Difference Quotient

[markraz]

In Difference Quotient formula why specifically do they use the letter H, does that have any actuall meaning? is it an abbreviation for something or did they just pick it randomly?

 

[stapel]

In Difference Quotient formula why specifically do they use the letter H, does that have any actuall meaning? is it an abbreviation for something or did they just pick it randomly?

Who is "they"? To which "Difference Quotient formula" are you making reference? Where is the "H", and for what does it stand?

Please be complete. Thank you.

 

[Bob Brown MSEE]

The h represents a "small" value that gets even smaller, going to zero in the limit.

There is nothing special about the letter h, any letter will do. Sometimes the letter x preceded by a triangle is used, that symbol is called "Delta x".

 

[markraz]

Who is "they"? To which "Difference Quotient formula" are you making reference? Where is the "H", and for what does it stand?

Please be complete. Thank you.

They would be who ever decided to use 'h'............ Isaac Newton maybe?
To make an analogy, with regards to a C++ "for loop" i is often used as the atomic variable. i stands for "index" or "increment" or integer, perhaps depending on context.

So with relation to the Difference Quotient formula what exactly does H stand for? anything specific? or did whoever decided to use H just pick it randomly with no real reason behind it.

 

[Bob Brown MSEE]

did whoever decided to use H just pick it randomly with no real reason behind it.

Yes, h could be any currently undefined variable. You could call it d for distance between x₂ and x₁ then...
QFormula = ( f(x₁+d) - f(x₁) ) / d

Or substitute
d = x₂ - x₁
QFormula = ( f(x₂) - f(x₁) ) / (x₂ - x₁)

 

[Bob Brown MSEE]

h has become commonly used when expressing an arbitrary "horizontal" distance along the x-axis.
I believe the choice of h is simply traditional. As you see, I used x = x_​1 and h=d (above) when it suited me (and I supplied definitions).

 

[Quaid]

did whoever decided to use H just pick it randomly with no real reason behind it

The first person to use 'h' probably did have a reason (eg: other letters were already in use), but, whatever the reason, it's probably not very noteworthy. The first eleven letters of the alphabet are generally used for constants (including parameters).

The letter 'e' wound up representing the base of the Natural logarithm. Some people claim that 'e' was chosen specifically because it's the first letter of the word exponential. Others claim that it's because the Swiss mathematician Euler was involved. Neither of these claims can be adequately demonstrated. I think that it was Eli Maor who wrote (in his book titled, "e -- The Story of a Number") that the choice of 'e' probably "just happened".

Maybe the same goes for 'h.

 

[markraz]

thanks

 

[markraz]

h has become commonly used when expressing an arbitrary "horizontal" distance along the x-axis.
I believe the choice of h is simply traditional. As you see, I used x = x_​1 and h=d (above) when it suited me (and I supplied definitions).

H for horizontal seems like a good fit
spot on thanks