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Friday, September 16
−
Lecture 3
:
Other special functions
:
Unitstep function
(Heaviside) and hyperbolic functions
(Refers to Section 2.1 to 2.3 in your text)
Students who have mastered the content of this lecture know about
:
Unitstep (Heaviside) functions
,
expressing a piecewise defined function as single
function
, the
hyperbolic functions sinh x
,
cosh
x
,
tanh
x, and deriving some of their
simplest properties.
3.1
Definition – The (
Heaviside
) unitstep function is the function is defined as:
Note that
h
(0) is sometimes defined as being equal to ½ or left undefined. It is a matter of
choice. In practice this is usually irrelevant. When plotted we obtain:
3.1.1
Example – If we wish to translate this step function to the right by 2 units,
h
(
x
– 2), we obtain
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View Full Document 3.1.2
Remark
−
The unitstep function, often called the
Heaviside
unitstep function
,
can provide a convenient way of expressing piecewise defined functions as a single
function. We provide a few examples.
a) Consider the function
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This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.
 Spring '11
 RobertAndre
 Calculus, Hyperbolic Functions

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