Math notes/Differential Equations/Laplace TransformsDelayed Inputs and Convolution — Cheat sheetCHEAT SHEET · FREELessonCheat sheet →Unit cheat sheet →Save as PDF ↓Choose “Save as PDF” in the print dialog.On this pageCore ruleWatch forCore ruleL[H(t−a)f(t−a)]=e−asF(s).\mathcal L[H(t-a)f(t-a)]=e^{-as}F(s).L[H(t−a)f(t−a)]=e−asF(s). Watch forAn ordinary step in forcing usually leaves the state continuous while changing its derivative. An impulse can cause a jump instead. Separate the forcing’s discontinuities from the response’s continuity requirements.← PREVIOUS LESSONLaplace Inversion and Initial-Value ProblemsNEXT LESSON →Impulse Inputs and Jump Conditions