Calculus, Metric Edition

James Stewart received the M.S. degree from Stanford University and the Ph.D. from the University of Toronto. After two years as a postdoctoral fellow at the University of London, he became Professor of Mathematics at McMaster University. His research has been in harmonic analysis and functional analysis. Stewart’s books include a series of high school textbooks as well as a best-selling series of calculus textbooks published by Cengage Learning. He is also co-author, with Lothar Redlin and Saleem Watson, of a series of college algebra and precalculus textbooks. Translations of his books include those into Spanish, Portuguese, French, Italian, Korean, Chinese, Greek, Indonesian and Japanese. A talented violinist, Stewart was concertmaster of the McMaster Symphony Orchestra for many years and played professionally in the Hamilton Philharmonic Orchestra. He has given more than 20 talks worldwide on mathematics and music. Stewart was named a Fellow of the Fields Institute in 2002 and was awarded an honorary D.Sc. in 2003 by McMaster University. The library of the Fields Institute is named after him. The James Stewart Mathematics Centre was opened in October, 2003, at McMaster University. Daniel Clegg received his B.A. in Mathematics from California State University, Fullerton and his M.A. in Mathematics from UCLA. He is currently a professor of mathematics at Palomar College near San Diego, California, where he has taught for more than 20 years. Clegg co-authored BRIEF APPLIED CALCULUS with James Stewart and also assisted Stewart with various aspects of his calculus texts and ancillaries for almost 20 years. Saleem Watson received his bachelor of science degree from Andrews University in Michigan. He completed his graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. Dr. Watson conducted subsequently research at the Mathematics Institute of the University of Warsaw in Poland. He taught mathematics at Pennsylvania State University before serving at California State University, Long Beach, where he is currently professor emeritus. Dr. Watson's research encompasses the field of functional analysis. Dr. Watson is an important co-author for Dr. Stewart's best-selling calculus textbook series as well as his popular precalculus, college algebra and trigonometry texts.

• Preface. To the Student. Diagnostic Tests. A Preview of Calculus. 1. FUNCTIONS AND LIMITS.Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Review. Principles of Problem Solving. 2. DERIVATIVES. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Differentiation Formulas. Applied Project: Building a Better Roller Coaster. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Discovery Project: Families of Implicit Curves. Rates of Change in the Natural and Social Sciences. Related Rates. Linear Approximations and Differentials. Discovery Project: Polynomial Approximations. Review. Problems Plus.3. APPLICATIONS OF DIFFERENTIATION.Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. What Derivatives Tell Us About the Shape of a Graph. Limits at Infinity; Horizontal Asymptotes. Summary of Curve Sketching. Graphing with Calculus and Technology. Optimization Problems. Applied Project: The Shape of a Can. Applied Project: Planes and Birds: Minimizing Energy. Newton’s Method. Antiderivatives. Review. Problems Plus. 4. INTEGRALS. The Area and Distance Problems. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus.5. APPLICATIONS OF INTEGRATION.Areas Between Curves. Applied Project: The Gini Index. Volumes. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Review. Problems Plus.6. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.Inverse Functions. Instructors may cover either Sections 6.2–6.4 or Sections 6.2*–6.4*. Exponential Functions and Their Derivatives. Logarithmic Functions. Derivatives of Logarithmic Functions. The Natural Logarithmic Function. The Natural Exponential Function. General Logarithmic and Exponential Functions. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Inverse Trigonometric Functions. Applied Project: Where to Sit at the Movies. Hyperbolic Functions. Indeterminate Forms and l’Hospital’s Rule. Writing Project: The Origins of l’Hospital’s Rule. Review. Problems Plus. 7. TECHNIQUES OF INTEGRATION.Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Technology. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus.8. FURTHER APPLICATIONS OF INTEGRATION. Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus.9. DIFFERENTIAL EQUATIONS. Modeling with Differential Equations. Direction Fields and Euler’s Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Models for Population Growth. Linear Equations. Applied Project: Which Is Faster, Going Up or Coming Down? Predator-Prey Systems. Review. Problems Plus.10. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Curves Defined by Parametric Equations. Discovery Project: Running Circles Around Circles. Calculus with Parametric Curves. Discovery Project: Bézier Curves. Polar Coordinates. Discovery Project: Families of Polar Curves. Calculus in Polar Coordinates. Conic Sections. Conic Sections