1. Functions
1.1 Functions and Their Graphs
1.2 Combining Functions; Shifting and Scaling Graphs
1.3 Trigonometric Functions
1.4 Graphing with Calculators and Computers
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
2. Limits and Derivatives
2.1 Rates of Change and Tangents to Curves
2.2 Limit of a Function and Limit Laws
2.3 Precise Definition of a Limit
2.4 One-Sided Limits
2.5 Continuity
2.6 Limits Involving Infinity, Asymptotes of Graphs
3. Differentiation
3.1 Tangents and the Derivative at a Point
3.2 The Derivative as a Function
3.3 Rules for Polynomials, Exponentials, Products, and Quotients
3.4 The Derivative as a Rate of Change
3.5 Derivatives of Trigonometric Functions
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of Inverse Functions and Logarithms
3.9 Inverse Trigonometric Functions
3.10 Related Rates
3.11 Linearization and Differentials
4. Applications of Derivatives
4.1 Extreme Values of Functions
4.2 The Mean Value Theorem
4.3 Monotonic Functions and the First Derivative Test
4.4 Concavity and Curve Sketching
4.5 Indeterminate Forms and L'Hopital's Rule
4.6 Applied Optimization
4.7 Newton's Method
4.8 Antiderivatives
5. Integration
5.1 Area and Estimating with Finite Sums
5.2 Sigma Notation and Limits of Finite Sums
5.3 The Definite Integral
5.4 The Fundamental Theorem of Calculus
5.5 Indefinite Integrals and the Substitution Rule
5.6 Substitution and Area Between Curves
6. Applications of Definite Integrals
6.1 Volumes Using Cross-Sections
6.2 Volumes Using Cylindrical Shells
6.3 Arc Length
6.4 Areas of Surfaces of Revolution
6.5 Work and Fluid Forces
6.6 Moments and Centers of Mass
7. Integrals and Transcendental Functions
7.1 The Logarithm Defined as an Integral
7.2 Exponential Change and Separable Differential Equations
7.3 Hyperbolic Functions
7.4 Relative Rates of Growth
8. Techniques of Integration
8.1 Integration by Parts
8.2 Trigonometric Integrals
8.3 Trigonometric Substitutions
8.4 Integration of Rational Functions by Partial Fractions
8.5 Integral Tables and Computer Algebra Systems
8.6 Numerical Integration
8.7 Improper Integrals
9. First-Order Differential Equations
9.1 Solutions, Slope Fields, and Euler's Method
9.2 First-Order Linear Equations
9.3 Applications
9.4 Graphical Solutions of Autonomous Equations
9.5 Systems of Equations and Phase Planes
10. Infinite Sequences and Series
10.1 Sequences
10.2 Infinite Series
10.3 The Integral Test
10.4 Comparison Tests
10.5 The Ratio and Root Tests
10.6 Alternating Series, Absolute and Conditional Convergence
10.7 Power Series
10.8 Taylor and Maclaurin Series
10.9 Convergence of Taylor Series
10.10 The Binomial Series and Applications of Taylor Series
11. Parametric Equations and Polar Coordinates
11.1 Parametrizations of Plane Curves
11.2 Calculus with Parametric Curves
11.3 Polar Coordinates
11.4 Graphing in Polar Coordinates
11.5 Areas and Lengths in Polar Coordinates
11.6 Conic Sections
11.7 Conics in Polar Coordinates
