Calculus of a Single Variable

Chapter P: Preparation for Calculus
	Graphs and Models
	Linear Models and Rates of Change
	Functions and Their Graphs
	Fitting Models to Data
	Review Exercises
Chapter 1: Limits and Their Properties
	A Preview of Calculus
	Finding Limits Graphically and Numerically
	Evaluating Limits Analytically
	Continuity and One-Sided Limits
	Infinite Limits
	Review Exercises
Chapter 2: Differentiation
	The Derivative and the Tangent Line Problem
	Basic Differentiation Rules and Rates of Change
	The Product and Quotient Rules and Higher-Order Derivatives
	The Chain Rule
	Implicit Differentiation
	Related Rates
	Review Exercises
Chapter 3: Applications of Differentiation
	Extrema on an Interval
	Rolles Theorem and the Mean Value Theorem
	Increasing and Decreasing Functions and the First Derivative Test
	Concavity and the Second Derivative Test
	Limits at Infinity
	A Summary of Curve Sketching
	Optimization Problems
	Newton’s Method
	Differentials
	Business and Economics Applications
	Review Exercises
Chapter 4: Integration
	Antiderivatives and Indefinite Integration
	Area
	Riemann Sums and Definite Integrals
	The Fundamental Theorem of Calculus
	Integration by Substitution
	Numerical Integration
	Review Exercises
Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
	The Natural Logarithmic Function and Differentiation
	The Natural Logarithmic Function and Integration
	Inverse Functions
	Exponential Functions: Differentiation and Integration
	Bases Other than e and Applications
	Differential Equations: Growth and Decay
	Differential Equations: Separation of Variables
	Inverse Trigonometric Functions and Differentiation
	Inverse Trigonometric Functions and Integration
	Hyperbolic Functions
	Review Exercises
Chapter 6: Applications of Integration
	Area of a Region Between Two Curves
	Volume: The Disc Method
	Volume: The Shell Method
	Arc Length and the Surfaces of Revolution
	Work
	Moments, Centers of Mass, and Centroids
	Fluid Pressure and Fluid Force
	Review Exercises
Chapter 7: Integration Techniques, Lhopitals Rule, and Improper Integrals
	Basic Integration Rules
	Integration by Parts
	Trigonometric Integrals
	Trigonometric Substitution
	Partial Fractions
	Integration by Tables and Other Integration Techniques
	Indeterminate Forms and Lhopitals Rule
	Improper Integrals
	Review Exercises
Chapter 8: Infinite Series
	Sequences
	Series and Convergence
	The Integral Test and p-Series
	Comparisons of Series
	Alternating Series
	The Ratio and Root Tests
	Taylor Polynomials and Approximations
	Power Series
	Representation of Functions by Power Series
	Taylor and Maclaurin Series
	Review Exercises
Chapter 9: Conics, Parametric Equations, and Polar Coordinates
	Conics and Calculus
	Plane Curves and Parametric Equations
	Parametric Equations and Calculus
	Polar Coordinates and Polar Graphs
	Area and Arc Length in Polar Coordinates
	Polar Equations of Conics and Keplers Laws
	Review Exercises
Appendix A: Precalculus Review
	Real Numbers and the Real Line
	The Cartesian Plane
	Review of Trigonometric Functions
Appendix B: Proofs of Selected Theorems
Appendix C: Basic Differentiation Rules for Elementary Functions
Appendix D: Integration Tables
Appendix E: Rotation and the General Second-Degree Equation
Appendix F: Complex Numbers
Answers to Odd-Numbered Exercises
Index