TRANSFORMATIONS: A MATHEMATICAL APPROACH – FUNDAMENTAL CONCEPTS

by

Carlos Polanco

DOI: 10.2174/97816810871151180101
eISBN: 978-1-68108-711-5, 2018
ISBN: 978-1-68108-712-2



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Mathematical transformations have applications in many everyday artistic (computer graphics and design), industrial (manufacturing) an...[view complete introduction]
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Table of Contents

Foreword

- Pp. i
Jorge Alberto Castanon Gonzalez
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Preface

- Pp. ii
Carlos Polanco
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List of Contributors

- Pp. iii
Carlos Polanco
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Introduction

- Pp. 1
Carlos Polanco
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Affine Transformations

- Pp. 2-7 (6)
Carlos Polanco
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Linear Transformations

- Pp. 8-29 (22)
Carlos Polanco
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Nonlinear Transformations

- Pp. 30-40 (11)
Carlos Polanco
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Acoustics

- Pp. 41-44 (4)
Carlos Polanco
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Actuary

- Pp. 45-49 (5)
Carlos Polanco and Danae Itzel Alvarez
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Bioinformatics

- Pp. 50-56 (7)
Carlos Polanco
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Calculus

- Pp. 57-64 (8)
Carlos Polanco
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Cybernetics

- Pp. 65-66 (2)
Carlos Polanco
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Epidemiology

- Pp. 67-68 (2)
Carlos Polanco
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Genetics

- Pp. 69-78 (10)
Carlos Polanco and Carlos Ignacio Herrera
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Optics

- Pp. 79-81 (3)
Carlos Polanco
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Probability

- Pp. 82-86 (5)
Carlos Polanco and Alma Fernanda Sanchez
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Vector Analysis

- Pp. 87-90 (4)
Carlos Polanco
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References

- Pp. 91-94 (4)
Carlos Polanco
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Subject Index

- Pp. 95-97 (3)
Carlos Polanco
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Foreword

In this book, Dr. Carlos Polanco overcomes the usual gap between mathematicians and application users, describing with several examples the mathematical operator named transformation. This book can be used as auxiliary for students interested in this field as well as a reference book for seasoned Researcher.

Jorge Alberto Castañón González
Department of Critical Care Medicine
Hospital Juárez de México
México City
México



Preface

A “transformation”, in its broadest sense, is an operator that relates two quantities. Its use permeates many every day artistic and scientific activities. An example of this would be its use in the manufacturing of tools to build and transform objects in different artistic expressions such as painting, sculpture, and theatre to determine the correct distance and size of things. In the scientific field, they are used in different disciplines such as Optics and Physics and more recently in Genomics and Bioinformatics. Due to the role transformations play in a broad spectrum of human creation, it is surprising to realize that few publications have been allocated to its study, not only in its mathematical context but also in its application to other disciplines. The reader will find in this book a study of this mathematical operator described by a large number of carefully selected examples, the reading and application, which can be easily understood without any rigorous mathematical knowledge. The first part introduces the affine transformations as mathematical operators, their properties, and their definition. The second part describes the differences between linear and nonlinear transformations. And the third part applies transformations in Acoustics, Actuary, Bioinformatics, Calculus, Cybernetics, Epidemiology, Genetics, Optics, Physics, Probability, and Vector Analysis. The author hopes the reader interested in Transformation theory finds useful the material presented here and that those who start studying this field, find this information motivating.

CONSENT FOR PUBLICATION

Not applicable.

CONFLICT OF INTEREST

The authors declare no conflict of interest, financial or otherwise.

ACKNOWLEDGEMENTS

Foremost, I would like to express my sincere gratitude to all contributors from the Faculty of Sciences at Universidad Nacional Autónoma de México for their collaboration in the preparation of this book.

Carlos Polanco
Department of Mathematics, Faculty of Sciences
Universidad Nacional Autónoma de México
México


List of Contributors

Author(s):
Carlos Polanco




Contributor(s):
Alma Fernanda Sánchez Guerrero
Department of Mathematics
Faculty of Sciences
Universidad Nacional Autónoma de México
México


Carlos Ignacio Herrera Nolasco
Department of Mathematics
Faculty of Sciences
Universidad Nacional Autónoma de México
México


Carlos Polanco
Department of Mathematics
Faculty of Sciences
Universidad Nacional Autónoma de México
México


Dánae Itzel Álvarez Figueroa
Department of Actuary
Faculty of Sciences
Universidad Nacional Autónoma de México
México




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