Thomas' Calculus: Multivariable

Paperback | October 7, 2013

byGeorge B. Thomas, Maurice D. Weir, Joel R. Hass

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This text is designed for the multivariable component a three-semester or four-quarter calculus course (math, engineering, and science majors).

Thomas’ Calculus, Multivariable, Thirteenth Edition, introduces readers to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded–always with the goal of developing technical competence while furthering readers’ appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today's learners.

 

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This text is designed for the multivariable component a three-semester or four-quarter calculus course (math, engineering, and science majors). Thomas’ Calculus, Multivariable, Thirteenth Edition, introduces readers to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has ...

Joel Hass received his PhD from the University of California—Berkeley. He is currently a professor of mathematics at the University of California—Davis. He has coauthored six widely used calculus texts as well as two calculus study guides. He is currently on the editorial board of Geometriae Dedicata and Media-Enhanced Mathematics. H...

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Format:PaperbackDimensions:600 pages, 10.8 × 8.5 × 0.9 inPublished:October 7, 2013Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0321884051

ISBN - 13:9780321884053

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Table of Contents

10. Infinite Sequences and Series

10.1 Sequences

10.2 Infinite Series

10.3 The Integral Test

10.4 Comparison Tests

10.5 Absolute Convergence; The Ratio and Root Tests

10.6 Alternating Series and Conditional Convergence

10.7 Power Series

10.8 Taylor and Maclaurin Series

10.9 Convergence of Taylor Series

10.10 The Binomial Series and Applications of Taylor Series

 

11. Parametric Equations and Polar Coordinates

11.1 Parametrizations of Plane Curves

11.2 Calculus with Parametric Curves

11.3 Polar Coordinates

11.4 Graphing Polar Coordinate Equations

11.5 Areas and Lengths in Polar Coordinates

11.6 Conic Sections

11.7 Conics in Polar Coordinates

 

12. Vectors and the Geometry of Space

12.1 Three-Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 The Cross Product

12.5 Lines and Planes in Space

12.6 Cylinders and Quadric Surfaces

 

13. Vector-Valued Functions and Motion in Space

13.1 Curves in Space and Their Tangents

13.2 Integrals of Vector Functions; Projectile Motion

13.3 Arc Length in Space

13.4 Curvature and Normal Vectors of a Curve

13.5 Tangential and Normal Components of Acceleration

13.6 Velocity and Acceleration in Polar Coordinates

 

14. Partial Derivatives

14.1 Functions of Several Variables

14.2 Limits and Continuity in Higher Dimensions

14.3 Partial Derivatives

14.4 The Chain Rule

14.5 Directional Derivatives and Gradient Vectors

14.6 Tangent Planes and Differentials

14.7 Extreme Values and Saddle Points

14.8 Lagrange Multipliers

14.9 Taylor's Formula for Two Variables

14.10 Partial Derivatives with Constrained Variables

 

15. Multiple Integrals

15.1 Double and Iterated Integrals over Rectangles

15.2 Double Integrals over General Regions

15.3 Area by Double Integration

15.4 Double Integrals in Polar Form

15.5 Triple Integrals in Rectangular Coordinates

15.6 Moments and Centers of Mass

15.7 Triple Integrals in Cylindrical and Spherical Coordinates

15.8 Substitutions in Multiple Integrals

 

16. Integrals and Vector Fields

16.1 Line Integrals

16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux

16.3 Path Independence, Conservative Fields, and Potential Functions

16.4 Green's Theorem in the Plane

16.5 Surfaces and Area

16.6 Surface Integrals

16.7 Stokes' Theorem

16.8 The Divergence Theorem and a Unified Theory