Chapter 1 Set and Simple Logic 4
Ⅰ Set 4
1.1 Set 4
1.2 Subset,Universe,Complementary Set 8
1.3 Intersection,Union 11
1.4 Solutions of Inequalities with Absolute Value 15
1.5 Solutions of One-Variable Quadratic Inequalities 17
Reading Material Number of Elements in a Set 24
Ⅱ Simple Logic 26
1.6 Logical Connective 26
1.7 Four Types of Propositions 31
1.8 Sufficient Condition and Necessary Condition 37
Summary and Review 42
Reference Exercises for Review Ⅰ 46
Chapter 2 Function 50
Ⅰ Mapping and Function 50
2.1 Mapping 50
2.2 Function 55
2.3 Monotonicity and Parity of Function 63
2.4 Inverse Function 71
Ⅱ Exponent and Exponential Function 77
2.5 Exponent 77
2.6 Exponential Function 83
Ⅲ Logarithm and Logaithmic Function 87
2.7 Logarithm 87
Reading Material A Brief History of Logarithm and Exponent 93
2.8 Logarithmic Function 95
2.9 Examples for Function Applications 99
2.10 Field Work 104
Reading Material The Mathematical Model for the Motion of a Freely Falling Body h(t)=1/2gt2 106
Summary and Review 109
Reference Exercises for Review Ⅱ 117
Chapter 3 Number Sequence 122
3.1 Number Sequence 122
3.2 Arithmetic Series 127
3.3 The Surn of the First n Terms of Arithmetic Series 132
Reading Material Calculations on Deposits 138
3.4 Geometric Series 141
3.5 The Sum of the First n Terms of Geometric Series 145
3.6 Studies:Galculations about Payment by Installments 150
Summary and Review 154
Reference Exercises for Review Ⅲ 157
Appendix 161
Some Nouns in the Book with Chinese Translation 161