无穷小微积分“试点”，授课人备课必修（I）

    无穷小微积分教材授课人必须知道一个事实：在50个课时之内必须讲完微积分学基本定理。

   前四章各小节内容如下，

INTRODUCTION（引言）

1 REAL AND HVPERREAL NUMBERS 1

1.1 The Real Line 1

1.2 Functions of Real Numbers 6

1.3 Straight Lines 16

1.4 Slope and Velocity; The Hyperreal Line 21

1.5 Infinitesimal, Finite, and Infinite Numbers 27

1.6 Standard Parts 35

Extra Problems for Chapter I 41

2 DIFFERENTIATION 43

2.1 Derivatives 43

2.2 Differentials and Tangent Lines 53

2.3 Derivatives of Rational Functions 60

2.4 Inverse Functions 70

2.5 Transcendental Functions 78

2.6 Chain Rule 85

2.7 Higher Derivatives 94

2.8 Implicit Functions 97

Extra Problems for Chapter 2 103

3 CONTINUOUS FUNCTIONS 105

3.1 How to Set Up a Problem 105

3.2 Related Rates 110

3.3 Limits 117

3.4 Continuity 124

3.5 Maxima and Minima 134

3.6 Maxima and Minima - Applications 144

3.7 Derivatives and Curve Sketching 151

3.8 Properties of Continuous Functions 159

Extra Problems for Chapter 3 171

4 INTEGRATION 175

4.1 The Definite Integral 175

4.2 Fundamental Theorem of Calculus （微积分学基本定理）186

4.3 Indefinite Integrals 198

4.4 Integration by Change of Variables 209

4.5 Area between Two Curves 218

4.6 Numerical Integration 224

Extra Problems for Chapter 4 234

袁萌  7月18日