Title Details: | |
Laplace Transform with applications to differential equations |
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Authors: |
Tsitsas, Nikolaos |
Reviewer: |
Frantzeskakis, Dimitrios |
Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > FUNCTIONS OF A COMPLEX VARIABLE MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > FUNCTIONS OF A COMPLEX VARIABLE > SERIES EXPANSIONS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > ORDINARY DIFFERENTIAL EQUATIONS > GENERAL THEORY MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PARTIAL DIFFERENTIAL EQUATIONS > GENERAL HIGHER-ORDER EQUATIONS AND SYSTEMS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > ORDINARY DIFFERENTIAL EQUATIONS |
Description: | |
Abstract: |
The Laplace Transform provides a method for solving linear differential equations, which are commonly used in the physical and engineering sciences. The purpose of this chapter is to introduce the reader to some of its basic ideas and applications. The Laplace transform is an integral transform introduced with the aid of a suitable generalized integral. After defining the transform, its basic properties are formulated, including its inverse and fundamental properties. Subsequently, using the Laplace transform, elementary techniques for solving linear differential equations with constant coefficients and systems of differential equations are outlined. Finally, the key property of the Laplace transform concerning the convolution of two functions is formulated, enabling techniques for solving integral and integro-differential equations.
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Type: |
Chapter |
Creation Date: | 2015 |
Item Details: | |
License: |
http://creativecommons.org/licenses/by-nc-nd/3.0/gr |
Handle | http://hdl.handle.net/11419/1135 |
Bibliographic Reference: | Tsitsas, N. (2015). Laplace Transform with applications to differential equations [Chapter]. In Tsitsas, N. 2015. Applied Mathematics [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/1135 |
Language: |
Greek |
Is Part of: |
Applied Mathematics |
Publication Origin: |
Kallipos, Open Academic Editions |