December 7
section covered in text
7.6. Transforms of Discontinuous and Periodic Functions
objective
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to be able to
express discontinuous functions in terms of the step function
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to be able to
use the Translation in t Theorem to determine Laplacians and their
inverses
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to be able to
determine the Laplacians of periodic functions
key ideas and/or vocabulary
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unit step function
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Laplace transform of u(t-a)
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translation in t
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periodic functions
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gamma function
solved problems - using key ideas
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prove L{u(t-a)}(s) = (1/s)e-as
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sketching graphs involving step functions, #1,5,9
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computing their Laplacians
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using TI-89 when (x < 3,when(x< 2,when(x
< 1 , 0, 2), 1, 3)
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determining inverse Laplacians, #11,15
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modeling RLC series circuit, #19
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determining the Laplacian of periodic functions,
#21,25
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solving initial value problems, #29,33,37
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using the Taylor series, #47
announcements
Although no more assignments will be collected
you are encouraged to do the following exercises:
#4,7,9,10,11,14,18,23,28,31,36,40,49
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QUESTION OF THE DAY
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Find the inverse Laplacian transform of
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SOLUTION
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SOLUTION.
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