Mathematics for Circuits and Filters

3 The Laplace Transform

John R. Deller, Jr.

Michigan State University

DOI: 10.1201/9781315214023-3

• 3.1 Introduction
• 3.2 Motivational ExampleSeries RLC Circuit • Homogeneous Solution and the Natural Response • Nonhomogeneous Solution and the Forced Response • Total Solution • Scrutinizing the Solution • Generalizing the Phasor Concept: Onward to the Laplace Transform
• 3.3 Formal DevelopmentsDefinitions of the Unilateral and Bilateral Laplace Transforms • Existence of the Laplace Transform • Example of the Laplace Transform Computations and Table of Unilateral Laplace Transforms • Poles and Zeroes — Part I • Properties of the Laplace Transform • Inverse Laplace Transform
• 3.4 Laplace Transform Analysis of Linear SystemsSolution ...