Calculus, International 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.

• 1. Functions and Models.Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Principles of Problem Solving.2. Limits.The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity.3. 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?. Imlicit Differentiation. Rates of Change in the Natural and Social Sciences. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials.4. Applications of Differentiation.Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Limits at Infinity; Horizontal Asymptotes. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Newton''s Method. Antiderivatives.5. Integrals.Areas and Distances. 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.6. Applications of Integration.Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function.7. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions .Inverse Functions. (Instructors may cover either Sections 7.2-7.4 or Sections 7.2*-7.4*). 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. 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.8. Techniques of Integration.Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals.9. 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.10. Differential Equations.Modeling with Differential Equations. Direction Fields and Euler''s Method. Separable Equations. Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Applied Project: Calculus and Baseball. Linear Equations. Predator-Prey Systems.11. Parametric Equations and Polar Coordinates.Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bezier Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates.12. Infinite Sequences and Series.Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representation of Functions as Power Series. Taylor and Maclaurin Series. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars.13.