Textbook in PDF format The strengths of these texts are characterized by mathematical integrity, comprehensive discussions of the concepts of calculus, and an impressively large collection of worked examples and illustrative figures. Preface Acknowledgments Ancillaries For the Student Precalculus review Algebra Functions and Their Graphs Trigonometry Exponentials and Logarithms Conic Sections Limits and continuity Introduction to Limits Definition of Limit Techniques for Finding Limits Limits Involving Infinity Continuous Functions Chapter I Review Exercises Extended Problems and Group Projects The derivative Tangent Lines and Rates of Change Definition of Derivative Techniques of Differentiation Derivatives of the Trigonometric Functions The Chain Rule Implicit Differentiation Related Rates Linear Approximations and Differentials Newton’s Method Chapter 2 Review Exercises Extended Problems and Group Projects Applications of the derivative Extrema of Functions The Mean Value Theorem The First Derivative Test Concavity and the Second Derivative Test Summary of Graphical Methods Optimization Problems Velocity and Acceleration Applications to Economics, Social Sciences, and Life Sciences Chapter 3 Review Exercises Extended Problems and Group Projects Integrals Antiderivatives, Indefinite Integrals, and Simple Differential Equations Change of Variables in Indefinite Integrals Summation Notation and Area The Definite Integral Properties of the Definite Integral The Fundamental Theorem of Calculus Numerical Integration Chapter 4 Review Exercises Extended Problems and Group Projects Applications of the definite integral Area Solids of Revolution Volumes by Cylindrical Shells Volumes by Cross Sections Arc Length and Surfaces of Revolution Work Moments and Centers of Mass Other Applications Chapter 5 Review Exercises Extended Problems and Group Projects Transcendental functions The Derivative of the Inverse Function The Natural Logarithm Function The Exponential Function Integration Using Natural Logarithm and Exponential Functions General Exponential and Logarithmic Functions Separable Differential Equations and Laws of Growth and Decay Inverse Trigonometric Functions Hyperbolic and Inverse Hyperbolic Functions Indeterminate Forms and I’ H6pital’s Rule Chapter 6 Review Exercises Extended Problems and Group Projects Techniques of integration Integration by Parts Trigonometric Integrals Trigonometric Substitutions Integrals of Rational Functions Quadratic Expressions and Miscellaneous Substitutions Tables of Integrals and Computer Algebra Systems Improper Integrals Chapter 7 Review Exercises Extended Problems and Group Projects Infinite series Sequences Convergent or Divergent Series Positive-term Series The Ratio and Root Tests Alternating Series and Absolute Convergence Power Series Power Series Representations of Functions Maclaurin and Taylor Series Applications of Taylor Polynomials Chapter 8 Review Exercises Extended Problems and Group Projects Parametric equations and polar coordinates Parametric Equations Arc Length and Surface Area Polar Coordinates Integrals in Polar Coordinates Translation and Rotation of Axes Chapter 9 Review Exercises Extended Problems and Group Projects Appendices Theorems on Limits and Integrals Table of Integrals The Binomial Theorem Answers to Selected Exercises Index