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What does H mean?!

by jaja1990
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jaja1990
#1
Feb21-12, 08:24 AM
P: 26
I have this question in my assignment paper:-

8. Sketch the graph of:
(a)
y = |2x − 2|;
(b)
y = 2H(x − 4)

(a) is obvious, but how do I sketch (b)? Does "H" stand for some specific constant?
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JJacquelin
#2
Feb21-12, 09:10 AM
P: 759
Possibly, the Heaviside step function H(x)
http://mathworld.wolfram.com/HeavisideStepFunction.html
jaja1990
#3
Feb21-12, 10:10 AM
P: 26
The webpage in the link you've given says:-
The function is:-
0 when x < 0,
1/2 when x = 0,
1 when x > 0.
But here: http://simple.wikipedia.org/wiki/Heaviside_Function, defines the function as:-
1 when x => 0,
0 when x < 0.

To begin with, which should I follow?

JJacquelin
#4
Feb21-12, 10:23 AM
P: 759
What does H mean?!

I think that H(0)=0 correponds to an old definition remaining from history and that the standard definition is with H(0)=1/2.
Generally this is of no consequence in partical applications.
chiro
#5
Feb21-12, 11:00 PM
P: 4,573
Quote Quote by JJacquelin View Post
I think that H(0)=0 correponds to an old definition remaining from history and that the standard definition is with H(0)=1/2.
Generally this is of no consequence in partical applications.
If one wanted to use an approximation like a fourier series version, then it makes sense to define H(0) as 1/2 based on properties of fourier series when you have this kind of 'Gibbs' phenomenon.


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