Textbook

# Calculus Multivariable 9th Edition

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Ch 11   Three-Dimensional Space; Vectors

11.1     Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces

11.2     Vectors

11.3     Dot Product; Projections

11.4     Cross Product

11.5     Parametric Equations of Lines

11.6     Planes in 3-Space

11.8     Cylindrical and Spherical Coordinates

Ch 12   Vector-Valued Functions

12.1     Introduction to Vector-Valued Functions

12.2     Calculus of Vector-Valued Functions

12.3     Change of Parameter; Arc Length

12.4     Unit Tangent, Normal, and Binormal Vectors

12.5     Curvature

12.6     Motion Along a Curve

12.7     Kepler's Laws of Planetary Motion

Ch 13   Partial Derivatives

13.1     Functions of Two or More Variables

13.2     Limits and Continuity

13.3     Partial Derivatives

13.4     Differentiability, Differentials, and Local Linearity

13.5     The Chain Rule

13.7     Tangent Planes and Normal Vectors

13.8     Maxima and Minima of Functions of Two Variables

13.9     Lagrange Multipliers

Ch 14   Multiple Integrals

14.1     Double Integrals

14.2     Double Integrals over Nonrectangular Regions

14.3     Double Integrals in Polar Coordinates

14.4     Surface Area; Parametric Surfaces}

14.5     Triple Integrals

14.6     Triple Integrals in Cylindrical and Spherical Coordinates

14.7     Change of Variable in Multiple Integrals; Jacobians

14.8     Centers of Gravity Using Multiple Integrals

Ch 15   Topics in Vector Calculus

15.1     Vector Fields

15.2     Line Integrals

15.3     Independence of Path; Conservative Vector Fields

15.4     Green's Theorem

15.5     Surface Integrals

15.6     Applications of Surface Integrals; Flux

15.7     The Divergence Theorem

15.8     Stokes' Theorem

Appendix   [order of sections TBD]

A         Graphing Functions Using Calculators and Computer Algebra Systems

B         Trigonometry Review

C         Solving Polynomial Equations

D         Mathematical Models

E          Selected Proofs

Web Appendices

F          Real Numbers, Intervals, and Inequalities

G         Absolute Value

H         Coordinate Planes, Lines, and Linear Functions

I           Distance, Circles, and Quadratic Functions

J           Second-Order Linear Homogeneous Differential Equations; The Vibrating String

K         The Discriminant

PHOTOCREDITS

INDEX

New To This Edition
• Exercise Sets: New true/false exercises and new expository writing exercises have been added.
• Making Connections: Contains a select group of exercises that draw on ideas developed in the entire chapter rather than focusing on a single section as with the regular exercise sets.
• New Chapter 0: The review material from Chapter 1 is now in Chapter 0.
• Visualization: Illustrations make extensive use of modern computer graphics to clarify concepts and to develop the student's ability to visualize mathematical objects, particularly those in 3-space. For students working with graphing technology, many exercises develop the ability to generate and analyze mathematical curves and surfaces.
• Additional Student-Friendly Reorganization The sections "Graphing Functions Using Calculators and Computer Algebra Systems" and "Mathematical Models" are now text appendices; and the section "Second-Order Linear Homogeneous Differential Equations; The Vibrating String" is now posted on the web site that supports this text.
Hallmark Features
• Readability Balanced with Rigor: The authors' goal is to present precise mathematics to the fullest extent possible in an introductory treatment.
• Commitment to Student Success: Clear writing, effective pedagogy--including special exercises designed for self-assessment--and visual representations of the mathematics help students from a variety of backgrounds to learn. Recognizing variations in learning styles, the authors take a "rule of four" approach, presenting concepts from the verbal, algebraic, visual, and numerical points of view to foster deeper understanding whenever appropriate.
• Dependability: Anton provides thorough topic coverage organized to fit standard curricula and carefully-constructed exercise sets that users of previous editions have come to depend upon.
• Flexibility: This edition is designed to serve a broad spectrum of calculus philosophies-from traditional to "reform." Technology can be emphasized or not, and the order of many topics can be adapted to accommodate each instructor's specific needs.
• Quick Check Exercises: Each exercise set begins with approximately five exercises (answers included) that are designed to provide the student with an immediate assessment of whether he or she has mastered key ideas from the section. They require a minimum of computation and can usually be answered by filling in the blanks.
• Focus on Concepts Exercises: Each exercise set contains a clearly-identified group of problems that focus on the main ideas of the section.
• Technology Exercises: Most sections include exercises that are designed to be solve using either a graphing calculator or a computer algebra system such as Mathematica, Maple, or Derive. These exercises are marked with an icon for easy identification.
• Expository Excellence: Clear explanations allow students to build confidence and provide flexibility for the instructor to use class time for problem solving, applications and explanation of difficult concepts.
• Mathematical Level: The book is written at a mathematical level that is suitable for students planning on careers in engineering or science.
• Applicability of Calculus: One of the primary goals of this text is to link calculus to the real world and the student s own experience. This theme is carried through in the examples and exercises.
• Historical Notes: The biographies and historical notes have been a hallmark of this text from its first edition and have been maintained in this edition. All of the biographical materials have been distilled from standard sources with the goal of capturing the personalities of the great mathematicians and bringing them to life for the student.

## Available Versions

Calculus Multivariable, 9th Edition
by Howard Anton, Irl C. Bivens, Stephen Davis
ISBN 978-0-470-18346-5
Hardcover, 448 pages
Calculus Multivariable 9th edition Binder Ready Version
by Howard Anton, Irl C. Bivens, Stephen Davis
ISBN 978-0-470-41815-4
Paperback, 448 pages