Thomas' Calculus Early Transcendentals / Edition 12

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Overview

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: Early Transcendentals, 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, and improved conceptual flow.

This is the full version of the text contains Chapters 1-16. ISBN-10:0321628837 ISBN-13:9780321628831 Thomas Calculus Early Transcendentals, Single Variable) contains Chapters 1-11. The Multivariable version of the text contains Chapters 11-16. MyMathLab access is not included with this ISBN.

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Product Details

  • ISBN-13: 9780321588760
  • Publisher: Pearson
  • Publication date: 1/1/2010
  • Series: Thomas Calculus 12th Edition Series
  • Edition description: Older Edition
  • Edition number: 12
  • Pages: 1160
  • Sales rank: 307,651
  • Product dimensions: 8.80 (w) x 11.00 (h) x 1.70 (d)

Meet the Author

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.

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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

1.5 Exponential Functions

1.6 Inverse Functions and Logarithms

2. Limits and Derivatives

2.1 Rates of Change and Tangents to Curves

2.2 Limit of a Function and Limit Laws

2.3 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 Rules for Polynomials, Exponentials, Products, and Quotients

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 Derivatives of Inverse Functions and Logarithms

3.9 Inverse Trigonometric Functions

3.10 Related Rates

3.11 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 Indeterminate Forms and L'Hopital's Rule

4.6 Applied Optimization

4.7 Newton's Method

4.8 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 Rule

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. Integrals and Transcendental Functions

7.1 The Logarithm Defined as an Integral

7.2 Exponential Change and Separable Differential Equations

7.3 Hyperbolic Functions

7.4 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

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Sort by: Showing all of 2 Customer Reviews
  • Anonymous

    Posted April 13, 2004

    Book is for review not first timers

    I agree with the previous review. I am currently using this book and it seems that the newer editions of math books are traversing away from complete understanding of the assigned problems. I get lost in the verbage. The few examples that are covered don't really help you understand the assigned problems. I am finding myself reviewing older editions that I have since 1999 in order to attain full understanding. My personal opinion is that it seems the book is written as a review for people who have already taken the series of calculus classes this book represents.

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  • Anonymous

    Posted November 17, 2003

    Really Bad Calculus Book

    This book stinks! It clearly is written for a Math instructor, or someone who has already taken Calculus before. Text material will drone on, and on about some topic, never give you any real meat about it, then the problems expect the reader to make some leap of understanding. This is a terrible book for students first learning Calc. In the solution manual, I have even seen problems solved using a method that isn't intorduced in that section but a later section. The reading material doesn't give you anything good to hang on to. Some of the problems even rely on you having done a previous problem to understand how to conquer it, yet it doesn't refer you to that problem to get that bit of vital information. I haven't been alone in my poor opinion of the book; although the instructor keeps trying to sell it, the students all think it's really a bad text. Some students have picked up other texts from the library to read the material we're supposed to be covering, so they can get some better understanding of it than what this text offers. Reeeeeeally BAD, from the student's perspective!

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