### Chapter 1: Prerequisites for Calculus

• 1.1 Linear Functions
• 1.2 Functions and Graphs
• 1.3 Exponential Functions
• 1.4 Parametric Equations
• 1.5 Inverse Functions and Logarithms
• 1.6 Trigonometric Functions

### Chapter 2: Limits and Continuity

• 2.1 Rates of Change and Limits
• 2.2 Limits Involving Infinity
• 2.3 Continuity
• 2.4 Rates of Change, Tangent Lines, and Sensitivity

### Chapter 3: Derivatives

• 3.1 Derivative of a Function
• 3.2 Differentiability
• 3.3 Rules for Differentiation
• 3.4 Velocity and Other Rates of Change
• 3.5 Derivatives of Trigonometric Functions

### Chapter 4: More Derivatives

• 4.1 Chain Rule
• 4.2 Implicit Differentiation
• 4.3 Derivatives of Inverse Trigonometric Functions
• 4.4 Derivatives of Exponential and Logarithmic Functions

### Chapter 5: Applications of Derivatives

• 5.1 Extreme Values of Functions
• 5.2 Mean Value Theorem
• 5.3 Connecting ƒ_ and ƒ _ with the Graph of ƒ
• 5.4 Modeling and Optimization
• 5.5 Linearization, Sensitivity, and Differentials
• 5.6 Related Rates

### Chapter 6: The Definite Integral

• 6.1 Estimating with Finite Sums
• 6.2 Definite Integrals
• 6.3 Definite Integrals and Antiderivatives
• 6.4 Fundamental Theorem of Calculus
• 6.5 Trapezoidal Rule

### Chapter 7: Differential Equations and Mathematical Modeling

• 7.1 Slope Fields and Euler’s Method
• 7.2 Antidifferentiation by Substitution
• 7.3 Antidifferentiation by Parts
• 7.4 Exponential Growth and Decay
• 7.5 Logistic Growth

### Chapter 8: Applications of Definite Integrals

• 8.1 Accumulation and Net Change
• 8.2 Areas in the Plane
• 8.3 Volumes
• 8.4 Lengths of Curves
• 8.5 Applications from Science and Statistics

### Chapter 9: Sequences, L’Hospital’s Rule, and Improper Integrals

• 9.1 Sequences
• 9.2 L ’Hospital’s Rule
• 9.3 Relative Rates of Growth
• 9.4 Improper Integrals

### Chapter 10: Infinite Series

• 10.1 Power Series
• 10.2 Taylor Series
• 10.3 Taylor’s Theorem
• 10.5 Testing Convergence at Endpoints

### Chapter 11: Parametric, Vector, and Polar Functions

• 11.1 Parametric Functions
• 11.2 Vectors in the Plane
• 11.3 Polar Functions

### Appendices

• A1 Formulas from Precalculus Mathematics
• A2 A Formal Definition of Limit
• A3 A Proof of the Chain Rule
• A4 Hyperbolic Functions
• A5 A Very Brief Table of Integrals
• Glossary