扫一扫
关注中图网
官方微博
本类五星书更多>
-
>
宇宙、量子和人类心灵
-
>
(精)BBC地球故事系列-星际旅行
-
>
从一到无穷大
-
>
图说相对论(32开平装)
-
>
一本有趣又有料的化学书
-
>
刘薰宇的数学三书:原来数学可以这样学全3册
-
>
光学零件制造工艺学
广义三角函数与双曲函数:英文 版权信息
- ISBN:9787576709391
- 条形码:9787576709391 ; 978-7-5767-0939-1
- 装帧:平装-胶订
- 册数:暂无
- 重量:暂无
- 所属分类:>>
广义三角函数与双曲函数:英文 内容简介
本书的主要目的是引入并研究被称为广义三角函数和双曲函数的各种主题。该方法和相关分析基本上是作者自己的研究成果,并且在许多情况下,这些内容与该主题之前的数学研究没有联系。一般来说,作者获得的结果是通过使用“严格的启发式”数学分析风格得出并讨论的。然而,尽管有些人可能认为这种研究方法是有限制的,但此过程允许我们遵循非常有趣的结果。学习并理解本书内容需要读者已经掌握了基本平面几何、三角学和一年的微积分课程的相关知识。
广义三角函数与双曲函数:英文 目录
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
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
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
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
展开全部
书友推荐
- >
烟与镜
烟与镜
¥28.4¥48.0 - >
朝闻道
朝闻道
¥11.7¥23.8 - >
名家带你读鲁迅:朝花夕拾
名家带你读鲁迅:朝花夕拾
¥10.5¥21.0 - >
月亮虎
月亮虎
¥19.7¥48.0 - >
苦雨斋序跋文-周作人自编集
苦雨斋序跋文-周作人自编集
¥6.9¥16.0 - >
自卑与超越
自卑与超越
¥13.5¥39.8 - >
【精装绘本】画给孩子的中国神话
【精装绘本】画给孩子的中国神话
¥17.6¥55.0 - >
经典常谈
经典常谈
¥25.9¥39.8
本类畅销
-
时间简史-普及版
¥16.3¥38 -
严士健谈数学教育
¥8.5¥25 -
分割与积累
¥10.8¥25 -
统计学七支柱
¥27.3¥39 -
2022图书×抽奖盲袋
¥9.9¥25 -
2023读书月阅读盲盒——天黑,闭眼,刀谁?
¥42.3¥158