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All Journal ComTech: Computer, Mathematics and Engineering Applications Engineering, Mathematics and Computer Science Journal (EMACS)
Wikaria Gazali
Bina Nusantara University
Civil Engineering, Building, Construction & Architecture Computer Science & IT Engineering Industrial & Manufacturing Engineering Mathematics

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Journal : Engineering, Mathematics and Computer Science Journal (EMACS)

 1 
Euler Formula Derivation Wikaria Gazali
Engineering, MAthematics and Computer Science (EMACS) Journal Vol. 4 No. 1 (2022): EMACS
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/emacsjournal.v4i1.7999

Abstract

This paper discusses the derivation of Euler's formula. To obtain this model, the writer derives Euler's formula from ex+iy by first finding the norm and argument of ex+iy. In this derivation we substitute the norm and argument of ex+iy on complex numbers in polar coordinates, until we get the derivation of Euler's formula.
Asal Usul Rumus Dasar Transformasi Laplace Wikaria Gazali
Engineering, MAthematics and Computer Science (EMACS) Journal Vol. 4 No. 2 (2022): EMACS
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/emacsjournal.v4i2.8185

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.
The Origin of The Basic Formula of The Fourier Series Wikaria Gazali
Engineering, MAthematics and Computer Science (EMACS) Journal Vol. 5 No. 1 (2023): EMACS
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/emacsjournal.v5i1.9398

Abstract

This paper discusses the Origin of the Basic Formula for the Fourier Series f(t)=a0/2+∑∞k=1 [ak cos⁡(kπt/L)+bk sin⁡(kπt/L) ] To obtain this model, the author derives the basic formula for the Fourier Series from Elementary Linear Algebra. In this derivation, we use the best approximation: least squares method whose details will be elaborated in this paper until we obtain the formula for the Fourier Series.
Co-Authors Putri Nurmala Widodo Budiharto