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Generalized Trigonometric And Hyperbolic Functions

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Generalized Trigonometric And Hyperbolic Functions

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Author : Ronald E. Mickens
language : en
Publisher:
Release Date : 2024

Generalized Trigonometric And Hyperbolic Functions written by Ronald E. Mickens and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Exponential functions categories.

Generalized Trigonometric And Hyperbolic Functions

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Author : Ronald E. Mickens
language : en
Publisher: CRC Press
Release Date : 2019-01-15

Generalized Trigonometric And Hyperbolic Functions written by Ronald E. Mickens and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-15 with Mathematics categories.

Generalized Trigonometric and Hyperbolic Functions highlights, to those in the area of generalized trigonometric functions, an alternative path to the creation and analysis of these classes of functions. Previous efforts have started with integral representations for the inverse generalized sine functions, followed by the construction of the associated cosine functions, and from this, various properties of the generalized trigonometric functions are derived. However, the results contained in this book are based on the application of both geometrical phase space and dynamical systems methodologies. Features Clear, direct construction of a new set of generalized trigonometric and hyperbolic functions Presentation of why x2+y2 = 1, and related expressions, may be interpreted in three distinct ways All the constructions, proofs, and derivations can be readily followed and understood by students, researchers, and professionals in the natural and mathematical sciences

Generalized Trigonometric And Hyperbolic Functions

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Author : Ronald E. Mickens
language : en
Publisher: CRC Press
Release Date : 2019-01-15

Generalized Hyperbolic And Trigonometric Functions

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Author : Lawrence Kirk Tolman
language : en
Publisher:
Release Date : 1961

Generalized Hyperbolic And Trigonometric Functions written by Lawrence Kirk Tolman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Exponential functions categories.

Hyperbolic Functions

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Author : James McMahon
language : en
Publisher:
Release Date : 1896

Hyperbolic Functions written by James McMahon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1896 with Exponential functions categories.

Hyperbolic Functions

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Author : V. G. Shervatov
language : en
Publisher: Courier Corporation
Release Date : 2013-11-07

Hyperbolic Functions written by V. G. Shervatov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-07 with Mathematics categories.

This single-volume compilation consists of Hyperbolic Functions, introducing the hyperbolic sine, cosine, and tangent; Configuration Theorems, concerning collinear points and concurrent lines; and Equivalent and Equidecomposable Figures, regarding polyhedrons. 1963 edition.

The Remarkable Sine Functions

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Author : A. I. Markushevich
language : en
Publisher: Elsevier
Release Date : 2014-05-12

The Remarkable Sine Functions written by A. I. Markushevich and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.

The Remarkable Sine Functions focuses on the trigonometric functions of sine and cosine. The publication first offers information on the geometric definition of circular, hyperbolic, and lemniscate functions, generalized sines, and integration in the complex plane. Discussions focus on the properties and characteristics of circular, lemniscate, and hyperbolic functions, uniform approach to generalized sines, and the process of integration in complex variables. The text then elaborates on the use of Euler's method in deriving the addition theorems and study of complex values, including the employment of the relationship between the sine and cosine in rewriting addition theorems and formulas that can be used in the determination of real values. The manuscript ponders on zeros and poles, simple and double periodicity, and the concept of an elliptic function. Concerns include circular and hyperbolic functions, Jacobian functions, and the functions of sine and cosine. The book is a valuable reference for mathematicians and researchers interested in the functions of sine and cosine.

Squigonometry The Study Of Imperfect Circles

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Author : Robert D. Poodiack
language : en
Publisher: Springer Nature
Release Date : 2022-12-15

Squigonometry The Study Of Imperfect Circles written by Robert D. Poodiack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-15 with Mathematics categories.

This textbook introduces generalized trigonometric functions through the exploration of imperfect circles: curves defined by |x|p + |y|p = 1 where p ≥ 1. Grounded in visualization and computations, this accessible, modern perspective encompasses new and old results, casting a fresh light on duality, special functions, geometric curves, and differential equations. Projects and opportunities for research abound, as we explore how similar (or different) the trigonometric and squigonometric worlds might be. Comprised of many short chapters, the book begins with core definitions and techniques. Successive chapters cover inverse squigonometric functions, the many possible re-interpretations of π, two deeper dives into parameterizing the squigonometric functions, and integration. Applications include a celebration of Piet Hein’s work in design. From here, more technical pathways offer further exploration. Topics include infinite series; hyperbolic, exponential, and logarithmic functions; metrics and norms; and lemniscatic and elliptic functions. Illuminating illustrations accompany the text throughout, along with historical anecdotes, engaging exercises, and wry humor. Squigonometry: The Study of Imperfect Circles invites readers to extend familiar notions from trigonometry into a new setting. Ideal for an undergraduate reading course in mathematics or a senior capstone, this book offers scaffolding for active discovery. Knowledge of the trigonometric functions, single-variable calculus, and initial-value problems is assumed, while familiarity with multivariable calculus and linear algebra will allow additional insights into certain later material.

The Fractional Trigonometry

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Author : Carl F. Lorenzo
language : en
Publisher: John Wiley & Sons
Release Date : 2016-11-07

The Fractional Trigonometry written by Carl F. Lorenzo and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-07 with Mathematics categories.

Addresses the rapidly growing field of fractional calculus and provides simplified solutions for linear commensurate-order fractional differential equations The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science is the result of the authors’ work in fractional calculus, and more particularly, in functions for the solutions of fractional differential equations, which is fostered in the behavior of generalized exponential functions. The authors discuss how fractional trigonometry plays a role analogous to the classical trigonometry for the fractional calculus by providing solutions to linear fractional differential equations. The book begins with an introductory chapter that offers insight into the fundamentals of fractional calculus, and topical coverage is then organized in two main parts. Part One develops the definitions and theories of fractional exponentials and fractional trigonometry. Part Two provides insight into various areas of potential application within the sciences. The fractional exponential function via the fundamental fractional differential equation, the generalized exponential function, and R-function relationships are discussed in addition to the fractional hyperboletry, the R1-fractional trigonometry, the R2-fractional trigonometry, and the R3-trigonometric functions. The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science also: Presents fractional trigonometry as a tool for scientists and engineers and discusses how to apply fractional-order methods to the current toolbox of mathematical modelers Employs a mathematically clear presentation in an e ort to make the topic broadly accessible Includes solutions to linear fractional differential equations and generously features graphical forms of functions to help readers visualize the presented concepts Provides effective and efficient methods to describe complex structures The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science is an ideal reference for academic researchers, research engineers, research scientists, mathematicians, physicists, biologists, and chemists who need to apply new fractional calculus methods to a variety of disciplines. The book is also appropriate as a textbook for graduate- and PhD-level courses in fractional calculus. Carl F. Lorenzo is Distinguished Research Associate at the NASA Glenn Research Center in Cleveland, Ohio. His past positions include chief engineer of the Instrumentation and Controls Division and chief of the Advanced Controls Technology and Systems Dynamics branches at NASA. He is internationally recognized for his work in the development and application of the fractional calculus and fractional trigonometry. Tom T. Hartley, PhD, is Emeritus Professor in the Department of Electrical and Computer Engineering at The University of Akron. Dr Hartley is a recognized expert in fractional-order systems, and together with Carl Lorenzo, has solved fundamental problems in the area including Riemann’s complementary-function initialization function problem. He received his PhD in Electrical Engineering from Vanderbilt University.

Hyperbolic Functions

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Author : James McMahon
language : en
Publisher:
Release Date : 2013-06-07

Hyperbolic Functions written by James McMahon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-07 with categories.

This compendium of hyperbolic trigonometry was first published as a chapter in Merriman and Woodward's Higher Mathematics. There is reason to believe that it supplies a need, being adapted to two or three different types of readers. College students who have had elementary courses in trigonometry, analytic geometry, and differential and integral calculus, and who wish to know something of the hyperbolic trigonometry on account of its important and historic relations to each of those branches, will, it is hoped, find these relations presented in a simple and comprehensive way in the first half of the work. Readers who have some interest in imaginaries are then introduced to the more general trigonometry of the complex plane, where the circular and hyperbolic functions merge into one class of transcendent, the singly periodic functions, having either a real or a pure imaginary period. For those who also wish to view the subject in some of its practical relations, numerous applications have been selected so as to illustrate the various parts of the theory, and to show its use to the physicist and engineer, appropriate numerical tables being supplied for these purposes.With all these things in mind, much thought has been given to the mode of approaching the subject, and to the presentation of fundamental notions, and it is hoped that some improvements are discernible. For instance, it has been customary to define the hyperbolic functions in relation to a sector of the rectangular hyperbola, and to take the initial radius of the sector coincident with the principal radius of the curve; in the present work, these and similar restrictions are discarded in the interest of analogy and generality, with a gain in symmetry and simplicity, and the functions are defined as certain characteristic ratios belonging to any sector of any hyperbola. Such definitions, in connection with the fruitful notion of correspondence of points on conics, lead to simple and general proofs of the addition-theorems, from which easily follow the conversion-formulas, the derivatives, the Maclaurin expansions, and the exponential expressions. The proofs are so arranged as to apply equally to the circular functions, regarded as the characteristic ratios belonging to any elliptic sector. For those, however, who may wish to start with the exponential expressions as the definitions of the hyperbolic functions, the appropriate order of procedure is indicated on page 27, and a direct mode of bringing such exponential definitions into geometrical relation with the hyperbolic sector is shown in the AppendixCONTENTS:1 Correspondence of Points on Conics2 Areas of Corresponding Triangles3 Areas of Corresponding Sectors4 Charactersitic Ratios of Sectorial Measures5 Ratios Expressed as Triangle-measures6 Functional Relations for Ellipse7 Functional Relations for Hyperbola8 Relations Among Hyperbolic Functions9 Variations of the Hyperbolic Functions10 Anti-hyperbolic Functions11 Functions of Sums and Difference12 Conversion Formulas13 Limiting Ratios14 Derivatives of Hyperbolic Functions15 Derivatives of Anti-hyperbolic Functions16 Expansion of Hyperbolic Functions17 Exponential Expressions18 Expansion of Anti-functions19 Logarithmic Expression of Anti-Functions20 The Gudermanian Function21 Circular Functions of Gudermanian22 Gudermanian Angle23 Derivatives of Gudermanian and Inverse24 Series for Gudermanian and its Inverse25 Graphs of Hyperbolic Functions26 Elementary Integrals27 Functions of Complex Numbers28 Addition-Theorems for Complexes29 Functions of Pure Imaginaries30 Functions of x + iy in the Form X + iY31 The Catenary32 Catenary of Uniform Strength.33 The Elastic Catenary34 The Tractory35 The Loxodrome36 Combined Flexure and Tension37 Alternating Currents38 Miscellaneous Applications39 Explanation of Tables40 Appendix40.1 Historical and Bibliographical40.2 Exponential Expressions as Definitions

Generalized Trigonometric And Hyperbolic Functions

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