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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
Exercise 3.1
3.2 Basic Differentiation Properties
3.2.1 Constant Function Rule
3.2.2 The Power Rule
3.2.3 Sum and Difference Rule
3.2.4 Derivative of Polynomials
Exercise 3.2
3.3 Differentials
3.3.1 Differentials
3.3.2 Linear Approximation
Exercise 3.3
Summary and Review
Chapter 4 Additional Derivative Topics
4.1 Derivatives of Products and Quotients
4.1.1 Derivatives of Products
4.1.2 Derivatives of Quotients
Exercise 4.1
4.2 The Chain Rule
4.2.1 Composite Functions
4.2.2 Proof of the Chain Rule
4.2.3 The General Power Rule
Exercise 4.2
4.3 Logarithmic Function
4.3.1 Inverse Function
4.3.2 Differentiability of Inverses
4.3.3 Logarithmic Functions
Exercise 4.3
4.4 Derivative of e" and In x
4.4.1 Derivative of the Natural Exponential Functions
4.4.2 Derivative of Exponential Functions
4.4.3 Exponential Growth and Decay
4.4.4 Derivative of Logarithmic Functions
Exercise 4.4
4.5 Implicit Differentiation
Exercise 4.5
4.6 Related Rates
Exercise 4.6
Summary and Review
Chapter 5 Graphing and Optimization
5.1 Local Extrema and the Mean Value Theorem
5.1.1 Local Extrema
5.1.2 Critical Numbers
5.1.3 The Mean Value Theorem
Exercise 5.1
5.2 The First Derivatives and Graphs
5.2.1 The First Derivatives and Monotonicity
5.2.2 The First Derivative Test
Exercise 5.2
5.3 The Second Derivatives and Graphs
5.3.1 Higher Derivatives
5.3.2 Concavity
Exercise 5.3
5.4 Optimization
5.4.1 Locating Absolute Extrema
5.4.2 The Second Derivative and Extrema
5.4.3 The Second Derivative Test for Absolute Extrema
5.4.4 Optimization Problems
Exercise 5.4
5.5 L'Hospital's Rule
5.5.1 Indeterminate Forms
5.5.2 L'Hospital's Rule in Other Cases
5.5.3 Other Indeterminate Forms
Exercise 5.5
5.6 Periodicity and Trigonometric Functions
5.6.1 Definition of Periodic Function
5.6.2 Trigonometric Functions
Exercise 5.6
5.7 Graphing of Functions
Exercise 5.7
Summary and Review
Chapter 6 Integration
6.1 Antiderivatives and Indefinite Integrals
6.1.1 Antiderivatives
6.1.2 Indefinite Integrals
6.1.3 Indefinite Integrals List