Asal Usul Rumus Dasar Transformasi Laplace
DOI:
https://doi.org/10.21512/emacsjournal.v4i2.8185Keywords:
Laplace Transform, Power Series, Maclaurin SeriesAbstract
This paper discusses the Origin of the Basic Formula of the Laplace Transform L{f(t)}=∫_0^∞▒〖e^(-st) f(t) 〗 dt=F(s). To obtain this model, the author derives the basic formula for the Laplace Transform from a Power Series. In this derivation, we use Euler’s number to the power of the function and the Maclaurin Series to obtain the derivation of the Basic Formula for the Laplace Transform where the Maclaurin Series is derived from the Taylor Series.
Plum Analytics
References
Binmore, K., Davies, J. (2002). Calculus: Concepts and Methods. CAMBRIDGE Published.
Briggs, W., Cochran, L., et al. (2018). Calculus: Early Transcendentals Third Edition. Pearson Published.
Buck, R.C. (2003). Advanced Calculus. Waveland Pr Inc Published.
Friedman, A. (2007). Advanced Calculus. DOVER PUBN INC Published.
Gazali, W. (2007). Kalkulus Edisi 2. Yogyakarta: Penerbit Graha Ilmu.
Gazali, W. (2018). Kalkulus Lanjut Edisi 3. Yogyakarta: Penerbit Graha Ilmu.
Gazali, W. (2022). Euler Formula Derivation. Engineering, MAthematics and Computer Science (EMACS) Journal, 4(1), 15-17.
Larson, R., H. Edwards, B. (2017). Calculus. CENGAGE Published.
Loomis, L.H., Sternberg, S. (2014). Advanced Calculus Revisesd Edition. World Scientific Published.
Mattuck, A. (2008). (1:2) Where the Laplace Transform comes from. MIT: https://www.youtube.com/watch?v=zvbdoSeGAgI&t=93s
Mattuck, A. (2008). (2:2) Where the Laplace Transform comes from. MIT: https://www.youtube.com/watch?v=hqOboV2jgVo&t=232s
Morris, C.C., Stark, R.M. (2015). Fundamentals of Calculus. Wiley Published.
Neill, Hugh. (2018). Calculus: A Complete Introduction. TEACH YOURSELF Published.
Nickerson, H.K., Spencer, D.C., Steenrod, N.E. (2011). Advanced Calculus. Dover Publication, Inc.
STEWART, J. (2008). CALCULUS Early Transcendentals Sixth Edition. Mc MASTER UNIVERSITY: Thomson Brooks/ Cole.
Wrede, R., Spiegel, M.R. (2019). Schuam’s Outline of Theory and Problems in Advanced Calculus Second Editi2). Kalkulus Edisi 2. Yogyakarta: Penerbit Graha Ilmu.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Engineering, MAthematics and Computer Science (EMACS) Journal
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
a. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License - Share Alike that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
b. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
c. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
USER RIGHTS
All articles published Open Access will be immediately and permanently free for everyone to read and download. We are continuously working with our author communities to select the best choice of license options, currently being defined for this journal as follows: Creative Commons Attribution-Share Alike (CC BY-SA)
