纯数学教程 纪念版
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￥ 75.72 7.6折 ￥ 99 全新
库存8件
作者[英] G. H. Hardy
出版社世界图书出版公司
ISBN9787519253622
出版时间2019-11
装帧平装
开本16开
定价99元
货号28491421
上书时间2024-10-26
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导语摘要
《纯数学教程(纪念版)》是“剑桥数学图书馆”系列丛书之一。这部部世纪经典著作，以简洁易懂的数学语言，全面系统地介绍了基础数学的各个方面，并对许多经典的数学论证给出了严谨的证明。本书共分10章，在介绍了实数、复数的概念后，从第4章和第5章引入了极限的概念，较之一般书的处理方法更为轻松自然、易于接受。另外，书中每章后面配有大量有代表性的杂例，供读者参考练习以巩固所学知识。本书适合高校数学系及对相关专业学生和教师学习和参考。
目次：实变量；实变函数；复数；正整变量函数的极限；一个连续变量的函数之极限，连续函数和不连续函数；导数和积分；微分学和积分学中另外一些定理；无穷级数和无穷积分的收敛性；单实变对数函数、指数函数和三角函数；对数函数、指数函数以及三角函数的一般理论。附录：Hlder不等式和Minkowski不等式；每个方程都有一个根的证明；关于二重极限问题的一个注记；分析与几何中的无穷。
作者简介G.H.Hardy，英国数学界和英国分析学派的领袖，享誉世界的数学大师，在数论和分析学方面有着巨大的贡献和深远影响。培养和指导了众多数学大家，其中包括印度数学奇才拉马努金和我国数学家华罗庚等。他还著有《数论导引》、《不等式》（世图已影印出版）和《一个数学家的自白》等。
目录
CHAPTER I REAL VARIABLES
1-2.Rational numbers
3-7.Irrational numbers
8.Real numbers
9.Relations of magnitude between real numbers
10-11.Algebraical operations with real numbers
12.The number√2
13-14.Quadratic surds
15.The continuum
16.The continuous real variable
17.Sections of the real numbers. Dedekinds theorem
18.Points of accumulation
19.Weierstrasss theorem
Miscellaneous examples
CHAPTER II FUNCTIONS OF REAL VARIABLES
20.The idea of a function
21.The graphical representation of functions. Coordinates
22.Polar coordinates
23.Polynomia s
24-25.Rational functions
26-27.Algebraical functions
28-29.Transcendental functions
30.Graphical solution of equations
31.Functions of two variables and their graphical representation
32.Curves in a plane
33.Loci in space
Miscellaneous examples
CHAPTER Ⅲ COMPLEX NUMBER
34-38.Displacements
39-42.Complex numbers
43.The quadratic equation with real coefficients
44.Argands diagram
45.De Moivres theorem
46.Rational functions of a complex variable
47-49.Roots of complex numbers
Miscellaneous examples
CHAPTER IV LIMITS OF FUNCTIONS OF A POSITIVE INTEGRAL VARIABLE
50.Functions of a positive integral variable
51.Interpolation
52.Finite and infinite classes
53-57.Properties possessed by a function of n for large values of n
58-61.Definition of a limit and other definitions
62.Oscillating functions
63-68.General theorems concerning limits
69-70.Steadily increasing or decreasing functions
71.Alternative proof of Weierstrasss theorem
72.The limit of xn
73.The limit of (1+1) n
74.Some algebraical lemmas
……
76-77.Infinite series
78.The infinite geometrical series
79.The representation of functions of a continuous real variable by means of limits
80.The bounds of a bounded aggregate
81.The bounds of a bounded function
82.The limits of indetermination of a bounded function
83-84.The general principle of convergence
85-86.Limits of complex functions and series of complex terms
87-88.Applications to zn and the geometrical series
89.The symbols 0, o, ～
Miscellaneous examples
CHAPTER V LIMITSOFFUNCTIONSOFACONTINUOUSVARIABLE.CONTINUOUS AND DISCONTINUOUS FUNCTIONS
90-92.Limits as x→ ∞ or x → ∞
93-97.Limits as x → a
98.The symbols O, o, ～: orders of smallness and greatness
99-100.Continuous functions of a real variable
101-105.Properties of continuous functions. Bounded functions The oscillation of a function in an interval
106-107.Sets of intervals on a line. The Heine-Borel theorem
108.Continuous functions of several variables
109-110.Implicit and inverse functions
Miscellaneous examples
CHAPTER VI DERIVATIVES AND INTEGRALS
111-113.Derivatives
114.General rules for diferentiation
115.Derivatives of complex functions
116.The notation of the differential calculus
117.Differentiation of polynomials
118.Differentiation of rational functions
119.Differentiation of algebraical functions
120.Differentiation of transcendental functions
121.Repeated differentiation
122.General theorems concerning derivatives Rolles theorem
123-125.Maxima and minima
126-127.The mean value theorem
128.Cauchys mean value theorem
129.A theorem of Darboux
130-131.Integration. The logarithmic function
132.Integration of polynomials
133-134.Integration of rational functions
135-142.Integration of algebraical functions. Integration by rationalisation. Integration by parts
143-147. Integration of transcendental functions
148.Areas of plane curves
149.Lengths of plane curves
Miscellaneous examples
CHAPTER VII ADDTTTONAL THEOREMS IN THE DIFFERENTIAL AND INTEGRAL CALCULUS
150-151.Taylors theorem
152.Taylors series
153.Applications of Taylors theorem to maxima and minima
154.The calculation of certain limits
155.The contact of plane curves
156-158. Differentiation of functions of several variables
159.The mean value theorem for functions of two variables
160.Differentials
161-162.Definite integrals
163.The circular functions
164.Calculation of the definite integral as the limit of a sum
165.General properties of the definite integral
166.Integration by parts and by substitution
167.Alternative proof of Taylors theorem
168.Application to the binomial series
169.Approximate formulae for definite integrals. Simpsons rule
170.Integrals of complex functions
Miscellaneous examples
CHAPTER VIII THE CONVERGENCE OF INFINITE SERIES AND INFINITE INTEGRALS
171-174.Series of positive terms.Cauchys and dAlemberts tests of convergence
175.Ratio tests
176.Dirichlets theorem
177.Multiplication of series of positive terms
178-180.Further tests for convergence. Abels theorem. Maclaurlns integral test
181.The series ∑n-3
182.Cauchys condensation test
183.Further ratio tests
184-189.Infinite integrals
190.Series of positive and negative terms
191-192.Absolutely convergent series
193-194.Conditionally convergent series
195.Alternating series
196.Abels and Dirichlets tests of convergence
197.Series of complex terms
198-201.Power series
202.Multiplication of series
203.Absolutely and conditionally convergent infinite integrals
Miscellaneous examples
CHAPTER IX THE LOGARITHMIC, EXPONENTIAL, AND CIRCULAR FUNCTIONS OF A REAL VARIABLE
204-205.The logarithmic function
206.The functional equation satisfied by log x
207-209.The behaviour of log x as x tends to infinity or to zero
210.The logarithmic scale of infinity
211.The number e
212-213.The exponential function
214.The general power ax
215.The exponential limit
216.The logarithmic limit
217.Common logarithms
218.Logarithmic tests of convergence
219.The exponential series
220.The logarithmic series
221.The series for arc tan x
222.The binomial series
223.Alternative development of the theory
224-226.The analytical theory of the circular functions
Miscellaneous examples
CHAPTER X THE GENERAL THEORY OF THE LOGARITHMIC, EXPONENTIAL, AND CIRCULAR FUNCTIONS
227-228.Functions of a complex variable
229.Curvilincar integrals
230.Definition of the logarithmic function
231.The values of the logarithmic function
232-234.The exponential function
235-236.The general power aζ
237-240.The trigonometrical and hyperbolic functions
241.The connection between the logarithmic and inverse trigonometrical functions
242.The exponential series
243.The series for cos z and sin z
244-245.The logarithmic series
246.The exponential limit
247.The binomial series
Miscellaneous examples
APPENDIX I The proof that every equation has a root
APPENDIX II A note on double limit problems
APPENDIX III The infinite in analysis and geometry
APPENDIX IV The infinite in analysis and geometry
INDEX
内容摘要《纯数学教程(纪念版)》是“剑桥数学图书馆”系列丛书之一。这部部世纪经典著作，以简洁易懂的数学语言，全面系统地介绍了基础数学的各个方面，并对许多经典的数学论证给出了严谨的证明。本书共分10章，在介绍了实数、复数的概念后，从第4章和第5章引入了极限的概念，较之一般书的处理方法更为轻松自然、易于接受。另外，书中每章后面配有大量有代表性的杂例，供读者参考练习以巩固所学知识。本书适合高校数学系及对相关专业学生和教师学习和参考。
目次：实变量；实变函数；复数；正整变量函数的极限；一个连续变量的函数之极限，连续函数和不连续函数；导数和积分；微分学和积分学中另外一些定理；无穷级数和无穷积分的收敛性；单实变对数函数、指数函数和三角函数；对数函数、指数函数以及三角函数的一般理论。附录：Hlder不等式和Minkowski不等式；每个方程都有一个根的证明；关于二重极限问题的一个注记；分析与几何中的无穷。
主编推荐G.H.Hardy，英国数学界和英国分析学派的领袖，享誉世界的数学大师，在数论和分析学方面有着巨大的贡献和深远影响。培养和指导了众多数学大家，其中包括印度数学奇才拉马努金和我国数学家华罗庚等。他还著有《数论导引》、《不等式》（世图已影印出版）和《一个数学家的自白》等。
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