The laplace transform of the sectionally-continuous derivative of a sectionally-continuous function

✍ Scribed by Bernard Rasof

• Publisher: Elsevier Science
• Year: 1964
• Tongue: English
• Weight: 532 KB
• Volume: 277
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(64)90062-6

✦ Synopsis

One of the most important and valuable merits and attributes of the Laplace transform is the straightforward and ejkient manner with which sectionally-continuous functions can be treated. This feature of the Laplace transform is the basis for some of its most interesting and useful applications, such as to the solution of the dij'erential equations which characterize electrical and mechanical transients and the dejlection of structures under concentrated loads. To prepare students for these and other applications, textbooks on the Laplace transform usually derive the Laplace transform of functions which are continuous but which have a derivative that is sectionally-continuous. In certain important applications, both the function and its derivative are sectionallycontinuous, with a common abscissa of discontinuity. The few textbooks which discuss this problem give as its answer a result'that is ambiguous and not at all useful.