純數學教程（英文版第10版）（英）G.H.Hardy|17149 下載 mobi epub pdf 電子書 2024

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圖書介紹

店鋪：互動齣版網圖書專營店

齣版社：機械工業齣版社

ISBN：711113785X

商品編碼：11781056717

叢書名：經典原版書庫

齣版時間：2004-02-01

頁數：509

圖書描述

書名：	純數學教程（英文版·第10版）\|17149
圖書定價：	65元
圖書作者：	（英）G.H.Hardy
齣版社：	機械工業齣版社
齣版日期：	2004/2/1 0:00:00
ISBN號：	711113785X
開本：	16開
頁數：	509
版次：	10-1

作者簡介

6. H．Hardy英國數學傢(1877—1947)。1896年考入劍橋三一學院，並子1900年在劍橋獲得史密斯奬。之後，在英國牛津大學。劍橋大學任教，是20世紀初著名的數學分析傢之一。他的貢獻包括數論中的丟番圖逼近、堆壘數論、素數分布理論與黎曼函數，調和分析中的三角級數理論。發散級數求和與陶伯定理。不等式、積分變換與積分方程等方麵，對分析學的發展有深刻的影響。以他的名字命名的Hp空間(哈代空間)，至今仍是數學研究中十分活躍的領域。除本書外，他還著有《不等式》、《發散級數》等10多部書籍與300多篇文章。

內容簡介

自從1908年齣版以來，這本書已經成為一部經典之著。一代又一代嶄露頭角的數學傢正是通過這本書的指引，步入瞭數學的殿堂。在本書中，作者懷著對教育工作的無限熱忱，以一種嚴格的純粹學者的態度，揭示瞭微積分的基本思想、無窮級數的性質以及包括極限概念在內的其他題材。

CONTENTS
(Entries in small print at the end of the contents of each chapter
refer to subjects discussed incidentally in the examples)
CHAPTER I
REAL VARIABLES
SECT.
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 continum
16. The continuous real variable
17. Sections of the real numbers. Dedekind's theorem
18. Points of accumulation
19. Weierstrass's 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. Polynomias
24-25. Rational functions
26-27. Aigebraical functious
28-29. Transcendental functions
30. Graphical solution of equations
31. Functions of two variables and their graphical repre-
sentation
32. Curves in a plane
33. Loci in space
Miscellaneous examples
CHAPTER III
COMPLEX NUMBERS
SECT.
34-38. Displacements
39-42. Complex numbers
43. The quadratic equation with real coefficients
44. Argand's diagram
45. De Moivre's 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 Weierstrass's theorem
72. The limit of xn
73. The limit of(1+
74. Some algebraical lemmas
75. The limit of n(nX-1)
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 O, o,
Miscellaneous examples
CHAPTER V
LIMITS OF FUNCTIONS OF A CONTINUOUS VARIABLE. CONTINUOUS
AND DISCONTINUOUS FUNCTIONS
90-92. Limits as x-- or x---
93-97. Limits as z-, 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 differentiation
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, Rolle's
theorem
123-125. Maxima and minima
126-127. The mean value theorem
128. Cauchy's mean value theorem
SECT.
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
ADDITIONAL THEOREMS IN THE DIFFERENTIAL AND INTEGRAL CALCULUS
150-151. Taylor's theorem
152. Taylor's series
153. Applications of Taylor's 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 Taylor's theorem
168. Application to the binomial series
169. Approximate formulae for definite integrals. Simpson's
rule
170. Integrals of complex functions
Miscellaneous examples
CHAPTER VIII
THE CONVERGENCE OF INFINITE SERIES AND INFINITE INTEGRALS
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