Chapter 1 Prerequisites for Calculus
1.1 Lines
1.2 Functions and Graphs
1.3 Exponential Functions
1.4 Parametric Equations
1.5 Functions and Logarithms
1.6 Trigonometric Functions
Key Terms
Review Exercises
Chapter 2 Limits and Contunity
2.1 Rates of Change and Limits
2.2 Limits Involcing Infinity
2.3 Continuity
2.4 Rates of Change and Tangent Lines
Key Terms
Review Exercises
Chapter 3 Derivatives
3.1 Derivative of a Function
3.2 Differentiability
3.3 Rules of Differentiation
3.4 Velocity and Other Rates of Change
3.5 Derivatives of Trigonometric Functions
Key Terms
Review Exercises
Chapter 4 More Derivatives
4.1 Chain Rule
4.2 Implicit Differentiation
4.3 Derivatives of Invers Trigonometric Functions
4.4 Derivatives of Exponential and Logarithmic Functions
Key Terms
Review Exercises
Chapter 5 Applications of Derivatives
5.1 Extreme Values of Functions
5.2 Mean Value Theorem
5.3 Connecting f' and f'' with the Graph of f
5.4 Modeling and Optimization
5.5 Linearization and Differentials
5.6 Related Rates
Key Terms
Review Exercises
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
Key Terms
Review Exercises
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
Key Terms
Review Exercises
Chapter 8 Applications of Definite Integrals
8.1 Integral As Net Change
8.2 Areas in the Plane
8.3 Volumes
8.4 Lengths of Curves
8.5 Applications from Science and Statistics
Key Terms
Review Exercises
Chapter 9 Sequences, L'Hopital's Rule, and Improper Integrals
9.1 Sequences
9.2 L'Hopital's Rule
9.3 Relative Rates of Growth
9.4 Improper Integrals
Key Terms
Review Exercises
Chapter 10 Infinite Series
10.1 Power Series
10.2 Taylor Series
10.3 Taylor's Theorem
10.4 Radius of Convergence
10.5 Testing Convergence at Endpoints
Key Terms
Review Exercises
Chapter 11 Parametric, Vector, and Polar Functions
11.1 Parametric Functions
11.2 Vectors in the Plane
11.3 Polar Functions
Key Terms
Review Exercises
Appendix
A1 Formulas from Precalculus Mathematics
A2 Mathematical Induction
A3 Using the Limit Definition
A4 Proof of the Chain Rule
A5 Conic Sections
A6 Hyperbolic Functions
A7 A Brief Table of Integrals
Glossary
Selected Answers
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Applications Index
Index