عنوان

Generalized trigonometric and hyperbolic functions /

(Number (ISBN

0429446233

(Number (ISBN

0429821077

(Number (ISBN

0429821085

(Number (ISBN

0429821093

(Number (ISBN

9780429446238

(Number (ISBN

9780429821073

(Number (ISBN

9780429821080

(Number (ISBN

9780429821097

Erroneous ISBN

1138333018

Erroneous ISBN

9781138333017

Title Proper

Generalized trigonometric and hyperbolic functions /

General Material Designation

[Book]

First Statement of Responsibility

Ronald E. Mickens.

Place of Publication, Distribution, etc.

Boca Raton, Florida :

Name of Publisher, Distributor, etc.

CRC Press,

Date of Publication, Distribution, etc.

[2019]

Date of Publication, Distribution, etc.

©2019

Specific Material Designation and Extent of Item

1 online resource

Text of Note

Includes bibliographical references.

Text of Note

Cover; Half Title; Title Page; Copyright Page; Table of Contents; Dedication; List of Figures; Preface; Author; 1: TRIGONOMETRIC AND HYPERBOLIC SINE AND COSINE FUNCTIONS; 1.1 INTRODUCTION; 1.2 SINE AND COSINE: GEOMETRIC DEFINITIONS; 1.3 SINE AND COSINE: ANALYTIC DEFINITION; 1.3.1 Derivatives; 1.3.2 Integrals; 1.3.3 Taylor Series; 1.3.4 Addition and Subtraction Rules; 1.3.5 Product Rules; 1.4 SINE AND COSINE: DYNAMIC SYSTEM APPROACH; 1.4.1 x-y Phase-Space; 1.4.2 Symmetry Properties of Trajectories in Phase-Space; 1.4.3 Null-Clines; 1.4.4 Geometric Proof that All Trajectories Are Closed

Text of Note

1.5 HYPERBOLIC SINE AND COSINE: DERIVED FROM SINE AND COSINE1.6 HYPERBOLIC FUNCTIONS: DYNAMIC SYSTEM DERIVATION; 1.7 [Theta]-PERIODIC HYPERBOLIC FUNCTIONS; 1.8 DISCUSSION; Notes and References; 2: ELLIPTIC FUNCTIONS; 2.1 INTRODUCTION; 2.2 [Theta]-PERIODIC ELLIPTIC FUNCTIONS; 2.3 ELLIPTIC HAMILTONIAN DYNAMICS; 2.4 JACOBI, CN, SN, AND DN FUNCTIONS; 2.4.1 Elementary Properties of Jacobi Elliptic Functions; 2.4.2 First Derivatives; 2.4.3 Differential Equations; 2.4.4 Calculation of u(theta) and the Period for cn, sn, dn; 2.4.5 Special Values of Jacobi Elliptic Functions

Text of Note

2.5 ADDITIONAL PROPERTIES OF JACOBI ELLIPTIC FUNCTIONS2.5.1 Fundamental Relations for Square of Functions; 2.5.2 Addition Theorems; 2.5.3 Product Relations; 2.5.4 cn, sn, dn for Special k Values; 2.5.5 Fourier Series; 2.6 DYNAMICAL SYSTEM INTERPRETATION OF ELLIPTIC JACOBI FUNCTIONS; 2.6.1 Definition of the Dynamic System; 2.6.2 Limits k → 0+ and k → 1-; 2.6.3 First Integrals; 2.6.4 Bounds and Symmetries; 2.6.5 Second-Order Differential Equations; 2.6.6 Discussion; 2.7 HYPERBOLIC ELLIPTIC FUNCTIONS AS A DYNAMIC SYSTEM; 2.8 HYPERBOLIC Theta-PERIODIC ELLIPTIC FUNCTIONS; 2.9 DISCUSSION

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8

8

Text of Note

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

Exponential functions.

Hyperbola.

Trigonometry.

Exponential functions.

Hyperbola.

MATHEMATICS-- Arithmetic.

MATHEMATICS-- Functional Analysis.

MATHEMATICS-- Geometry-- General.

MATHEMATICS-- Number Theory.

Trigonometry.

MAT-- 004000

MAT-- 012000

MAT-- 022000

MAT-- 037000

PBKF

Number

Edition

Class number

Book number

Mickens, Ronald E.,1943-

Date of Transaction

20200822162102.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y