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Solution of ODEs using Laplace Transforms

1 Solution of Solution of ODEs ODEs using using Laplace Laplace TransformsTransformsProcess Dynamics and ControlProcess Dynamics and Control2 Linear Linear ODEsODEs For linear ODEs, we can solve without integrating byusing Laplace Transforms Integrate out time and transform to Laplace domainMultiplicationMultiplicationIntegr ationIntegration3 Common TransformsCommon TransformsUseful Useful Laplace Laplace TransformsTransforms1. Exponential1. Exponential2. Cosine2. Cosine4 Common TransformsCommon TransformsUseful Useful Laplace Laplace TransformsTransforms3. Sine3. Sine5 Common TransformsCommon TransformsOperators1. Derivative of a function, ,2. Integral of a function6 Common TransformsCommon TransformsOperatorsOperators3. Delayed function7 Common TransformsCommon TransformsInput Signals1. Constant1. Constant2. Step2. Step3. Ramp function3. Ramp function8 Common TransformsCommon TransformsInput SignalsInput Signals4.

Solution is obtained by a getting the inverse Laplace transform from a table Alternatively we can use partial fraction expansion to compute the solution using simple inverse transforms. 14 Solution of Linear ODEs ... CHEE319_notes_2011_lecture3.ppt Author: Martin Guay

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