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The negative exponential transformation: a linear algebraic approach to the Laplace transform.
- Source :
-
International Journal of Mathematical Education in Science & Technology . May2024, Vol. 55 Issue 6, p1524-1533. 10p. - Publication Year :
- 2024
-
Abstract
- We view the (real) Laplace transform through the lens of linear algebra as a continuous analogue of the power series by a negative exponential transformation that switches the basis of power functions to the basis of exponential functions. This approach immediately points to how the complex Laplace transform is a generalisation of the Fourier transform where the pole of the transform realises the linear algebraic intuition. The exponential transformation also motivates the Taylor inversion of the real Laplace transform. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0020739X
- Volume :
- 55
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- International Journal of Mathematical Education in Science & Technology
- Publication Type :
- Academic Journal
- Accession number :
- 176985823
- Full Text :
- https://doi.org/10.1080/0020739X.2023.2219262