# Alignment: Calculus • Jon Rogawski & Colin Adams • Third Edition

• Chapter 1 Precalculus Review
• 1.1 Real Numbers, Functions, and Graphs
• 1.2 Linear and Quadratic Functions
• 1.3 The Basic Classes of Functions
• 1.4 Trigonometric Functions
• 1.5 Technology: Calculators and Computers
• Chapter 2 Limits
• 2.1 Limits, Rates of Change, and Tangent Lines
• 2.2 Limits: A Numerical and Graphical Approach
• 2.3 Basic Limit Laws
• 2.4 Limits and Continuity
• 2.5 Evaluating Limits Algebraically
• 2.6 Trigonometric Limits
• 2.7 Limits at Infinity
• 2.8 Intermediate Value Theorem
• 2.9 The Formal Definition of a Limit
• Chapter 3 Differentiation
• 3.1 Definition of the Derivative
• 3.2 The Derivative as a Function
• 3.3 Product and Quotient Rules
• 3.4 Rates of Change
• 3.5 Higher Derivatives
• 3.6 Trigonometric Functions
• 3.7 The Chain Rule
• 3.8 Implicit Differentiation
• 3.9 Related Rates
• Chapter 4 Applications of the Derivative
• 4.1 Linear Approximation and Applications
• 4.2 Extreme Values
• 4.3 The Mean Value Theorem and Monotonicity
• 4.4 The Shape of a Graph
• 4.5 Graph Sketching and Asymptotes
• 4.6 Applied Optimization
• 4.7 Newton’s Method
• Chapter 5 The Integral
• 5.1 Approximating and Computing Area
• 5.2 The Definite Integral
• 5.3 The Indefinite Integral
• 5.4 The Fundamental Theorem of Calculus, Part I
• 5.5 The Fundamental Theorem of Calculus, Part II
• 5.6 Net Change as the Integral of a Rate of Change
• 5.7 Substitution Method
• Chapter 6 Applications of the Integral
• 6.1 Area between Two Curves
• 6.2 Setting up Integrals: Volume, Density, Average Value
• 6.3 Volumes of Revolution
• 6.4 The Method of Cylindrical Shells
• 6.5 Work and Energy
• Chapter 7 Exponential Functions
• 7.1 Derivative of 𝑓(𝑥) = 𝑏^𝑥 and the Number 𝑒
• 7.2 Inverse Functions
• 7.3 Logarithms and Their Derivatives
• 7.4 Exponential Growth and Decay
• 7.5 Compound Interest and Present Value
• 7.6 Models Involving 𝑦′ = 𝑘(𝑦 − 𝑏)
• 7.7 L’Hôpital’s Rule
• 7.8 Inverse Trigonometric Functions
• 7.9 Hyperbolic Functions
• Chapter 8 Techniques of Integration
• 8.1 Integration by Parts
• 8.2 Trigonometric Integrals
• 8.3 Trigonometric Substitution
• 8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
• 8.5 The Method of Partial Fractions
• 8.6 Strategies for Integration
• 8.7 Improper Integrals
• 8.8 Probability and Integration
• 8.9 Numerical Integration
• Chapter 9 Further Applications of the Integral and Taylor Polynomials
• 9.1 Arc Length and Surface Area
• 9.2 Fluid Pressure and Force
• 9.3 Center of Mass
• 9.4 Taylor Polynomials
• Chapter 10 Introduction to Differential Equations
• 10.1 Solving Differential Equations
• 10.2 Graphical and Numerical Methods
• 10.3 The Logistic Equation
• 10.4 First-Order Linear Equations
• Chapter 11 Infinite Series
• 11.1 Sequences
• 11.2 Summing an Infinite Series
• 11.3 Convergence of Series with Positive Terms
• 11.4 Absolute and Conditional Convergence
• 11.5 The Ratio and Root Tests and Strategies for Choosing Tests
• 11.6 Power Series
• 11.7 Taylor Series
• Chapter 12 Parametric Equations, Polar Coordinates, and Conic Sections
• 12.1 Parametric Equations
• 12.2 Arc Length and Speed
• 12.3 Polar Coordinates
• 12.4 Area and Arc Length in Polar Coordinates
• 12.5 Conic Sections
• Chapter 13 Vector Geometry
• 13.1 Vectors in the Plane
• 13.2 Vectors in Three Dimensions
• 13.3 Dot Product and the Angle between Two Vectors
• 13.4 The Cross Product
• 13.5 Planes in 3-Space
• 13.6 A Survey of Quadric Surfaces
• 13.7 Cylindrical and Spherical Coordinates
• Chapter 14 Calculus of Vector-Valued Functions
• 14.1 Vector-Valued Functions
• 14.2 Calculus of Vector-Valued Functions
• 14.3 Arc Length and Speed
• 14.4 Curvature
• 14.5 Motion in 3-Space
• 14.6 Planetary Motion According to Kepler and Newton
• Chapter 15 Differentiation in Several Variables
• 15.1 Functions of Two or More Variables
• 15.2 Limits and Continuity in Several Variables
• 15.3 Partial Derivatives
• 15.4 Differentiability and Tangent Planes
• 15.5 The Gradient and Directional Derivatives
• 15.6 The Chain Rule
• 15.7 Optimization in Several Variables
• 15.8 Lagrange Multipliers: Optimizing with a Constraint
• Chapter 16 Multiple Integration
• 16.1 Integration in Two Variables
• 16.2 Double Integrals over More General Regions
• 16.3 Triple Integrals
• 16.4 Integration in Polar, Cylindrical, and Spherical Coordinates
• 16.5 Applications of Multiple Integrals
• 16.6 Change of Variables
• Chapter 17 Line and Surface Integrals
• 17.1 Vector Fields
• 17.2 Line Integrals
• 17.3 Conservative Vector Fields
• 17.4 Parametrized Surfaces and Surface Integrals
• 17.5 Surface Integrals of Vector Fields
• Chapter 18 Fundamental Theorems of Vector Analysis
• 18.1 Green’s Theorem
• 18.2 Stokes’ Theorem
• 18.3 Divergence Theorem
• Appendices
• A The Language of Mathematics
• B Properties of Real Numbers
• C Induction and the Binomial Theorem