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# Class Note for MATH 3331 with Professor He at UH

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COURSE
PROF.
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TYPE
Class Notes
PAGES
12
WORDS
KARMA
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This 12 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 17 views.

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Date Created: 02/06/15
Section 51 Definition Existence Use of the Laplace Transform 0 Technique for solving linear DEs with constant coefficients 0 Useful for discontinuous forcings I Differential Equation I gt I Laplace Transform I gt I Algebraic Equation I I Solve Algebraic Equation I gt I Inverse Laplace Transform I gt I Solution I Jiwen He University of Houston Math 3331 Section 19470 Lecture 18 March 6 2009 2 12 Def Given a real or complex func tion ft the Laplace L transform of f is the following function of s Fs Ame 8tftdt Iim Te Stftdt T gtoo 0 Notation FS f8 fts H Math 3331 Section 19470 Lecture 18 March 6 2009 3 12 in 405w ae gUngg 4w hm gym Wu mums znmmwm z 7 4mm z mung z m amqu the mm msm a 09 mp Wm Ha sf m mm Wu mm M Section 51 Piecewise Continuous Functions Def ft is piecewise continuous if c in any finite interval 0 lt t lt T there are at most finitely many discontinuities c at any point of discontinuity td the left and right limits fF exist lied time fwd tggflttgt 0 if Olttlt1 Ex ft t1 if gt1 has a discontinuity at td 1 121 0 f1 1 Ill 1012 Math 3331 Section 19470 Lecture 18 March 6 2009 Jiwen He University of Houston Section 51 Functions of Exponential Order Def ft is of exponential order if there are constants Ca st ft g C39th for all t Meaning ft grows at most exponentially if t gt oo EX 6 52 is not of exponential order Ex 610700075 is of exponential order Iill Jiwen He University of Houston Math 3331 5 Section 19470 Lecture 1 March 6 2009 11 12 Section 51 Definition Existence Existence of the Laplace Transform Thm If ft is piecewise continu ous in 0 g t lt 00 and of exponential order then fs exists for s gt a Jiwen He University of Houston Math 3331 Section 19470 Lecture 18 March 6 2009 12 12 Lecture 13 510mmquot nun Lav aceTvansanm 1W He Wm M WM WW M mm m KVLuNnvmmzn

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