Lecture 3.pdf

# Lecture 3.pdf - Laplace Transform 2 Lecture 3 28-Jan-18...

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Laplace Transform 2 Lecture 3 28-Jan-18 System Dynamics and Control: Dr Tesleem Asafa 1

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What is the Laplace transform of the followings? 28-Jan-18 System Dynamics and Control: Dr Tesleem Asafa 2 7 7t
Definitions and symbols 28-Jan-18 System Dynamics and Control: Dr Tesleem Asafa 3

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28-Jan-18 System Dynamics and Control: Dr Tesleem Asafa 4 Inverse Laplace transform
Existence of Laplace transform 28-Jan-18 System Dynamics and Control: Dr Tesleem Asafa 5 must converge if f(t) must have a Laplace transform Laplace integral can converge in two ways: 1. f(t) must be piecewise continuous in every finite interval for t > 0 ; i.e. 0< t < ∞ OR t range between 0 and t o and t o and 2. f(t) is of exponential order such that for real positive constant σ exists such that the following equation approaches 0 as t approaches

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Laplace transform exist if f(t) is: For functions that increase faster than the exponential , Laplace transform does not exist if f(t) is: 28-Jan-18 System Dynamics and Control: Dr Tesleem Asafa 6 However, Laplace transform exists for: Existence of a Laplace transform
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• Fall '13
• Bazoune
• Laplace, Heaviside step function, Elementary special functions, Dr Tesleem Asafa

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