Introduction to the Division by Zero Calculus PDF Download
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Author: SABUROU SAITOH
Publisher: Scientific Research Publishing, Inc. USA
ISBN: 1649970897
Category : Mathematics
Languages : en
Pages : 203
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Book Description
The common sense on the division by zero with the long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on differential coefficients we have a great missing since tan(π/2) = 0. Our mathematics is also wrong in elementary mathematics on the division by zero. In this book in a new and definite sense, we will show and give various applications of the division by zero 0/0 = 1/0 = z/0 = 0. In particular, we will introduce several fundamental concepts in calculus, Euclidean geometry, analytic geometry, complex analysis and differential equations. We will see new properties on the Laurent expansion, singularity, derivative, extension of solutions of differential equations beyond analytical and isolated singularities, and reduction problems of differential equations. On Euclidean geometry and analytic geometry, we will find new fields by the concept of the division by zero. We will collect many concrete properties in mathematical sciences from the viewpoint of the division by zero. We will know that the division by zero is our elementary and fundamental mathematics.
Author: SABUROU SAITOH
Publisher: Scientific Research Publishing, Inc. USA
ISBN: 1649970897
Category : Mathematics
Languages : en
Pages : 203
Get Book Here
Book Description
The common sense on the division by zero with the long and mysterious history is wrong and our basic idea on the space around the point at infinity is also wrong since Euclid. On the gradient or on differential coefficients we have a great missing since tan(π/2) = 0. Our mathematics is also wrong in elementary mathematics on the division by zero. In this book in a new and definite sense, we will show and give various applications of the division by zero 0/0 = 1/0 = z/0 = 0. In particular, we will introduce several fundamental concepts in calculus, Euclidean geometry, analytic geometry, complex analysis and differential equations. We will see new properties on the Laurent expansion, singularity, derivative, extension of solutions of differential equations beyond analytical and isolated singularities, and reduction problems of differential equations. On Euclidean geometry and analytic geometry, we will find new fields by the concept of the division by zero. We will collect many concrete properties in mathematical sciences from the viewpoint of the division by zero. We will know that the division by zero is our elementary and fundamental mathematics.
Author: Luis Angel Caffarelli
Publisher: Edizioni della Normale
ISBN: 9788876422492
Category : Mathematics
Languages : en
Pages : 0
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Book Description
The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.
Author: Jose Manuel Vega
Publisher: Academic Press
ISBN: 0128227664
Category : Technology & Engineering
Languages : en
Pages : 322
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Book Description
Higher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industrial contexts to help readers understand and use this innovative algorithm. Data-driven modelling of complex systems is a rapidly evolving field, which has applications in domains including engineering, medical, biological, and physical sciences, where it is providing ground-breaking insights into complex systems that exhibit rich multi-scale phenomena in both time and space. Starting with an introductory summary of established order reduction techniques like POD, DEIM, Koopman, and DMD, this book proceeds to provide a detailed explanation of higher order DMD, and to explain its advantages over other methods. Technical details of how the HODMD can be applied to a range of industrial problems will help the reader decide how to use the method in the most appropriate way, along with example MATLAB codes and advice on how to analyse and present results. - Includes instructions for the implementation of the HODMD, MATLAB codes, and extended discussions of the algorithm - Includes descriptions of other order reduction techniques, and compares their strengths and weaknesses - Provides examples of applications involving complex flow fields, in contexts including aerospace engineering, geophysical flows, and wind turbine design
Author: Mohammed Hichem Mortad
Publisher: World Scientific
ISBN: 9813236272
Category : Mathematics
Languages : en
Pages : 656
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Book Description
This book is for third and fourth year university mathematics students (and Master students) as well as lecturers and tutors in mathematics and anyone who needs the basic facts on Operator Theory (e.g. Quantum Mechanists). The main setting for bounded linear operators here is a Hilbert space. There is, however, a generous part on General Functional Analysis (not too advanced though). There is also a chapter on Unbounded Closed Operators.The book is divided into two parts. The first part contains essential background on all of the covered topics with the sections: True or False Questions, Exercises, Tests and More Exercises. In the second part, readers may find answers and detailed solutions to the True or False Questions, Exercises and Tests.Another virtue of the book is the variety of the topics and the exercises and the way they are tackled. In many cases, the approaches are different from what is known in the literature. Also, some very recent results from research papers are included.
Author: Mary Somerville
Publisher:
ISBN:
Category : Astronomy
Languages : en
Pages : 710
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 168
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Book Description
Author: Allan Greenwood
Publisher: Wiley-Interscience
ISBN:
Category : Technology & Engineering
Languages : en
Pages : 778
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Book Description
The principles of the First Edition--to teach students and engineers the fundamentals of electrical transients and equip them with the skills to recognize and solve transient problems in power networks and components--also guide this Second Edition. While the text continues to stress the physical aspects of the phenomena involved in these problems, it also broadens and updates the computational treatment of transients. Necessarily, two new chapters address the subject of modeling and models for most types of equipment are discussed. The adequacy of the models, their validation and the relationship between model and the physical entity it represents are also examined. There are now chapters devoted entirely to isolation coordination and protection, reflecting the revolution that metal oxide surge arresters have caused in the power industry. Features additional and more complete illustrative material--figures, diagrams and worked examples. An entirely new chapter of case studies demonstrates modeling and computational techniques as they have been applied by engineers to specific problems.
Author: Laurence Sigler
Publisher: Springer Science & Business Media
ISBN: 1461300797
Category : Mathematics
Languages : en
Pages : 736
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Book Description
First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods.
Author: Gabbay Dov
Publisher:
ISBN: 9781848903814
Category :
Languages : en
Pages : 168
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Book Description
Author: Sandra D. Mitchell
Publisher: Cambridge University Press
ISBN: 9780521520799
Category : Philosophy
Languages : en
Pages : 264
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