Advanced Engineering Mathematics, 7th Edition

4.3 Translation Theorems

INTRODUCTION

It is not convenient to use Definition 4.1.1 each time we wish to find the Laplace transform of a given function f(t). For example, the integration by parts required to determine the transform of, say, f(t) = e^t t² sin 3t is formidable to say the least when done by hand. In this section and the next we present several labor-saving theorems that enable us to build up a more extensive list of transforms (see the table in Appendix C) without the necessity of using the definition of the Laplace transform.

4.3.1 Translation on the s-axis

Evaluating transforms such as {e^5tt³} and {e^−2t cos 4t} is straightforward ...