Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!
About the Author
James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage LearningBrooks/Cole, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.
Table of Contents
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. Review. Principles of Problem Solving.
2. LIMITS AND RATES OF CHANGE. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Tangents, Velocities, and Other Rates of Change. Review. Problems Plus.
3. DERIVATIVES. Derivatives, Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Differentiation Formulas. Rates of Change in the Natural and Social Sciences. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Higher Derivatives, Applied Project: Where Should a Pilot Start Descent?, Applied Project: Building a Better Roller Coaster. Related Rates. Linear Approximations and Differentials, Laboratory Project: Taylor Polynomials. Review. Problems Plus.
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. Applications to Business and Economics. Newton's Method. Antiderivatives. Review. Problems Plus.
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 theInvention of Calculus. The Substitution Rule. Review. Problems Plus.
6. APPLICATIONS OF INTEGRATION. Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Review. Problems Plus. Appendixes. Answers To Odd-Numbered Exercises. Index.