拉普拉斯變換及其應用

Abstract

在本篇論文主要是討論拉普拉斯變換與逆變換，拉普 拉斯變換是一個很重要的變換，應用上也不難，大學生在 大一學習微積分課程時就已具備使用拉普拉斯變換的能 力了，但對於它延伸的性質和演算背後使用的數學性質或 意義，卻很少去探索，我希望寫一篇大學生也能看懂的文 章，了解許多我們習以為常的運算，其背後的原理和進一 步延伸的性質與應用，往往是非常豐富，甚至是由其它看 似關聯性較低的主題推導得來。

In this thesis, we discuss Laplace transform and Inverse transform. For some complicated integration Laplace transform is very important. It is significant and not that hard to use. Students have learnt how to perform Laplace transform in the course of calculus. However, they seldom study its extended properties and the mathematical meanings behind thoroughly. Therefore, I would like to produce a readable article for undergraduates, letting them know our regular computations and their used principles. The properties and applications can be various. Furthermore, they might come from other little related themes.