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by: Paul Spencer


Paul Spencer
Virginia Commonwealth University
GPA 3.98

Hassan Sedaghat

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Hassan Sedaghat
Class Notes
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This 1 page Class Notes was uploaded by Paul Spencer on Wednesday October 28, 2015. The Class Notes belongs to MATH 301 at Virginia Commonwealth University taught by Hassan Sedaghat in Fall. Since its upload, it has received 18 views. For similar materials see /class/230618/math-301-virginia-commonwealth-university in Applied Math at Virginia Commonwealth University.

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Date Created: 10/28/15
Lecture Notes in Differential Equations Dr Hassan Sedaghat Importantl These instructor notes are made available for convenience to reduce the amount of note taking in class and also in case it is not possible to attend class due to circumstances beyond control eg illness These notes are not intended as a replacement for class attendance and participation nor as a substitute for using the textbook The class presentation may differ from these notes and further7 these notes do not contain solutions for homework problems which may be discussed in class Section 74 Operational Properties ll Section 741 Derivatives of a transform ln Section 722 we discussed the Laplace transfarms 0f derivatives and obtained a formula for fquott Laplace transform of the nth derivative of on the teaxis There is a seaxis version where we have a formula for the derivatives Of a Laplace transfurm7 175 NH FquotS 1quot13tquotft Alternatively7 this can be written as l375quotf75 1quotFquot5 Or equivalently7 we can write tquotft71quot ft This formula shows that multiplication 0n the teazis by the puwer functizm 75quot requires taking the niderivative 0f the Laplace transform So there is some resemblance to the 1st translation theorem on the seaxis which said eatft Fs 7 a This formula said that multiplication on the teaxis by e t translated or shifted the Laplace transform Example 1 Compute the Laplace transforms below a t sin 75 b t2 sin 75 c tgeat sin 75 a Since the formula for sin t is known we use it along with the derivatives of transforms formula to get d d 1 25 7 7 1i if 7 7 tsmt 7 1 ds tsmt d5 52 1 52 DZ


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