253-5-laplace-intro

# 253-5-laplace-intro - Laplace Transform Introduction...

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EECE 253: Laplace Transforms Introduction Slide 5.1 Laplace Transform Introduction • Motivation (Chap 15.1) • Definition of the L.T. (Chap 15.2) • Properties of the L.T. (Chap 15.3) • Inverse L.T. (Chap 15.4) • Convolution (Chap 15.5) • Application to IntegroDEs (Chap 15.6)

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EECE 253: Laplace Transforms Introduction Slide 5.2 Lessons from Phasor Analysis What good are phasors? dt t di L t Ri t v t v t v L R ) ( ) ( ) ( ) ( ) ( + = + = I I V V V L j R L R ω + = + = ( ) R L t L R V t i 1 2 2 tan cos ) ( ) ( + = () R L L R V L j R 1 2 2 tan 0 ) ( ° + = + = I V I Time domain How might we solve i(t) ? Phasor domain We’d much rather solve algebraic equations in the phasor domain than DEs in the time domain. Phasors are a tool that get the job done!
EECE 253: Laplace Transforms Introduction Slide 5.3 Motivation for Laplace Transforms View Laplace Xforms as a more generalized tool to get the job done . ) ( : Input t f ) ( : Output t g Time domain ( t -domain) Laplace/complex frequency domain ( s -domain) Laplace Xforms: • Change linear DEs into algebraic equations (easier to solve) • Handle a wider variety of inputs than just sinuosoids • Incorporate ICs in the solution automatically • Provide the total response (natural+forced) in one operation Circuit ) ( : Input s F ) ( : Output s G

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## This note was uploaded on 07/20/2009 for the course PHYS physics 10 taught by Professor Goatman during the Spring '08 term at UBC.

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253-5-laplace-intro - Laplace Transform Introduction...

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