Laplace Transform (Learning objectives)

Each student should master the following items. If an item is not clear or you are not confident in doing it, you must study the material again and solve some exercises until you are sure that you master that item.

- state Laplace transform definition.
- know sufficient conditions for existence of Laplace transform.
- determine if a function is of exponential order or not.
- know and use the sampling property of the impulse.
- obtain Laplace transform of simple functions (step,impulse, ramp, pulse, sin,cos,exp(-at) and others).
- obtain Laplace transform of functions expressed in graphical form.
- know basic integration rules (you should know integration by parts).
- know the linear property of Laplace transform.
- know Laplace transform of integral and derivatives (first and high orders derivatives)
- obtain inverse Laplace transform of simple function using the Table of Laplace transform pairs.
- know and use the method of partial fraction expansion to simply strictly proper functions as the some of simple factors (for the cases:simple poles, complex poles and repeated poles).
- able to perform long division and know why we may need to use it in inverse Laplace transform.
- obtain inverse Laplace transform.
- solve constant coefficient linear ordinary differential equations using Laplace transform.
- know the Laplace transform of time-delayed functions.
- know initial-value theorem and the condition under which it can be used.
- know final-value theorem and the condition under which it can be used.