May 3

section covered in text

7.6.  Transforms of Discontinuous and Periodic Functions
 

• to be able to express discontinuous functions in terms of  the step function
• to be able to use the Translation in t Theorem to determine Laplacians and their inverses
• to be able to determine the Laplacians of periodic functions

• unit step function
• Laplace transform of u(t-a)
• translation in t
• periodic functions
• gamma function

solved problems - using key ideas

• prove L{u(t-a)}(s) = (1/s)e^-as
• sketching graphs involving step functions, #1,5,9
• computing their Laplacians
• using TI-92 when (x <  3,when(x< 2,when(x < 1 , 0, 2), 1, 3)
• determining inverse Laplacians, #11,15
• modeling RLC series circuit, #19
• determining the Laplacian of periodic functions, #21,25
• solving initial value problems, #29,33,37
• using the Taylor series, #47

QUESTION OF THE DAY

Find the inverse Laplacian transform of

SOLUTION

SOLUTION.