CALCULUS: EARLY TRANSCENDENTALS, 9th Edition, provides you with the strongest foundation for a STEM future. James Stewart’s Calculus series is the topseller in the world because of its problemsolving focus, mathematical precision and accuracy, and outstanding examples and problem sets. Selected and mentored by Stewart, coauthors Daniel Clegg and Saleem Watson continue his legacy, and their careful refinements retain Stewart’s clarity of exposition and make the 9th Edition an even more usable learning tool. The accompanying WebAssign includes helpful learning support and new resources like Explore It interactive learning modules. Showing that Calculus is both practical and beautiful, the Stewart approach and WebAssign resources enhance understanding and build confidence for millions of students worldwide.
Preface.
To the Student.
Diagnostic Tests.
A Preview of Calculus.
1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving.
2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus.
3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Discovery Project: Families of Implicit Curves. Derivatives of Logarithmic Functions and Inverse Trigonometric Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Related Rates. Linear Approximations and Differentials. Discovery Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus.
4. 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. Indeterminate Forms and l'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. 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.
5. 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.
6. 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. Applied Project: Where to Sit at the Movies. 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? PredatorPrey 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 in Polar Coordinates. Review. Problems Plus.
11. SEQUENCES, SERIES, AND POWER SERIES.
Sequences. Discovery Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series and Absolute Convergence. The Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Discovery Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.
12. VECTORS AND THE GEOMETRY OF SPACE.
ThreeDimensional Coordinate Systems. Vectors. Discovery Project: The Shape of Hanging Chain. The Dot Product. The Cross Product. Discovery Project: The Geometry of a Tetrahedron. Equations of Lines and Planes. Discovery Project: Putting 3D in Perspective. Cylinders and Quadric Surfaces. Review. Problems Plus.
13. VECTOR FUNCTIONS.
Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Applied Project: Kepler’s Laws. Review. Problems Plus.
14. PARTIAL DERIVATIVES.
Functions of Several Variables. Limits and Continuity. Partial Derivatives. Discovery Project: Deriving the CobbDouglas Production Function. Tangent Planes and Linear Approximations. Applied Project: The Speedo LZR Racer. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Discovery Project: Quadratic Approximations and Critical Points. Lagrange Multipliers. Applied Project: Rocket Science. Applied Project: HydroTurbine Optimization. Review. Problems Plus.
15. MULTIPLE INTEGRALS.
Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Discovery Project: Volumes of Hyperspheres. Triple Integrals in Cylindrical Coordinates. Discovery Project: The Intersection of Three Cylinders. Triple Integrals in Spherical Coordinates. Applied Project: Roller Derby. Change of Variables in Multiple Integrals. Review. Problems Plus.
16. VECTOR CALCULUS.
Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green’s Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes’ Theorem. The Divergence Theorem. Summary. Review. Problems Plus.
APPENDIXES.
A: Numbers, Inequalities, and Absolute Values. B: Coordinate Geometry and Lines. C: Graphs of SecondDegree Equations. D: Trigonometry. E: Sigma Notation. F: Proofs of Theorems. G: The Logarithm Defined as an Integral. H: Answers to OddNumbered Exercises.
INDEX.

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 bestselling 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 coauthored 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 coauthor on Stewart's bestselling Calculus franchise.

NEW! WEBASSIGN EXERCISE TYPES: New homework exercises in WebAssign include Expanded Problems with multiple parts and automaticallygraded Proof Problems that develop conceptual understanding.

NEW! WEBASSIGN LEARNING RESOURCES: New digital resources in WebAssign include Explore It interactive learning modules and an eTextbook with a Media Index, Quick Prep modules and a Student Solutions Manual with worked solutions to the oddnumbered exercises.

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.

PROBLEMSOLVING EMPHASIS: George Polya’s problemsolving 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 problemsolving skills and intuition.

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

STEM APPLICATIONS: Stewart/Clegg/Watson answers the question, "When will I use this?" by showing how Calculus is used as a problemsolving 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 JustinTime 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: With over 8,000 exercises in all, each exercise set carefully progresses from skilldevelopment 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 presentday methods with those of the founders of Calculus. "Discovery Projects" anticipate results to be discussed later. "Applied Projects" feature realworld use of mathematics. "Laboratory Projects" anticipate results to be discussed later or encourage discovery through pattern recognition.

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: With over 8,000 exercises in all, each exercise set carefully progresses from skilldevelopment 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 presentday methods with those of the founders of Calculus. "Discovery Projects" anticipate results to be discussed later. "Applied Projects" feature realworld use of mathematics. "Laboratory Projects" anticipate results to be discussed later or encourage discovery through pattern recognition.

More challenging exercises called "Problems Plus" follow the endofchapter exercises. These sections 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.

Four carefullycrafted diagnostic tests in algebra, analytic geometry, functions, and trigonometry appear at the beginning of the text. These provide students with a convenient way to test their preexisting knowledge and brush up on skill techniques they need to successfully begin the course. Answers are included, and students who need to improve will be referred to points in the text or on the book's website where they can seek help.

Stewart's writing style speaks clearly and directly to students, guiding them through key ideas, theorems, and problemsolving steps, and encouraging them to think as they read and learn calculus.

Every concept is supported by thoughtfully worked examples—many with stepbystep explanations—and carefully chosen exercises. The quality of this pedagogical system is what sets Stewart's texts above others.

Examples are not only models for problem solving or a means of demonstrating techniques; they also encourage students to develop an analytic view of the subject. To provide further insight into mathematical concepts, many of these detailed examples display solutions that are presented graphically, analytically, and/or numerically. Margin notes expand on and clarify the steps of the solution.
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