高等数学 英文 上 第2版PDF电子书下载
- 电子书积分:12 积分如何计算积分?
- 作 者:北京邮电大学高等数学双语教学组编
- 出 版 社:北京:北京邮电大学出版社
- 出版年份:2017
- ISBN:9787563552726
- 页数:303 页
Chapter 1 Fundamental Knowledge of Calculus 1
1.1 Mappings and Functions 1
1.1.1 Sets and Their Operations 1
1.1.2 Mappings and Functions 6
1.1.3 Elementary Properties of Functions 11
1.1.4 Composite Functions and Inverse Functions 14
1.1.5 Basic Elementary Functions and Elementary Functions 16
Exercises 1.1 A 23
Exercises 1.1 B 25
1.2 Limits of Sequences 26
1.2.1 The Definition of Limit of a Sequence 26
1.2.2 Properties of Limits of Sequences 31
1.2.3 Operations of Limits of Sequences 35
1.2.4 Some Criteria for Existence of the Limit of a Sequence 38
Exercises 1.2 A 44
Exercises 1.2 B 46
1.3 The Limit of a Function 46
1.3.1 Concept of the Limit of a Function 47
1.3.2 Properties and Operations of Limits for Functions 53
1.3.3 Two Important Limits of Functions 58
Exercises 1.3A 61
Exercises 1.3 B 63
1.4 Infinitesimal and Infinite Quantities 63
1.4.1 Infinitesimal Quantities 63
1.4.2 Infinite Quantities 65
1.4.3 The Order of Infinitesimals and Infinite Quantities 67
Exercises 1.4 A 71
Exercises 1.4 B 73
1.5 Continuous Functions 73
1.5.1 Continuity of Functions 74
1.5.2 Properties and Operations of Continuous Functions 76
1.5.3 Continuity of Elementary Functions 78
1.5.4 Discontinuous Points and Their Classification 80
1.5.5 Properties of Continuous Functions on a Closed Interval 83
Exercises 1.5 A 87
Exercises 1.5 B 89
Chapter 2 Derivative and Differential 91
2.1 Concept of Derivatives 91
2.1.1 Introductory Examples 91
2.1.2 Definition of Derivatives 92
2.1.3 Geometric Meaning of the Derivative 96
2.1.4 Relationship between Derivability and Continuity 96
Exercises 2.1 A 98
Exercises 2.1 B 99
2.2 Rules of Finding Derivatives 99
2.2.1 Derivation Rules of Rational()perations 100
2.2.2 Derivation Rules of Composite Functions 101
2.2.3 Derivative of Inverse Functions 103
2.2.4 Derivation Formulas of Fundamental Elementary Functions 104
Exercises 2.2 A 105
Exereises 2.2 B 107
2.3 Higher Order Derivatives 107
Exercises 2.3 A 110
Exercises 2.3 B 111
2.4 Derivation of Implicit Functions and Parametric Equations,Related Rates 111
2.4.1 Derivation of Implicit Functions 111
2.4.2 Derivation of Parametric Equations 114
2.4.3 Related Rates 118
Exercises 2.4 A 120
Exercises 2.4 B 122
2.5 Differential of the Function 123
2.5.1 Concept of the Differential 123
2.5.2 Geometric Meaning of the Differential 125
2.5.3 Differential Rules of Elementary Functions 126
2.5.4 Differential in Linear Approximate Computation 127
Exercises 2.5 128
Chapter 3 The Mean Value Theorem and Applications of Derivatives 130
3.1 The Mean Value Theorem 130
3.1.1 Rolle's Theorem 130
3.1.2 Lagrange's Theorem 132
3.1.3 Cauchy's Theorem 135
Exercises 3.1 A 137
Exercises 3.1 B 138
3.2 L'Hospital's Rule 138
Exercises 3.2 A 144
Exercises 3.2 B 145
3.3 Taylor's Theorem 145
3.3.1 Taylor's Theorem 145
3.3.2 Applications of Taylor's Theorem 149
Exercises 3.3 A 150
Exercises 3.3 B 151
3.4 Monotonicity,Extreme Values,Global Maxima and Minima of Functions 151
3.4.1 Monotonicity of Functions 151
3.4.2 Extreme Values 153
3.4.3 Global Maxima and Minima and Its Application 156
Exercises 3.4 A 158
Exercises 3.4 B 160
3.5 Convexity of Functions,Inflections 160
Exercises 3.5 A 165
Exercises 3.5 B 166
3.6 Asymptotes and Graphing Functions 166
Exercises 3.6 170
Chapter 4 Indefinite Integrals 172
4.1 Concepts and Properties of Indefinite Integrals 172
4.1.1 Antiderivatives and Indefinite Integrals 172
4.1.2 Formulas for Indefinite Integrals 174
4.1.3Operation Rules of Indefinite Integrals 175
Exercises 4.1 A 176
Exercises 4.1 B 177
4.2 Integration by Substitution 177
4.2.1 Integration by the First Substitution 177
4.2.2 Integration by the Second Substitution 181
Exercises 4.2 A 184
Exercises 4.2 B 186
4.3 Integration by Parts 186
Exercises 4.3 A 193
Exercises 4.3 B 194
4.4 Integration of Rational Functions 194
4.4.1 Rational Functions and Partial Fractions 194
4.4.2 Integration of Rational Fractions 197
4.4.3 Antiderivatives Not Expressed by Elementary Functions 201
Exercises 4.4 201
Chapter 5 Definite Integrals 202
5.1 Concepts and Properties of Definite Integrals 202
5.1.1 Instances of Definite Integral Problems 202
5.1.2 The Definition of the Definite Integral 205
5.1.3 Properties of Definite Integrals 208
Exercises 5.1 A 213
Exercises 5.1 B 214
5.2 The Fundamental Theorems of Calculus 215
5.2.1 Fundamental Theorems of Calculus 215
5.2.2 Newton-Leibniz Formula for Evaluation of Definite Integrals 217
Exercises 5.2 A 219
Exercises 5.2 B 221
5.3 Integration by Substitution and by Parts in Definite Integrals 222
5.3.1 Substitution in Definite Integrals 222
5.3.2 Integration by Parts in Definite Integrals 225
Exercises 5.3 A 226
Exercises 5.3 B 228
5.4 Improper Integral 229
5.4.1 Integration on an Infinite Interval 229
5.4.2 Improper Integrals with Infinite Discontinuities 232
Exercises 5.4 A 235
Exercises 5.4 B 236
5.5 Applications of Definite Integrals 237
5.5.1 Method of Setting up Elements of Integration 237
5.5.2 The Area of a Plane Region 239
5.5.3 The Arc Length of Plane Curves 243
5.5.4 The Volume of a Solid by Slicing and Rotation about an Axis 247
5.5.5 Applications of Definite Integral in Physics 249
Exercises 5.5 A 252
Exercises 5.5 B 254
Chapter 6 Differential Equations 256
6.1 Basic Concepts of Differential Equations 256
6.1.1 Examples of Differential Equations 256
6.1.2 Basic Concepts 258
Exercises 6.1 259
6.2 First-Order Differential Equations 260
6.2.1 First-Order Separable Differential Equation 260
6.2.2 Equations can be Reduced to Equations with Variables Separable 262
6.2.3 First-Order Linear Equations 266
6.2.4 Bernoulli's Equation 269
6.2.5 Some Examples that can be Reduced to First-Order Linear Equations 270
Exereises 6.2 272
6.3 Reducible Second Order Differential Equations 273
Exercises 6.3 276
6.4 Higher-Order Linear Differential Equations 277
6.4.1 Some Examples of Linear Differential Equation of Higher-Order 277
6.4.2 Structure of Solutions of Linear Differential Equations 279
Exercises 6.4 282
6.5 Linear Equations with Constant Coefficients 283
6.5.1 Higher Order Linear Homogeneous Equations with Constant Coefficients 283
6.5.2 Higher-Order Linear Nonhomogeneous Equations with Constant Coefficients 287
Exercises 6.5 294
6.6Euler's Differential Equation 295
Exercises 6.6 296
6.7 Applications of Differential Equations 296
Exercises 6.7 301
Bibliography 303
- 《培智学校义务教育实验教科书教师教学用书 生活适应 二年级 上》人民教育出版社,课程教材研究所,特殊教育课程教材研究中心编著 2019
- 《MBA大师.2020年MBAMPAMPAcc管理类联考专用辅导教材 数学考点精讲》(中国)董璞 2019
- 《2013数学奥林匹克试题集锦 走向IMO》2013年IMO中国国家集训队教练组编 2013
- 《指向核心素养 北京十一学校名师教学设计 英语 七年级 上 配人教版》周志英总主编 2019
- 《一个数学家的辩白》(英)哈代(G.H.Hardy)著;李文林,戴宗铎,高嵘译 2019
- 《新课标背景下英语教学理论与教学活动研究》应丽君 2018
- 《高等数学试题与详解》西安电子科技大学高等数学教学团队 2019
- 《大学英语教学的跨文化交际视角研究与创新发展》许丽云,刘枫,尚利明著 2020
- 《中国少数民族唢呐教学曲选》胡美玲编 2019
- 《卓有成效的管理者 中英文双语版》(美)彼得·德鲁克许是祥译;那国毅审校 2019
- 《高等数学试题与详解》西安电子科技大学高等数学教学团队 2019
- 《北京生态环境保护》《北京环境保护丛书》编委会编著 2018
- 《上学就看 紧紧抓住梦想吧》北京少年儿童出版社 2015
- 《重庆市绿色建筑评价技术指南》重庆大学,重庆市建筑节能协会绿色建筑专业委员会主编 2018
- 《刘泽华全集 先秦政治思想史 下》刘泽华著;南开大学历史学院编 2019
- 《高等数学 上》东华大学应用数学系编 2019
- 《江苏中小企业生态环境评价报告》南京大学金陵学院企业生态研究中心 2019
- 《聋校义务教育实验教科书教师教学用书 数学 一年级 上》人民教育出版社,课程教材研究所,小学数学课程教材研究中心编著 2017
- 《AutoCAD机械设计实例精解 2019中文版》北京兆迪科技有限公司编著 2019
- 《国学 第6集》四川师范大学中华传统文化学院四川省人民政府文史研究馆 2018
- 《大学计算机实验指导及习题解答》曹成志,宋长龙 2019
- 《指向核心素养 北京十一学校名师教学设计 英语 七年级 上 配人教版》周志英总主编 2019
- 《大学生心理健康与人生发展》王琳责任编辑;(中国)肖宇 2019
- 《大学英语四级考试全真试题 标准模拟 四级》汪开虎主编 2012
- 《大学英语教学的跨文化交际视角研究与创新发展》许丽云,刘枫,尚利明著 2020
- 《北京生态环境保护》《北京环境保护丛书》编委会编著 2018
- 《复旦大学新闻学院教授学术丛书 新闻实务随想录》刘海贵 2019
- 《大学英语综合教程 1》王佃春,骆敏主编 2015
- 《大学物理简明教程 下 第2版》施卫主编 2020
- 《指向核心素养 北京十一学校名师教学设计 英语 九年级 上 配人教版》周志英总主编 2019