Abstract
This chapter focuses on the important theorems of Laplace transforms. Most of the theorems discussed in the chapter relate operations in one plane to operations in the other plane. In addition to their immediate value for taking inverse transforms, the theorems play a vital part in the development and extension of collected tables of Laplace transforms. Each theorem has been given a definite name and usually, the names are descriptive of the operation involved, which makes them easy to remember. The linear s-plane translation theorem, deals with an exponential factor in the time domain and it is certainly one of the more useful theorems in electronics work. The final and initial value theorems, serve as guides for checking solutions and in numerous cases allow a specific formula to be derived at a glance. The complex differentiation and integration theorems are useful in extending and modifying tables of Laplace transforms and also for increasing the general familiarity with operation in the time and complex frequency domains.
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