lect116_3 _f11

lect116_3 _f11 - Friday, September 16 Lecture 3 : Other...

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Friday, September 16 Lecture 3 : Other special functions : Unit-step 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 : Unit-step (Heaviside) functions , expressing a piece-wise 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 ) unit-step 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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3.1.2 Remark The unit-step function, often called the Heaviside unit-step 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.

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lect116_3 _f11 - Friday, September 16 Lecture 3 : Other...

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