Asal Usul Rumus Dasar Transformasi Laplace

Authors

  • Wikaria Gazali Bina Nusantara University

DOI:

https://doi.org/10.21512/emacsjournal.v4i2.8185

Keywords:

Laplace Transform, Power Series, Maclaurin Series

Abstract

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.

Dimensions

Plum Analytics

Author Biography

Wikaria Gazali, Bina Nusantara University

Mathematics Department, School of Computer Science

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.

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Published

2022-06-09

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