Table of Contents

Chapter 1 • Precalculus Review
 Distance on the Coordinate Plane: Pythagorean Formula
 Relations and Functions
 Graphing Cubic Functions
 Increasing and Decreasing Intervals of a Function
 Even and Odd Functions
 Linear Functions in Different Forms
 Linear Relationships
 Equation of a Straight Line: Slope–Intercept Form
 Equation of a Straight Line: Standard and Point–Slope Forms
 Equation of a Straight Line: General Form
 Solving Quadratic Equations: Quadratic Formula
 Completing the Square
 Composite Functions
 Domain and Range of a Piecewise Function
 Conversion between Radians and Degrees
 Evaluating Trigonometric Function Values with Angles 30,45, and 60
 Simple Trigonometric Equations
 Graphs of Trigonometric Functions
 Evaluating Trigonometric Functions
 Law of Cosines
 Inverse of a Function

Chapter 2 • Limits
 Average and Instantaneous Rates of Change
 Limits from Tables and Graphs
 Limits by Direct Substitution
 OneSided Limits
 Continuity at a Point
 Evaluating Limits Using Algebraic Techniques
 Limits of Trigonometric Functions
 Limits at Infinity and Unbounded Limits
 Horizontal and Vertical Asymptotes of a Function
 Intermediate Value Theorem

Chapter 3 • Differentiation
 Definition of the Derivative
 The Differentiability of a Function
 Power Rule of Derivatives
 The Product Rule
 The Quotient Rule
 Applications of Derivatives on Rectilinear Motion
 Second and HigherOrder Derivatives
 Differentiation of Trigonometric Functions
 Differentiation of Reciprocal Trigonometric Functions
 The Chain Rule
 Implicit Differentiation
 Derivatives of Inverse Trigonometric Functions
 Related Rates
 Chapter 4 • Applications of the Derivative

Chapter 5 • The Integral
 Riemann Sums
 Definite Integrals as Limits of Riemann Sums
 Properties of Definite Integrals
 The Fundamental Theorem of Calculus: Evaluating Definite Integrals
 Indefinite Integrals: The Power Rule
 The Fundamental Theorem of Calculus: Functions Defined by Integrals
 The Net Change Theorem
 Integration by Substitution: Indefinite Integrals
 Integration by Substitution: Definite Integrals
 Chapter 6 • Applications of the Integral

Chapter 7 • Exponential Functions
 Differentiation of Exponential Functions
 Indefinite Integrals: Exponential and Reciprocal Functions
 Differentiation of Inverse Functions
 Differentiation of Logarithmic Functions
 Logarithmic Differentiation
 Integrals Resulting in Logarithmic Functions
 Exponential Growth and Decay Models
 Exponential Growth and Decay
 Compound Interest
 The Logistic Model
 L’Hôpital’s Rule
 Inverse Trigonometric Functions
 Hyperbolic Functions

Chapter 8 • Techniques of Integration
 Integration by Parts
 Reduction Formulae for Integration
 Trigonometric Integrals
 Integrals Resulting in Inverse Trigonometric Functions
 Integration by Trigonometric Substitutions
 Integration by Partial Fractions with Linear Factors
 Integration by Partial Fractions with Quadratic Factors
 Integration by Partial Fractions of Improper Fractions
 Improper Integrals: Infinite Limits of Integration
 Improper Integrals: Discontinuous Integrands
 Numerical Integration: Riemann Sums
 Numerical Integration: The Trapezoidal Rule
 Numerical Integration: Simpson’s Rule
 Chapter 9 • Further Applications of the Integral and Taylor Polynomials
 Chapter 10 • Introduction to Differential Equations
 Chapter 11 • Infinite Series
 Chapter 12 • Parametric Equations, Polar Coordinates, and Conic Sections

Chapter 13 • Vector Geometry
 Adding and Subtracting Vectors in 2D
 Vector Operations in 2D
 Graphical Operations on Vectors
 Vectors in Terms of Fundamental Unit Vectors
 Scalar Multiplication and Unit Vectors
 Points, Midpoints, and Distances in Space
 Equation of a Sphere
 Equation of a Straight Line in Space: Parametric Form
 Dot Product in 3D
 Cross Product in 3D
 Equation of a Plane: Intercept and Parametric Forms
 Cylindrical and Spherical Coordinates
 Chapter 14 • Calculus of VectorValued Functions

Chapter 15 • Differentiation in Several Variables
 Limits of Multivariable Functions
 Partial Derivatives
 Partial Derivatives and the Fundamental Theorem of Calculus
 Second and HigherOrder Partial Derivatives
 Tangent Planes and Linear approximation
 Gradient in Cylindrical and Spherical Coordinates
 Directional Derivatives and Gradient
 The Chain Rule for Multivariate Functions
 Extrema of a Multivariable Function
 Lagrange Multipliers
 Chapter 16 • Multiple Integration
 Chapter 17 • Line and Surface Integrals
 Chapter 18 • Fundamental Theorems of Vector Analysis
 Appendices
 Additional Proofs
 Additional Content