Pearson - Thomas' Calculus, 12/E - George B. Thomas, Jr., Maurice D. Weir & Joel Hass

In this section:

Description

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

Calculus hasn’t changed, but your students have. Today’s students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. Thomas’ Calculus, Twelfth Edition, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.

The text is available with a robust MyMathLab^® course–an online homework, tutorial, and study solution designed for today’s students. In addition to interactive multimedia features like Java^™ applets and animations, thousands of MathXL^® exercises are available for students to get the practice they need.

Features

Strong exercise sets feature a great breadth of problems–progressing from skills problems to applied and theoretical problems–to encourage students to think about and practice the concepts until they achieve mastery.
Figures are conceived and rendered to provide insight for students and support conceptual reasoning.
The flexible table of contents divides complex topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students. For example, the precise definition of the limit is contained in its own section and may be skipped.
Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogues studied earlier in the book.
A robust MyMathLab course contains 7,900 assignable exercises, a complete e-book, and built-in tutorials so students can get help whenever they need it.
A complete suite of instructor and student supplements saves class preparation time for instructors and improves students’ learning.

New To This Edition

950 new, updated, and improved exercises, including many new mid-level exercises, provide more ways for you to address your students’ needs
New examples in many sections clarify or deepen the meaning of the topics covered and help students understand their mathematical applications and consequences to science and engineering.
New figures have been added, and many others have been revised to enhance conceptual understanding.
MyMathLab now has more than 7,900 assignable exercises, including 670 that address prerequisite skills, giving you the selection you need to create the right homework assignments and assessments.
Content revisions are apparent throughout the text, and many of these changes were driven by suggestions from users:

Prerequisites coverage has been condensed to focus strictly on reviewing function concepts. Material covering real numbers, intervals, increments, straight lines, distances, circles, and parabolas has been moved to Appendices 1–3.
Limits: to improve the flow of the chapter on limits, the authors have combined the ideas of limits involving infinity and their associations with asymptotes to the graphs of functions, placing them in the final section of the chapter.
Differentiation: to coalesce the derivative concept into a single chapter, the authors have moved the section “Tangents and the Derivative at a Point” from the end of Chapter 2 to the beginning of Chapter 3. In addition, they have reorganized and increased the number of the related rates examples in Section 3.8, and have added new examples and exercises on graphing rational functions in Section 4.4.

L’Hôpital’s rule has been moved to Chapter 7 after the transcendental functions have been studied.
Integration coverage has been improved. Integrals, as “limits of Riemann sums,” motivated primarily by the problem of finding the areas of general regions with curved boundaries, now form the substance of Chapter 5. After carefully developing the integral concept, the authors turn the focus to its evaluation and connection to antiderivatives captured in the Fundamental Theorem of Calculus. The ensuing applications then define the various geometric ideas of area, volume, lengths of paths, and centroids all as limits of Riemann sums giving definite integrals, which can be evaluated by finding an antiderivative of the integrand.
Differential equations: The authors give an introductory treatment of first-order differential equations in Chapter 9, including a new section on systems and phase planes, with applications to the competitive-hunter and predator-prey models. An introduction to second-order differential equations is in Chapter 17, which is available on the Thomas' Calculus website (www.aw.com/thomas).
Series coverage is more accessible to students with the addition of a number of new figures and exercises as well as the revision of some of the proofs related to convergence of power series.
Parametric equations have been moved to Chapter 11, joining polar coordinates and conic sections, in order to better prepare students for coverage of vectors and multivariable calculus.
Vector-valued functions coverage has been streamlined to place more emphasis on the conceptual ideas supporting the later material on partial derivatives, the gradient vector, and line integrals. The authors have also condensed the discussions of the Frenet frame and Kepler’s three laws of planetary motion.
Multivariable calculus: the authors have reorganized the opening material on double integrals, and combined the applications of double and triple integrals to masses and moments into a single section covering both two- and three-dimensional cases. This reorganization allows for better flow of the key mathematical concepts, together with their properties and computational aspects.
Vector Fields: important theorems and results are stated more clearly and completely together with enhanced explanations of their hypotheses and mathematical consequences. The area of a surface is now organized into a single section, and surfaces defined implicitly or explicitly are treated as special cases of the more general parametric representation. Surface integrals and their applications then follow as a separate section.

Table of Contents

1. Functions

1.1 Functions and Their Graphs

1.2 Combining Functions; Shifting and Scaling Graphs

1.3 Trigonometric Functions

1.4 Graphing with Calculators and Computers

2. Limits and Continuity

2.1 Rates of Change and Tangents to Curves

2.2 Limit of a Function and Limit Laws

2.3 The Precise Definition of a Limit

2.4 One-Sided Limits

2.5 Continuity

2.6 Limits Involving Infinity; Asymptotes of Graphs

3. Differentiation

3.1 Tangents and the Derivative at a Point

3.2 The Derivative as a Function

3.3 Differentiation Rules

3.4 The Derivative as a Rate of Change

3.5 Derivatives of Trigonometric Functions

3.6 The Chain Rule

3.7 Implicit Differentiation

3.8 Related Rates

3.9 Linearization and Differentials

4. Applications of Derivatives

4.1 Extreme Values of Functions

4.2 The Mean Value Theorem

4.3 Monotonic Functions and the First Derivative Test

4.4 Concavity and Curve Sketching

4.5 Applied Optimization

4.6 Newton's Method

4.7 Antiderivatives

5. Integration

5.1 Area and Estimating with Finite Sums

5.2 Sigma Notation and Limits of Finite Sums

5.3 The Definite Integral

5.4 The Fundamental Theorem of Calculus

5.5 Indefinite Integrals and the Substitution Method

5.6 Substitution and Area Between Curves

6. Applications of Definite Integrals

6.1 Volumes Using Cross-Sections

6.2 Volumes Using Cylindrical Shells

6.3 Arc Length

6.4 Areas of Surfaces of Revolution

6.5 Work and Fluid Forces

6.6 Moments and Centers of Mass

7. Transcendental Functions

7.1 Inverse Functions and Their Derivatives

7.2 Natural Logarithms

7.3 Exponential Functions

7.4 Exponential Change and Separable Differential Equations

7.5 Indeterminate Forms and L'Hôpital's Rule

7.6 Inverse Trigonometric Functions

7.7 Hyperbolic Functions

7.8 Relative Rates of Growth

8. Techniques of Integration

8.1 Integration by Parts

8.2 Trigonometric Integrals

8.3 Trigonometric Substitutions

8.4 Integration of Rational Functions by Partial Fractions

8.5 Integral Tables and Computer Algebra Systems

8.6 Numerical Integration

8.7 Improper Integrals

9. First-Order Differential Equations

9.1 Solutions, Slope Fields, and Euler's Method

9.2 First-Order Linear Equations

9.3 Applications

9.4 Graphical Solutions of Autonomous Equations

9.5 Systems of Equations and Phase Planes

10. Infinite Sequences and Series

10.1 Sequences

10.2 Infinite Series

10.3 The Integral Test

10.4 Comparison Tests

10.5 The Ratio and Root Tests

10.6 Alternating Series, Absolute 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 in Polar Coordinates

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. Integration in 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

17. Second-Order Differential Equations (online)

17.1 Second-Order Linear Equations

17.2 Nonhomogeneous Linear Equations

17.3 Applications

17.4 Euler Equations

17.5 Power-Series Solutions

Appendices

1. Real Numbers and the Real Line

2. Mathematical Induction

3. Lines, Circles, and Parabolas

4. Proofs of Limit Theorems

5. Commonly Occurring Limits

6. Theory of the Real Numbers

7. Complex Numbers

8. The Distributive Law for Vector Cross Products

9. The Mixed Derivative Theorem and the Increment Theorem

Courses

Calculus [COMPLETE TEXTS (CALCULUS 1-3)] (Mathematics)

Previous Edition(s)

Thomas' Calculus, Media Upgrade, 11/E
Thomas, Weir, Hass & Giordano
©2008 | Pearson | Cloth; 1228 pp | Instock
ISBN-10: 032148987X | ISBN-13: 9780321489876
Net price: $148.50 (What's this?)Brief Description |
Calculus hasn’t changed, but your students have. Many of today’s students have seen calculus before at the high school level. However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. Thomas’ Calculus, Media Upgrade, Eleventh Edition responds to the needs of today’s students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course.

Thomas’ Calculus, Media Upgrade, Eleventh Edition is now available with an enhanced MyMathLab^™ course—the ultimate homework, tutorial and study solution for today’s students. The enhanced MyMathLab course includes a rich and flexible set of course materials and features innovative Java™ Applets, Group Projects, and new MathXL^® exercises. This text is also available with WebAssign^® and WeBWorK^®.
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Product Tours

Online Walkthrough

Author Bios

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. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass’s current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.

Maurice D. Weir holds a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He is a Professor Emeritus of the Department of Applied Mathematics at the Naval Postgraduate School in Monterey, California. Weir enjoys teaching Mathematical Modeling and Differential Equations. His current areas of research include modeling and simulation as well as mathematics education. Weir has been awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He has coauthored eight books, including the University Calculus series and the twelfth edition of Thomas’ Calculus.

George B. Thomas, Jr. (late) of the Massachusetts Institute of Technology, was a professor of mathematics for thirty-eight years; he served as the executive officer of the department for ten years and as graduate registration officer for five years. Thomas held a spot on the board of governors of the Mathematical Association of America and on the executive committee of the mathematics division of the American Society for Engineering Education. His book, Calculus and Analytic Geometry, was first published in 1951 and has since gone through multiple revisions. The text is now in its twelfth edition and continues to guide students through their calculus courses. He also co-authored monographs on mathematics, including the text Probability and Statistics.

Websites and Online Courses

In this section:

Websites and Online Courses

Companion Website for Calculus
Pearson
©2010 | Pearson | Website | Live
ISBN-10: 0321691105 | ISBN-13: 9780321691101
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MathXL -- Instant Access -- for Thomas' Calculus, 12/E
Thomas, Weir & Hass
©2010 | Pearson | On-line Supplement | Live
ISBN-10: 0321627199 | ISBN-13: 9780321627193
Online purchase price: $50.00More Info

MyMathLabPlus for Calculus, 12/E
Thomas
©2011 | Pearson | Website | Live
ISBN-10: 0558809316 | ISBN-13: 9780558809317
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Online Video Lectures with Optional Captioning for Thomas' Calculus (MyMathLab only), 12/E
Thomas, Weir & Hass
©2010 | Pearson | On-line Supplement | Live
ISBN-10: 0321600746 | ISBN-13: 9780321600745
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Course & Discipline Resources

For Calculus
For the Mathematics Discipline

Instructor's Solutions Manual, Multivariable for Thomas' Calculus & Thomas' Calculus Early Transcendentals, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Paper; 456 pp | Instock
ISBN-10: 032160072X | ISBN-13: 9780321600721

Instructor's Solutions Manual, Single Variable for Thomas' Calculus, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Paper; 778 pp | Instock
ISBN-10: 0321608070 | ISBN-13: 9780321608079

PowerPoint Slides (Download only) for Thomas' Calculus, 12/E
Thomas, Weir & Hass
©2010 | Pearson | On-line Supplement | Live
ISBN-10: 0321676017 | ISBN-13: 9780321676016

TestGen® Computerized Test Bank for Thomas' Calculus, 12/E
Thomas, Weir & Hass
©2010 | Pearson | On-line Supplement | Live
ISBN-10: 0321627210 | ISBN-13: 9780321627216

Websites and online courses

Instructor's Edition for Thomas' Calculus, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Cloth; 1184 pp | Instock
ISBN-10: 0321600754 | ISBN-13: 9780321600752
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Companion Website for Calculus
Pearson
©2010 | Pearson | Website | Live
ISBN-10: 0321691105 | ISBN-13: 9780321691101
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MyMathLabPlus for Calculus, 12/E
Thomas
©2011 | Pearson | Website | Live
ISBN-10: 0558809316 | ISBN-13: 9780558809317
Online purchase price: $92.00More Info

Companion Website for Calculus
Pearson
©2010 | Pearson | Website | Live
ISBN-10: 0321691105 | ISBN-13: 9780321691101
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Maple Manual (Download only) for Calculus
Stapleton
©2010 | Pearson | On-line Supplement | Live
ISBN-10: 0321608089 | ISBN-13: 9780321608086
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Mathematica Manual (Download only) for Calculus
Vanisko
©2010 | Pearson | On-line Supplement | Live
ISBN-10: 0321608097 | ISBN-13: 9780321608093
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MyMathLabPlus for Calculus, 12/E
Thomas
©2011 | Pearson | Website | Live
ISBN-10: 0558809316 | ISBN-13: 9780558809317
Online purchase price: $92.00More Info

TI-83/TI-84 Plus and TI-89 Calculator Manual (Download only) for Calculus
McDonald-Newman
©2010 | Pearson | On-line Supplement; 300 pp | Live
ISBN-10: 0321690044 | ISBN-13: 9780321690043
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Pearson's Calculus Review Card, Multivariable for Thomas' Calculus, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Study Card; 0 pp | Instock
ISBN-10: 0321600738 | ISBN-13: 9780321600738
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Pearson's Calculus Review Card, Single Variable for Thomas' Calculus, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Study Card; 0 pp | Instock
ISBN-10: 0321608100 | ISBN-13: 9780321608109
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Student Solutions Manual, Multivariable, for Thomas' Calculus and Thomas' Calculus: Early Transcendentals, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Paper; 216 pp | Instock
ISBN-10: 0321600711 | ISBN-13: 9780321600714
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Student Solutions Manual, Single Variable for Thomas' Calculus, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Paper; 250 pp | Instock
ISBN-10: 0321600703 | ISBN-13: 9780321600707
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Insight Into Calculus: Using Texas Instruments Graphics Calculators
Ward & Wilberscheid
©1997 | Pearson | Paper; 304 pp | Instock
ISBN-10: 0132553651 | ISBN-13: 9780132553650
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Just-In-Time Algebra and Trigonometry for Early Transcendentals Calculus, 3/E
Mueller & Brent
©2006 | Pearson | Paper; 224 pp | Instock
ISBN-10: 0321320506 | ISBN-13: 9780321320506
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Just-In-Time Algebra and Trigonometry for Students of Calculus, 3/E
Mueller & Brent
©2005 | Pearson | Paper; 224 pp | Instock
ISBN-10: 0321269438 | ISBN-13: 9780321269430
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Maple Approach Calculus, A, 2/E
Gresser
©2002 | Pearson | Paper; 340 pp | Instock
ISBN-10: 0130920142 | ISBN-13: 9780130920140
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For the Mathematics Discipline

Allied Health Study Card, 2/E
Forshier
©2006 | Pearson | Study Card | Instock
ISBN-10: 0321394747 | ISBN-13: 9780321394743
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Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Pearson | Study Card; 6 pp | Instock
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Center for Excellence Sticker
Addison Wesley Higher Education Group
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Concept Videos: Algebra
Addison-Wesley
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Concept Videos: Basic Math & Prealgebra
Addison-Wesley
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ISBN-10: 032151758X | ISBN-13: 9780321517586
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Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997 | Pearson | Paper; 195 pp | Instock
ISBN-10: 0136492037 | ISBN-13: 9780136492030
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Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000 | Pearson | Paper | Instock
ISBN-10: 0321069188 | ISBN-13: 9780321069184
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Prealgebra Review Workbook
Wheel
©2006 | Pearson | Paper; 300 pp | Instock
ISBN-10: 0321473329 | ISBN-13: 9780321473325
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Review of Algebra, A
Howard
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ISBN-10: 0201773473 | ISBN-13: 9780201773477
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Spanish Basic Math Study Card
Leonarte
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TestGen All-in-One 2005 Package
Addison-Wesley
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Companion Website for Calculus
Pearson
©2010 | Pearson | Website | Live
ISBN-10: 0321691105 | ISBN-13: 9780321691101
More Info

MyMathLabPlus for Calculus, 12/E
Thomas
©2011 | Pearson | Website | Live
ISBN-10: 0558809316 | ISBN-13: 9780558809317
Online purchase price: $92.00More Info

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Thomas' Calculus plus MyMathLab Student Access Kit, 12/E
Thomas, Weir, Hass & Giordano
©2010 | Pearson | Kit/Package/ShrinkWrap | Instock
ISBN-10: 0321614690 | ISBN-13: 9780321614698
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Thomas' Calculus, Books a la Carte Edition, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Unbound (Saleable); 1080 pp | Instock
ISBN-10: 0321730674 | ISBN-13: 9780321730671
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Thomas' Calculus, Coursesmart eTextbook, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Electronic Book; 1236 pp | Available
ISBN-10: 0321614402 | ISBN-13: 9780321614407
Online purchase price: $78.99More Info | Students, buy access
Thomas' Calculus, Multivariable, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Paper; 584 pp | Instock
ISBN-10: 0321643690 | ISBN-13: 9780321643698
Net price: $76.00 (What's this?)Brief Description |
This text is designed for the multivariable component a three-semester or four-quarter calculus course (math, engineering, and science majors).

Calculus hasn’t changed, but your students have. Today’s students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. Thomas’ Calculus, Twelfth Edition, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.

The text is available with a robust MyMathLab^® course–an online homework, tutorial, and study solution designed for today’s students. In addition to interactive multimedia features like Java^™ applets and animations, thousands of MathXL^® exercises are available for students to get the practice they need.
More Info
Thomas' Calculus, Single Variable, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Paper; 936 pp | Instock
ISBN-10: 0321637429 | ISBN-13: 9780321637420
Net price: $76.00 (What's this?)Brief Description |
This text is designed for the single-variable component of a three-semester or four-quarter calculus course (math, engineering, and science majors).

Calculus hasn’t changed, but your students have. Today’s students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. Thomas’ Calculus, Twelfth Edition, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.

The text is available with a robust MyMathLab^® course–an online homework, tutorial, and study solution designed for today’s students. In addition to interactive multimedia features like Java^™ applets and animations, thousands of MathXL^® exercises are available for students to get the practice they need.
More Info
Thomas' Calculus, Single Variable Plus MyMathLab/MyStatLab Student Access Kit, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Kit/Package/ShrinkWrap | Instock
ISBN-10: 0321648447 | ISBN-13: 9780321648440
Net price: $83.50 (What's this?)More Info
Thomas' Calculus, Single Variable, Books a la Carte Edition, 12/E
Thomas, Weir & Hass
©2010 | Pearson | Unbound (Saleable); 750 pp | Instock
ISBN-10: 0321730682 | ISBN-13: 9780321730688
Net price: $45.60 (What's this?)More Info

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