廣義三角函數與雙曲函數 9787576709391 (美)羅納德.E.米肯斯(Ronald E. Mickens
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物品所在地：中國大陸
原出版社：哈爾濱工業大學
物品所在地：中國大陸
原出版社：哈爾濱工業大學
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| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202401*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：廣義三角函數與雙曲函數 ISBN：9787576709391 出版社：哈爾濱工業大學 著編譯者：(美)羅納德.E.米肯斯(Ronald E. Mickens 叢書名：國外優秀數學著作原版系列 頁數：14201 所在地：中國大陸 *此為代購商品 書號：1628440 可大量預訂，請先連絡。 【台灣高等教育出版社簡體書】 廣義三角函數與雙曲函數 787576709391 (美)羅納德.E.米肯斯(Ronald E. Mickens 內容簡介 本書的主要目的是引入並研究被稱為廣義三角函數和雙曲函數的各種主題。該方法和相關分析基本上是作者自己的研究成果，並且在許多情況下，這些內容與該主題之前的數學研究沒有聯繫。一般來說，作者獲得的結果是通過使用「嚴格的啟髮式」數學分析風格得出並討論的。然而，儘管有些人可能認為這種研究方法是有限制的，但此過程允許我們遵循非常有趣的結果。學習並理解本書內容需要讀者已經掌握了基本平面幾何、三角學和一年的微積分課程的相關知識。目錄 DedicationList 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 1 5 HYPERBOLIC SINE AND COSINE: DERIVED FROM SINE AND COSINE 1 6 HYPERBOLIC FUNCTIONS: DYNAMIC SYSTEM DERIVATION 1 7 0-PERIODIC HYPERBOLIC FUNCTIONS 1 8 DISCUSSION Notes and References 2 ELLIPTIC FUNCTIONS 2 1 INTRODUCTION 2 2 0-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(0) and the Period for cn， sn， dn 2 4 5 Special Values of Jacobi Elliptic Functions 2 5 ADDITIONAL PROPERTIES OF JACOBI ELLIPTIC FUNCTIONS 2 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 Limitsk→0+ andk→l- 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 0-PERIODIC ELLIPTIC FUNCTIONS 2 9 DISCUSSION Notes and References 3 SQUARE FUNCTIONS 3 1 INTRODUCTION 3 2 PROPERTIES OF THE SQUARE TRIGONOMETRIC FUNCTIONS 3 3 PERIOD OF THE SQUARE TRIGONOMETRIC FUNCTIONS IN THE VARIABLE 3 4 FOURIER SERIES OF THE SQUARE TRIGONOMETRIC FUNCTIONS 3 5 DYNAMIC SYSTEM INTERPRETATION OF｜x｜+｜y｜ = 1 3 6 HYPERBOLIC SQUARE FUNCTIONS: DYNAMICS SYSTEM APPROACH 3 7 PERIODIC HYPERBOLIC SQUARE FUNCTIONS Notes and References 4 PARABOLIC TRIGONOMETRIC FUNCTIONS 4 1 INTRODUCTION 4 2 H(x， y) =｜y｜+ (1/2) x2 AS A DYNAMIC SYSTEM 4 3 GEOMETRIC ANALYSIS OF｜y｜+(1/2)x2 = 1/2=1 AS A DYNAMIC SYSTEM 4 4 lyl-(1/2)x2=1/2 4 5 GEOMETRIC ANALYSIS OF｜y｜+(1/2)x2 =1/2 Notes and References 5 GENERALIZED PERIODIC SOLUTIONS OF f(t)2 + g(t)2 = 1 5 1 INTRODUCTION 5 2 GENERALIZED COSINE AND SINE FUNCTIONS 5 3 MATHEMATICAL STRUCTURE OF O(t) 5 4 AN EXAMPLE: A(t)=alsin(2π/T)t 5 5 DIFFERENTIAL EQUATION FOR f(t) AND g(t) 5 6 DISCUSSION 5 7 NON-PERIODIC SOLUTION; OF f2(t)+g2(t)=1 Notes and References 6 RESUME OF (SOME) PREVIOUS RESULTS ON GENERALIZED TRIGONOMETRIC FUNCTIONS 6 1 INTRODUCTION 6 2 DIFFERENTIAL EQUATION FORMULATION 6 3 DEFINITION AS INTEGRAL FORMS 6 4 GEOMETRIC APPROACH 6 5 SYMMETRY CONSIDERATIONS AND CONSEQUENCES 6 5 1 Symmetry Transformation and Consequences 6 5 2 Hamiltonian Formulation 6 5 3 Area of Enclosed Curve 6 5 4 Period 6 6 SUMMARY Notes and References 7 GENERALIZED TRIGONOMETRIC FUNCTIONS:｜y｜p+｜x｜q=1 7 1 INTRODUCTION 7 2 METHODOLOGY 7 3 SUMMARY 7 4 GALLERY OF PARTICULAR SOLUTIONS 8 GENERALIZED TRIGONOMETRIC HYPERBOLIC FUNCTIONS:｜y｜p+｜x｜q=1 8 1 INTRODUCTION 8 2 SOLUTIONS 8 3 GALLERY OF SPECIAL SOLUTIONS 9 APPLICATIONS AND ADVANCED TOPICS 9 1 INTRODUCTION 9 2 ODD-PARITY SYSTEMS AND THEIR FOURIER REPRESENTATIONS 9 3 TRULY NONLINEAR OSCILLATORS 9 3 1 Antisymmetric， Constant Force Oscillator 9 3 2 Particle in a Box 9 3 3 Restricted Duffing Equation 9 4 ATEB PERIODIC FUNCTIONS 9 5 EXACT DISCRETIZATION OF THE JACOBI ELLIPTI 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
