Numerical Tribute to Achievements of Euler

Carlos Figueroa(1*), Lamberto Castro(2), Julio C. Campos(3)

(1) Industrial Engineering Department. University of Sonora. Central Campus, Mexico
(2) Department of Mathematics, Physics and Engineering. University of Sonora. South Campus, Mexico
(3) Department of Mathematics, Physics and Engineering. University of Sonora. Cajeme Campus, Mexico
(*) Corresponding author


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Abstract


This paper aims to make a tribute to one of the world's brightest personalities, the mathematical physicist Leonhard Euler (1707-1783). Our purpose is to expose, in a concise and entertaining way by utilizing modern computational techniques, a better understanding of the influence of Euler; also, to establish the remarkable significance in  the history of science. A first analysis was done with the series that defines Euler and Bernoulli numbers and polynomials of Bernoulli and Euler; an additional result is the characterization of the functions that lead to the Euler-Mascheroni constant. In hydrodynamics it is also feasible to evaluate graphically the connection between sizes in diameter and the exit angle of the height of Euler for turbo-machines. In differential equations of Cauchy-Euler solutions in the cases of distinct real roots and complex roots are generated. Furthermore we report the generation of the Fourier series and the Fourier transform calculated by using direct Matlab commands. In calculus of variations, it is conceivable to obtain plots from a problem of the Euler Lagrange equations. Finally, Euler totient function is graphically analyzed. We seek the following benefits: The association between Euler numbers and generating functions is more effectively understood, also the nature of the Euler constant and the Euler function  The Fourier transform is more comprehensible; also, it can be established that Matlab is an alternative way to study the conceptual development of achievements of physics and mathematics. We show that the abundance of Euler work and the history of mathematics, acquire better knowledge with the application of numerical tools
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Keywords


Calculus of Variations; Euler Height; Euler Mascheroni Constant; Euler Totient Function; Fourier Series; Taylor Polynomials

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References


V.S. Varadarajan. Euler through times, a new look at old themes, American Mathematical Society (2006).

O. Ladyzhenskaya. Sixth problem of the millennium: Navier Stokes equation, existence and smoothness, Russian Mathematical Surveys 58 251-286 (2003).

A. Meneses, J. Delgado and F. Monroe. The mathematical legacy of Leonhard Euler. Edited by UAM, Mexico (2009).

D.Huylebrouck. Similarities in Irrationally Proofs for π, ln2, ζ(2), Amer. Math. Monthly 108 222-231 (2001).

H. H. Erbil, A Simple Solution of the Relativistic Dirac Equation for a Particle in a Central Potential and an Example, (2013) International Review of Physics (IREPHY), 7 (5), pp. 376-384.

Euler’s Glossary, Mathematics Magazine 56 315-325 (1983).

W. Dunham. Euler the Master of all mathematicians. Edited by Nivola, Spain (2006).

D. Schattschneider. A tribute to Leonhard Euler, 56 5 Mathematics Magazine

C.E. Sandifer. The early mathematics of Leonhard Euler. Edited by the Mathematical Association of America, USA. (2007).

D. E. Knuth and T.J. Buckholtz. Computation of Tangent, Euler and Bernoulli Numbers. Mathematics of Computation 21 100 pp 663-688. (1967).

D.S. Kim and T. Kim. Some New identities of Frobenius Euler numbers and polynomials. Journal of Inequalities and Applicationes.307 (2012).

D. Bailey. Numerical Results on the Transcendence of Constant. Mathematics of Computation. 50 181 275-281 (1988).

E.K. Karatsuba. On the computation of the Euler constant γ. Numerical Algorithms 24 pp 83-97 (2000).

J.Havil Gamma exploring Euler constant. Edit. Princeton USA (2003).

S. Lynch. Dynamical Systems with applications using Matlab. Edited by Birkhauser, USA (2004).

J. Polking and D. Arnold. Ordinary Differential Equations using Matlab. Second edition, edited by Prentice hall, USA (1999).

G. M. Ortigoza. Solving differential equations with Mathematica and Maple .Journal of Physics. 53 2 155-167 (2007).

C.A. Truesdell. Essay in the history of mechanics. Edited by Springer Verlag, USA (1968).

P.J. Nahin. Dr. Euler fabulous formula. Edit. Princeton USA (2011).

R. Menzel. A Fourier Series Derivation of the Euler Lagrange Equation. The American Mathematical Monthly.74 5 587-588 (1967).

V. Lampret. The Euler Maclaurin and Taylor formulas. Mathematics magazine 74 2 (2001).

T. Apostol. Elementary view of Euler’s summation formula. The American Mathematical monthly 106 5 409-414 (1999).

E. Weisstein. Manual of mathematics. Edited by Chapman & Hall/Croc pp 570, USA (1999).

S. Campbell and R. Haberman. Introduction to Differential Equations. Edited by McGraw Hill pp 209-211, Mexico (1998).

D. G. Zill and M.R. Cullen. Advanced Mathematics for Engineering. II edition McGraw Hill pp 501-502, Mexico (2008).

J. Garcia Acosta. Solved problems of hydraulic machines. Edited by University of Navarra, Spain (2009).

G. Marquez. Bernoulli polynomials .Edited by University of Venezuela. Venezuela (2008).

S. Abdalah, K. Al Naimee, M. Ciszak, F. Marino, R. Meucci, F. T. Arecchi, Chaos and Mixed Mode Oscillations in Optoelectronic Networks, (2013) International Review of Physics (IREPHY), 7 (3), pp. 278-282.

K. Gepreel, T Nofal and F. Altobail. Numerical solutions for the time and space fractional nonlinear partial differential equation. Journal of Applied Mathematics. 7 4 pp 323-330 (2013).

D. Baez and O. Cervantes. Matlab with applications. Second edition .Edited by Alfaomega pp 234-235, Mexico (2012).

B. Y. Al-Negashi, T. A. El-Azim, I. A. M. Abdul-Magead, Neutral Higgs-Boson Production in Association with a Pair of Muon-Sneutrino at e- e+ Linear Colliders, (2013) International Review of Physics (IREPHY), 7 (3), pp. 259-268.


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