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Lax. "The Flowering of applied Mathematics in America", Siam Review, Volume 31, Number 4, DOI:10.1137/1031123, December of 1989. [283] N. You can turn an anafunctor into a proper functor by invoking the axiom of choice to choose a single object from each isomorphism class. Gagliardi. [26] Non-Newtonian Calculus is cited in a 2009 doctoral dissertation on nonlinear dynamical systems by David Malkin at University College London. [36] The geometric calculus is cited by Daniel Karrasch in his 2012 doctoral dissertation "Hyperbolicity and invariant manifolds for finite time processes" at the Technical University of Dresden in Germany. [141] The geometric calculus is cited in the article "Investigation of the solutions of the Cauchy problem and boundary-value problems for the ordinary differential equations with continuously changing order of the derivative" by N.

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Not much error checking, or optimization... for ($i = 0; $i < count($arr); $i++) for ($i = 0; $i < count($arr); $i++) return $sos / (count($arr)-1); // denominator = n-1; i.e. estimating based on sample Wouldn't the following function do the same but a lot easier than the one in the comment before? I predict that non-Newtonian calculus will come to be recognized as the most important mathematical discovery of the Twentieth Century." - James R.

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They knew that posting information on the Internet would be an effective way to inform people about non-Newtonian calculus. These may be used as a self test on the graphs of trigonometric functions. Cautiously optimistic, we patiently waited to see if anybody would discover some application(s) of NNC. In fact, one must acknowledge that it’s only under the effort of Grossman & Katz (1972) ... that such a non-Newtonian calculus emerged to give a natural answer to many growth phenomena. ...

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The geometric calculus was used by Ali Uzer (Fatih University in Turkey) in an article on wave theory in physics: "Improvement of the diffraction coefficient of GTD by using multiplicative [the geometric] calculus". [185] In the abstract to the article he states: "The given approximation techniques [based on the geometric calculus] ... can be extended to other high frequency techniques in electromagnetics." A constructor can be used to create an empty table or to create a table and initialize some of its fields.

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The sea-creatures make music when you touch them - like notes on an underwater keyboard! 8. Math - Calculus: Good list of problems with solutions. So, it should come as no surprise that when I was given an opportunity to speak at Singularity Summit last fall, a conference largely concerned with exponential trends in technology, I decided to try to persuade people of the utility of multiplicative calculus and the value of mathematical abstractions." (The expression "multiplicative calculus" refers here to the geometric calculus.) - Christopher Olah, Thiel Fellow; from Christopher Olah's Blog, 07 May 2013. [134, 135, 164] "In this [project] you will explore alternative 'calculi'.

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We will not charge you for the book until it ships. The authors have written this book for engineers and scientists, as well as for mathematicians. ... Both the program and the research have a focus on conceptual understanding intertwined with the other components of math proficiency. While writing the book, we surprised ourselves by creating infinitely more non-Newtonian calculi, including the bigeometric calculus. And we sink deeper and deeper from democracy into a state of mediocrity and even idiocracy."

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Throughout, this book exhibits a clarity of vision characteristic of important mathematical creations. ... Non-Newtonian Calculus, ISBN 0912938013, 1972. [15] Michael Grossman. Some of the specific mathematical theories they use include probability theory and non-Newtonian calculus. It's quite obvious that the Mathematica way is cheating, but it isn't that easy to formulate a rule which clearly forbids it. Some real applications of nonlinear exponential signals will be selected to demonstrate the applicability and efficiency of proposed representation." - Ali Ozyapici (Cyprus International University in Cyprus/Turkey) and Bulent Bilgehan (Girne American University in Cyprus/Turkey); from their 2015 article "Finite product representation via multiplicative calculus and its applications to exponential signal processing" [225] "The main goal of this paper is chaos examination in systems described with multiplicative [bigeometric] differential equations." - Dorota Aniszewska and Marek Rybaczuk, both from Wroclaw University of Technology in Poland; from their 2010 article "Chaos in multiplicative systems". [126] "Theory and applications of [geometric] and [bigeometric] calculi have been evolving rapidly over the recent years.

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Unfortunately, some critics of non-Newtonian calculus have fallaciously argued that it follows from that fact that the non-Newtonian calculi are useless. Special angles together with their sine and cosine displayed on a unit circle. I think if the US are the ONLY people saying ‘Math’ then you’re clearly in the wrong, regardless of any convoluted explanation you try and apply to it. An author index appears in the last issue of each volume.

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Reidel Publishing Company, Volume 26, page 181, 1973. [75] Mathematical Education, India University Grants Commission, Volume 2, 1985. [76] Institute of Mathematical Statistics Bulletin, Institute of Mathematical Statistics, Volumes 1-2, 1972. [77] Search, Australian & New Zealand Association for the Advancement of Science (ANZAAS), Volume 3, page 457, 1972. [78] Ali Uzer. "Multiplicative type complex calculus as an alternative to the classical calculus", Computers & Mathematics with Applications, DOI:10.1016/j.camwa.2010.08.089, Elsevier, 2010. [79] Praxis der Mathematik, Aulis Verlag Deubner, Volume 23, page 94, 1981. [80] Indian Journal of Theoretical Physics, Institute of Theoretical Physics (India), Volume 31, page 176, 1983. [81] Economic Books: Current Selections, University of Pittsburgh, Department of Economics, Volume 9, page 29, 1982. [82] Diana Andrada Filip and Cyrille Piatecki. "A non-Newtonian examination of the theory of exogenous economic growth", hal.archives-ouvertes.fr/hal-00945781, CNCSIS - UEFISCSU (project number PNII IDEI 2366/2008) and Laboratoire d’Economie d’Orléans (LEO), Mathematica Aeterna, Volume 4, Number 2, Hilaris, 2014. [83] Physique au Canada, Canadian Association of Physicists, Volumes 27-28, page 88, 1971. [84] Emine Misirli and Yusuf Gurefe. "Multiplicative Adams Bashforth–Moulton methods", Numerical Algorithms, DOI: 10.1007/s11075-010-9437-2, Volume 57, Number 4, pages 425 - 439, Springer, 2011. [85] James D.

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I think I'll just say that it's "historically inconsistent". They gave us unconditional love, unlimited attention, and inspired us by the examples they set. The six books on non-Newtonian calculus and related matters by Jane Grossman, Michael Grossman, and Robert Katz are indicated below, and are available at some academic libraries, public libraries, and booksellers such as Amazon.com. Instead of "real" and "imaginary", you can think of a complex number as a point in the xy-plane -- the real part is the x coordinate, the imaginary part the y coordinate.