM
Am I in the wrong path? heltei15 Academic Guidance 4 January 26th, 2012 09:55 AM
a rectifiable path Few_But_Ripe Complex Analysis 3 November 8th, 2011 03:27 PM
Path Connected Set? matthematical Real Analysis 4 October 5th, 2011 02:20 PM
path-connected TTB3 Real Analysis 1 December 11th, 2009 03:55 PM





Copyright © 2018 My Math Forum. All rights reserved.