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分析 1 影印版 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （法）戈德门特（GodementR.）著 著
- 出版社： 北京：高等教育出版社
- ISBN：9787040279559
- 出版时间：2009
- 标注页数：430页
- 文件大小：193MB
- 文件页数：452页
- 主题词：分析（数学）－英文
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图书目录
Ⅰ-Sets and Functions1
1．Set Theory7
1-Membership,equality,empty set7
2-The set defined by a relation.Intersections and unions10
3-Whole numbers.Infinite sets13
4-Ordered pairs,Cartesian products,sets of subsets17
5-Functions,maps,correspondences19
6-Injections,surjections,bijections23
7-Equipotent sets.Countable sets25
8-The different types of infinity28
9-Ordinals and cardinals31
2．The logic of logicians39
Ⅱ-Convergence:Discrete variables45
1．Convergent sequences and series45
0-Introduction: what is a real number?45
1-Algebraic operations and the order relation:axioms of R53
2-Inequalities and intervals56
3-Local or asymptotic properties59
4-The concept of limit.Continuity and differentiability63
5-Convergent sequences:definition and examples67
6-The language of series76
7-The marvels of the harmonic series81
8-Algebraic operations on limits95
2．Absolutely convergent series98
9-Increasing sequences. Upper bound of a set of real numbers98
10-The function logx. Roots of a positive number103
11-What is an integral?110
12-Series with positive terms114
13-Alternating series119
14-Classical absolutely convergent series123
15-Unconditional convergence:general case127
16-Comparison relations.Criteria of Cauchy and d'Alembert132
17-Infinite limits138
18-Unconditional convergence:associativity139
3．First concepts of analytic functions148
19-The Taylor series148
20-The principle of analytic continuation158
21-The function cot x and the series Σ1/n2k162
22-Multiplication of series.Composition of analytic func-tions.Formal series167
23-The elliptic functions of Weierstrass178
Ⅲ-Convergence:Continuous variables187
1．The intermediate value theorem187
1-Limit values of a function.Open and closed sets187
2-Continuous functions192
3-Right and left limits of a monotone function197
4-The intermediate value theorem200
2．Uniform convergence205
5-Limits of continuous functions205
6-A slip up of Cauchy's211
7-The uniform metric216
8-Series of continuous functions.Normal convergence220
3．Bolzano-Weierstrass and Cauchy's criterion225
9-Nested intervals,Bolzano-Weierstrass,compact sets225
10-Cauchy's general convergence criterion228
11-Cauchy's criterion for series:examples234
12-Limits of limits239
13-Passing to the limit in a series of functions241
4．Differentiable functions244
14-Derivatives of a function244
15-Rules for calculating derivatives252
16-The mean value theorem260
17-Sequences and series of differentiable functions265
18-Extensions to unconditional convergence270
5．Differentiable functions of several variables273
19-Partial derivatives and differentials273
20-Differentiability of functions of class C1276
21-Diferentiation of composite functions279
22-Limits of differentiable functions284
23-Interchanging the order of differentiation287
24-Implicit functions290
Appendix to Chapter Ⅲ303
1-Cartesian spaces and general metric spaces303
2-Open and closed sets306
3-Limits and Cauchy's criterion in a metric space;complete spaces308
4-Continuous functions311
5-Absolutely convergent series in a Banach space313
6-Continuous linear maps316
7-Compact spaces320
8-Topological spaces322
Ⅳ-Powers,Exponentials,Logarithms,Trigonometric Functions325
1．Direct construction325
1-Rational exponents325
2-Definition of real powers327
3-The calculus of real exponents330
4-Logarithms to base a.Power functions332
5-Asymptotic behaviour333
6-Characterisations of the exponential,power and logarithmic functions336
7-Derivatives of the exponential functions:direct method339
8-Derivatives of exponential functions,powers and logarithms342
2．Series expansions345
9-The number e.Napierian logarithms345
10-Exponential and logarithmic series:direct method346
11-Newton's binomial series351
12-The power series for the logarithm359
13-The exponential function as a limit368
14-Imaginary exponentials and trigonometric functions372
15-Euler's relation chez Euler383
16-Hyperbolic functions388
3．Infinite products394
17-Absolutely convergent infinite products394
18-The infinite product for the sine function397
19-Expansion of an infinite product in series403
20-Strange identities407
4．The topology of the functions Arg(z)and Log z414
Index425