CHEN 4601 Lecture Notes - Lecture 7: Exponential Function

• School: UMN
• Department: Chemical Engineering
• Course: CHEN 4601
• Professor: Prodromos Daoutidious

Document Summary

Example - using the laplace transform to solve odes formal definition of laplace transform for some function u(t) for 1st, unit step change. Chen4601_processcontrol page 3 f(t) g(t) shifting in time by a constant amount is equivalent to multiplying by e -s. Unit impulse unit area of 1 infinitely tall and thin delta function. Chen4601_processcontrol page 4 can switch the order of integrating and taking the limit can use lhopital"s rule. Chen4601_processcontrol page 5 do by integration by parts. Example of how laplace transforms make odes easier see how c changes when ci changes. C"(t) for a step change of ci"(t) want to take laplace transform of this in time domain this is in terms of deviation variables starts at steady state, so starts at 0. Chen4601_processcontrol page 11 this is for unit step in before example, we just had 1/s for unit step of 1. Chen4601_processcontrol page 12 will exponentially decay into a new steady state.