عنوان

Generalized trigonometric and hyperbolic functions /

شابک

0429446233

شابک

0429821077

شابک

0429821085

شابک

0429821093

شابک

9780429446238

شابک

9780429821073

شابک

9780429821080

شابک

9780429821097

شابک اشتباه

1138333018

شابک اشتباه

9781138333017

عنوان اصلي

Generalized trigonometric and hyperbolic functions /

نام عام مواد

[Book]

نام نخستين پديدآور

Ronald E. Mickens.

محل نشرو پخش و غیره

Boca Raton, Florida :

نام ناشر، پخش کننده و غيره

CRC Press,

تاریخ نشرو بخش و غیره

[2019]

تاریخ نشرو بخش و غیره

©2019

نام خاص و کميت اثر

1 online resource

متن يادداشت

Includes bibliographical references.

متن يادداشت

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

متن يادداشت

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

متن يادداشت

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

بدون عنوان

0

بدون عنوان

8

بدون عنوان

8

متن يادداشت

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

موضوع مستند نشده

Exponential functions.

موضوع مستند نشده

Hyperbola.

موضوع مستند نشده

Trigonometry.

موضوع مستند نشده

Exponential functions.

موضوع مستند نشده

Hyperbola.

موضوع مستند نشده

MATHEMATICS-- Arithmetic.

موضوع مستند نشده

MATHEMATICS-- Functional Analysis.

موضوع مستند نشده

MATHEMATICS-- Geometry-- General.

موضوع مستند نشده

MATHEMATICS-- Number Theory.

موضوع مستند نشده

Trigonometry.

موضوع مستند نشده

MAT-- 004000

موضوع مستند نشده

MAT-- 012000

موضوع مستند نشده

MAT-- 022000

موضوع مستند نشده

MAT-- 037000

موضوع مستند نشده

PBKF

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Mickens, Ronald E.,1943-

تاريخ عمليات

20200822162102.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y