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

Use Nagwa in conjunction with your preferred textbook. The recommended lessons from Nagwa for each section of this textbook are provided below. This alignment is not affiliated with, sponsored by, or endorsed by the publisher of the referenced textbook. Nagwa is a registered trademark of Nagwa Limited. All other trademarks and registered trademarks are the property of their respective owners.

• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• 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 Review Exercises
• Chapter 18 Fundamental Theorems of Vector Analysis
• 18.1 Green’s Theorem
• 18.2 Stokes’ Theorem
• 18.3 Divergence Theorem
• Chapter Review Exercises
• Appendices
• A The Language of Mathematics
• B Properties of Real Numbers
• C Induction and the Binomial Theorem