SIPS2022 Volume 16 Intl. Symp on Mathematics, Modelling and Geomechanics

Editors: | F. Kongoli, E. Aifantis, T. Vougiouklis, A. Bountis, P. Mandell, R. Santilli, A. Konstantinidis, G. Efremidis. |

Publisher: | Flogen Star OUTREACH |

Publication Year: | 2022 |

Pages: | 235 pages |

ISBN: | 978-1-989820-64-3(CD) |

ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |

The importance of theoretical models in Science and Engineering far outweighs that of experimental based models. The result of our lack of transparency towards the use of a more unified approach to analytical integration for solving some of the most difficult problems related to the Physical and Biological Sciences has forced us to become dependent on the use of experimental based models. In reality, this has never been a matter of choice for all of us but rather a direct consequence in our failure to fully understand exactly why the vast majority of differential equations behave the way they do by not admitting highly predictable patterns of analytical solutions for resolving them.

In this talk I will begin by extending the traditional concept of a “differential” in Calculus by introducing an entirely new algorithm capable of representing all mathematical equations consisting of only algebraic and elementary functions in complete specialized differential form. Such a universal algorithm would involve the use of multivariate polynomials and the differential of multivariate polynomials all defined in a very unique algebraic configuration.

At first glance this may not sound like a major breakthrough in the Physical Sciences but progressively throughout this entire presentation, it will become very apparent that such a specialized differential representation of all mathematical equations would lead to some form of a unified theory of integration. It is only from the general numerical application of such a universal theory in mathematics that we can expect to arrive at some form of a unified theory of Physics. This would be constructed from the development of very advanced physical models that would be built exclusively on general rather than on the local analytical solutions of many well known fundamental differential equations of the Physical and Biological Sciences.