江苏大学出版社大学预科数学 PRE-UPUREMATHEMATICS/张弘

Chapter l Algebra I
1．1 Sets and numbers
1．1．1 Set theory
1．1．2 Rational and irrational numbers
1．1．3 Real numbers
1．2 Indices
1．2．1 Laws of indices
1．2．2 Properties of indices
1．2．3 Exponential equations
1．3 Polynomials
1．4 Factorization
1，5 Solving quadratic equations
1．6 Simultaneous equations
1．6．1 Simultaneous linear equations
1．6．2 Simultaneous equations：linear and non-linear
1．7 Summary
1．8 Further problems

Chapter 2 Coordinate Geometry
2，1 Introduction
2．1．1 The distance between two points
2．1．2 The midpoint of a line segment
2．1．3 The slope of a line joining two points
2．2 Equations of a straight line
2．3 Inequalities
2．3．1 Symbols
2．3．2 Properties
2．3．3 Solving linear inequalities involving one variable
2．3．4 Solving linear inequalities involving two variables
2．4 The equation of a circle
2．4．1 Terminology
2．4．2 Cartesian coordinates
2．5 Summary
2．6 Further problems

Chapter 3 Functions
3．1 Mappings and functions
3．1．1 Relations and mappings
3．1．2 Functions
3．1．3 Four ways to represent a function
3．1．4 Injective， surjective and bijective functions
3．1．5 Piecewise-defined functions
3．2 Inverse functions
3．2．1How to find the inverse of a function
3．2．2 How to graph the inverse of a function
3．3 Composite functions
3．3．1 Arithmetic combinations of functions
3．3．2 Composition of functions
3．4 Transformation of graphs and functions
3．5 Odd， even and periodic functions
3．6 Exponentials
3．6．1 Graphs of exponential functions
3．6．2 Transformations of graphs of exponential functions
3．6．3 The natural base e
3．6．4 Properties of exponential functions
3．7 Logarithms
3．7．1 Graphs of logarithmic functions
3．7．2 Natural logarithmic functions
3．7．3 Properties of logarithmic functions
3．8 Summary
3．9 Further problems
……

Chapter 4 Algebra II
Chapter 5 Trigonometry
Chapter 6 Vectors
Chapter 7 Mathematical arguments and proofs