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Solution of ODEs using Laplace Transforms - Queen's U

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.

Solution of ODEs We can continue taking Laplace transforms and generate a catalogue of Laplace domain functions. The final aim is the solution of ordinary differential equations. Example Using Laplace Transform, solve Result

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