Transcription of Lecture Notes for Laplace Transform
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Lecture Notes for Laplace Transform
Lecture Notes for Laplace TransformWen ShenApril 2009NB! These Notes are used by myself. They are provided to students as a supplement to thetextbook. They can not substitute the textbook. Laplace Transform is used to handle piecewise continuous or impulsive : Definition of the Laplace Transform (1)Topics: Definition of Laplace Transform , Compute Laplace Transform by definition, including piecewise continuous :Given a functionf(t),t 0, its Laplace transformF(s) =L{f(t)}is defined asF(s) =L{f(t)}.= 0e stf(t) limA A0e stf(t)dtWe say the Transform converges if the limit exists, and diverges if we will give examples on computing the Laplace Transform of given functions by (t) = 1 fort (s) =L{f(t)}= limA A0e st 1dt= limA 1se st A0= limA 1s[e]
Solutions of initial value problems. We will go through one example flrst. Example 14. (Two distinct real roots.) Solve the initial value problem by Laplace transform,
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