Chapter 1 Functions
1.1 Lines in the Plane
1.1.1 Coordinates on the Line
1.1.2 Cartesian Coordinates in the Plane
1.1.3 Linear Equations
1.1.4 Equations of Lines
Exercise 1.1
1,2 Concept of Function
1.2.1 Basic Conception
1.2.2 Function Notation
1.2.3 Even and Odd Functions
1.2.4 Increasing and Decreasing Functions
Exercise 1.2
1.3 Polynomial and Rational Functions
1.3.1 Linear Functions and Straight Lines
1.3.2 Quadratic Functions
1.3.3 Polynomial Functions and Rational Functions
Exercise 1.3
Summary and Review
Chapter 2 Limits
2.1 Concept of Limit
2.1.1 Intuitive Definition of Limits
2.1.2 Properties of Limits
Exercise 2.1
2.2 Infinite Limits
2.2.1 Infinite Limits
2.2.2 Vertical Asymptote
Exercise 2.2
2.3 Continuity
2.3.1 Concept of Continuity
2.3.2 Continuity Properties
2.3.3 The Extreme Value Theorem
2.3.4 The Intermediate Value Theorem
2.3.5 Solving Inequalities Using Continuity Properties
Exercise 2.3
2.4 Limits at Infinity
2.4.1 Horizontal Asymptotes
2.4.2 Exponential Functions
Exercise 2.4
2.5 Precise Definition of Limits
2.5.1 Limits at Finite Points that Have Finite Values
2.5.2 Infinite Limits
2.5.3 Definition of Limits at Infinity
Exercise 2.5
Summary and Review
Chapter 3 Derivatives
3.1 Definition of the Derivative
3.1.1 Instantaneous Rates of Change
3.1.2 Geometric Interpretation
3.1.3 Differentiability and Continuity
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