- 作 者：王冬冬，郭云编著
- 出 版 社：徐州：中国矿业大学出版社
- 出版年份：2001
- ISBN：7810703498
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Chapter 1 Functions 1
§1 Sets and Real Numbers 1
§2 Functions 3
§3 Some Basic Properties of Functions 6
§4 Inverse Functions 8
§5 Composite Functions 11
§6 Elementary Functions 12
Chapter 2 Limit Theory 18
§1 Limit of a Sequence 18
§2 Limit of a Function 27
§3 Basic Limit Theorems 33
§4 One-sided Limits and Limits at Infinity 38
Chapter 3 Continuity 47
§1 the Concepts of Continuity 48
§2 One-sided Continuity 51
§3 Two Special Theorems on Continuous Functions 56
Chapter 4 Derivatives 62
§1 Derivative 62
§2 Some Rules for Differentiation 69
§3 the Chain Rule 76
§4 Higher Derivatives 81
§1 the Mean Value Theorem 85
Chapter 5 Applications of the Derivative 85
§2 L Hospital Rule 90
§3 Increasing and Decreasing Functions 98
§4 Relative Extreme Values 101
Chapter 6 Indefinite Integral 106
§1 Indefinite Integral 106
§2 Integration by Substitution 112
§3 Integration by Parts 118
Chapter 7 the Definite Integral 122
§1 Preparation for the Definite Integral 122
§2 Some Properties of Integration 126
§3 Integration by Substitution 132
§4 Integration by Parts 137
Chapter 8 an Introduction to Differential Equations 140
§1 Basic Concepts of Differential Equations 140
§2 Separation of Variables 144
§3 First-order Linear Differential Equations 150
Chapter 9 Infinite Series 154
§1 Basic Concepts of Series 154
§2 Some Properties of Series 157
§3 Nonnegative Series 162
§4 Alternating Series and Absolute Convergence 170