大学数学 英文版PDF电子书下载

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