Single Variable Calculus,
9th Edition

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.

• James Stewart

  The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He conducted research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Dr. Stewart most recently served as a professor of mathematics at McMaster University, and his research focused on harmonic analysis. Dr. Stewart authored a best-selling calculus textbook series, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS and CALCULUS: CONCEPTS AND CONTEXTS as well as a series of successful precalculus texts.

• Daniel K. Clegg

  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

  Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis. Watson is a co-author on Stewart's best-selling Calculus franchise.

• NEW EXPLANATIONS AND EXAMPLES: Careful refinements throughout provide even greater clarity on key concepts such as computing volumes of revolution and setting up triple integrals.

• NEW SCAFFOLDED EXERCISES: At the beginning of problem sets, new basic exercises reinforce key skills and build student confidence to prepare them for more rigorous exercises and conceptual understanding.

• NEW SUBHEADINGS: Additional subsections within chapters help instructors and students find key content more easily to make the text an even more helpful teaching and learning tool.

• NEW WEBASSIGN RESOURCES: New digital resources in WebAssign include Explore It interactive learning modules, the MindTap reader for interactive and mobile ebook access, enhanced remediation support, and improved problem types.

• NEW EXPLANATIONS AND EXAMPLES: Careful refinements throughout provide even greater clarity on key concepts such as computing volumes of revolution and setting up triple integrals.

• NEW SCAFFOLDED EXERCISES: At the beginning of problem sets, new basic exercises reinforce key skills and build student confidence to prepare them for more rigorous exercises and conceptual understanding.

• NEW SUBHEADINGS: Additional subsections within chapters help instructors and students find key content more easily to make the text an even more helpful teaching and learning tool.

• NEW WEBASSIGN RESOURCES: New digital resources in WebAssign include Explore It interactive learning modules, the MindTap reader for interactive and mobile ebook access, enhanced remediation support, and improved problem types.

• PROBLEM-SOLVING EMPHASIS: George Polya’s problem-solving methodology is introduced at the beginning and reinforced throughout. "Strategies" sections help students select what techniques they'll need to solve problems in situations where the choice is not obvious and help them develop true problem-solving skills and intuition.

• CLEAR EXPOSITION: Dan Clegg and Saleem Watson have remained true to James Stewart's writing style speaking clearly and directly to students, guiding them through key ideas, theorems, and problem-solving steps, and encouraging them to think as they read and learn calculus.

• STEM APPLICATIONS: Stewart/Clegg/Watson answers "When will I use this?" by showing how calculus is used as a problem-solving tool in fields such as physics, engineering, chemistry, biology, medicine, and the social sciences.

• PREREQUISITE SUPPORT: Four diagnostic tests in algebra, analytic geometry, functions, and trigonometry enable students to test their preexisting knowledge and brush up on skills. Quick Prep and Just-in-Time exercises in WebAssign refresh and reinforce prerequisite knowledge.

• HELPFUL EXAMPLES: Every concept is supported by thoughtfully worked examples that encourage students to develop an analytic view of the subject. To provide further insight into mathematical concepts, many detailed examples display solutions graphically, analytically, and/or numerically. Margin notes expand on and clarify the steps of the solution.

• QUALITY EXERCISES: Each exercise set carefully progresses from skill-development problems to more challenging problems involving applications and proofs. Conceptual exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. More challenging “Problems Plus” exercises reinforce concepts by requiring students to apply techniques from more than one chapter of the text, and by patiently showing them how to approach a challenging problem.

• ENGAGING PROJECTS: A wealth of engaging projects reinforce concepts. "Writing Projects" ask students to compare present-day methods with those of the founders of calculus. "Discovery Projects" anticipate results to be discussed later. "Applied Projects" feature real-world use of mathematics. "Laboratory Projects" anticipate results to be discussed later or encourage discovery through pattern recognition.

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