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 April 12th, 2018, 02:57 AM #1 Member   Joined: Dec 2017 From: Tel Aviv Posts: 85 Thanks: 3 English What is the name of the thing that mark with ...? mx + n = y n is ... ax^2 + bx + c = y c is ...
 April 12th, 2018, 04:03 AM #2 Member   Joined: Dec 2017 From: Tel Aviv Posts: 85 Thanks: 3 And my next question is: What is the difference between this Thing and the Constant Of Integration? Last edited by skipjack; April 12th, 2018 at 04:06 AM.
 April 12th, 2018, 04:15 AM #3 Global Moderator   Joined: Dec 2006 Posts: 18,838 Thanks: 1564 The technical term is "ellipsis". It isn't related to integration.
 April 12th, 2018, 04:18 AM #4 Senior Member   Joined: Oct 2009 Posts: 350 Thanks: 113 I think he is refering to the "constant term".
 April 12th, 2018, 04:20 AM #5 Member   Joined: Dec 2017 From: Tel Aviv Posts: 85 Thanks: 3 I will it again What is the name of The Thing? mx + n = y n = The Thing ax^2 + bx + c = y c = The Thing. this is a "free number" in my bad English. If integration of f function is (Integral of f) + C what is the difference between c and the "free number"? Is there a connection between them? Last edited by skipjack; April 12th, 2018 at 06:50 AM.
 April 12th, 2018, 06:58 AM #6 Global Moderator   Joined: Dec 2006 Posts: 18,838 Thanks: 1564 In your equations, n and c appear to be constant terms, as there is nothing to suggest they vary as x varies. When you integrate with respect to x, the C that is added as a constant of integration doesn't vary as x varies, but (in certain circumstances) might vary as something else varies. I haven't come across the term "free number" in this type of context.
April 13th, 2018, 01:01 AM   #7
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Quote:
 Originally Posted by skipjack In your equations, n and c appear to be constant terms, as there is nothing to suggest they vary as x varies. When you integrate with respect to x, the C that is added as a constant of integration doesn't vary as x varies, but (in certain circumstances) might vary as something else varies. I haven't come across the term "free number" in this type of context.
What are the circumstances?

April 13th, 2018, 01:20 PM   #8
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Quote:
 Originally Posted by policer What are the circumstances?
If you have a "partial differential equation" that has more than one independent variable is one such circumstance.

For example, to solve the differential equation $\displaystyle \frac{\partial^2 z}{\partial x\partial y}= 0$, write it as $\displaystyle \frac{\partial}{\partial x}\left(\frac{\partial z}{\partial y}\right)= 0$. The "anti-derivative", with respect to x, would give $\displaystyle \frac{\partial z}{\partial y}$ plus a "constant". But since this is a partial derivative with respect to x, where we hold y constant, that "constant might in fact be some function of y! That is $\displaystyle \frac{\partial z}{\partial y}+ f(y)$. Now integrating with respect to y, we have $\displaystyle z= F(y)+ "C"$ where F is an anti-derivative of f. And, again, since we differentiated with respect to y, that "C" might be some function of x. If we call that function "G(x)", that becomes $\displaystyle z= F(y)+ G(x)$.

Last edited by skipjack; April 14th, 2018 at 03:48 AM.

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