**Essential Calculus: Early Transcendentals 2nd Edition by James Stewart, ISBN-13: 978-1133112280**

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- Publisher: Cengage Learning; 2nd edition (January 25, 2012)
- Language: English
- 960 pages
- ISBN-10: 1133112285
- ISBN-13: 978-1133112280

This book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers?

* ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS, Second Edition,* offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 900 pages–two-thirds the size of Stewart’s other calculus texts, and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book’s website, www.StewartCalculus.com. Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart’s other books. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart’s textbooks the best-selling calculus texts in the world.

**Table of Contents:**

Contents

Preface

To the Student

Diagnostic Tests

Ch 1: Functions and Limits

1.1 Functions and Their Representations

1.1 Exercises

1.2 A Catalog of Essential Functions

1.2 Exercises

1.3 The Limit of a Function

1.3 Exercises

1.4 Calculating Limits

1.4 Exercises

1.5 Continuity

1.5 Exercises

1.6 Limits Involving Infinity

1.6 Exercises

Chapter 1: Review

Ch 2: Derivatives

2.1 Derivatives and Rates of Change

2.1 Exercises

2.2 The Derivative as a Function

2.2 Exercises

2.3 Basic Differentiation Formulas

2.3 Exercises

2.4 The Product and Quotient Rules

2.4 Exercises

2.5 The Chain Rule

2.5 Exercises

2.6 Implicit Differentiation

2.6 Exercises

2.7 Related Rates

2.7 Exercises

2.8 Linear Approximations and Differentials

2.8 Exercises

Chapter 2: Review

Ch 3: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

3.1 Exponential Functions

3.1 Exercises

3.2 Inverse Functions and Logarithms

3.2 Exercises

3.3 Derivatives of Logarithmic and Exponential Functions

3.3 Exercises

3.4 Exponential Growth and Decay

3.4 Exercises

3.5 Inverse Trigonometric Functions

3.5 Exercises

3.6 Hyperbolic Functions

3.6 Exercises

3.7 Indeterminate Forms and L’Hospital’s Rule

3.7 Exercises

Chapter 3: Review

Ch 4: Applications of Differentiation

4.1 Maximum and Minimum Values

4.1 Exercises

4.2 The Mean Value Theorem

4.2 Exercises

4.3 Derivatives and the Shapes of Graphs

4.3 Exercises

4.4 Curve Sketching

4.4 Exercises

4.5 Optimization Problems

4.5 Exercises

4.6 Newton’s Method

4.6 Exercises

4.7 Antiderivatives

4.7 Exercises

Chapter 4: Review

Ch 5: Integrals

5.1 Areas and Distances

5.1 Exercises

5.2 The Definite Integral

5.2 Exercises

5.3 Evaluating Definite Integrals

5.3 Exercises

5.4 The Fundamental Theorem of Calculus

5.4 Exercises

5.5 The Substitution Rule

5.5 Exercises

Chapter 5: Review

Ch 6: Techniques of Integration

6.1 Integration by Parts

6.1 Exercises

6.2 Trigonometric Integrals and Substitutions

6.2 Exercises

6.3 Partial Fractions

6.3 Exercises

6.4 Integration with Tables and Computer Algebra Systems

6.4 Exercises

6.5 Approximate Integration

6.5 Exercises

6.6 Improper Integrals

6.6 Exercises

Chapter 6: Review

Ch 7: Applications of Integration

7.1 Areas between Curves

7.1 Exercises

7.2 Volumes

7.2 Exercises

7.3 Volumes by Cylindrical Shells

7.3 Exercises

7.4 Arc Length

7.4 Exercises

7.5 Area of a Surface of Revolution

7.5 Exercises

7.6 Applications to Physics and Engineering

7.6 Exercises

7.7 Differential Equations

7.7 Exercises

Chapter 7: Review

Ch 8: Series

8.1 Sequences

8.1 Exercises

8.2 Series

8.2 Exercises

8.3 The Integral and Comparison Tests

8.3 Exercises

8.4 Other Convergence Tests

8.4 Exercises

8.5 Power Series

8.5 Exercises

8.6 Representing Functions as Power Series

8.6 Exercises

8.7 Taylor and Maclaurin Series

8.7 Exercises

8.8 Applications of Taylor Polynomials

8.8 Exercises

Chapter 8: Review

Ch 9: Parametric Equations and Polar Coordinates

9.1 Parametric Curves

9.1 Exercises

9.2 Calculus with Parametric Curves

9.2 Exercises

9.3 Polar Coordinates

9.3 Exercises

9.4 Areas and Lengths in Polar Coordinates

9.4 Exercises

9.5 Conic Sections in Polar Coordinates

9.5 Exercises

Chapter 9: Review

Ch 10: Vectors and the Geometry of Space

10.1 Three-Dimensional Coordinate Systems

10.1 Exercises

10.2 Vectors

10.2 Exercises

10.3 The Dot Product

10.3 Exercises

10.4 The Cross Product

10.4 Exercises

10.5 Equations of Lines and Planes

10.5 Exercises

10.6 Cylinders and Quadric Surfaces

10.6 Exercises

10.7 Vector Functions and Space Curves

10.7 Exercises

10.8 Arc Length and Curvature

10.8 Exercises

10.9 Motion in Space: Velocity and Acceleration

10.9 Exercises

Chapter 10: Review

Ch 11: Partial Derivatives

11.1 Functions of Several Variables

11.1 Exercises

11.2 Limits and Continuity

11.2 Exercises

11.3 Partial Derivatives

11.3 Exercises

11.4 Tangent Planes and Linear Approximations

11.4 Exercises

11.5 The Chain Rule

11.5 Exercises

11.6 Directional Derivatives and the Gradient Vector

11.6 Exercises

11.7 Maximum and Minimum Values

11.7 Exercises

11.8 Lagrange Multipliers

11.8 Exercises

Chapter 11: Review

Ch 12: Multiple Integrals

12.1 Double Integrals over Rectangles

12.1 Exercises

12.2 Double Integrals over General Regions

12.2 Exercises

12.3 Double Integrals in Polar Coordinates

12.3 Exercises

12.4 Applications of Double Integrals

12.4 Exercises

12.5 Triple Integrals

12.5 Exercises

12.6 Triple Integrals in Cylindrical Coordinates

12.6 Exercises

12.7 Triple Integrals in Spherical Coordinates

12.7 Exercises

12.8 Change of Variables in Multiple Integrals

12.8 Exercises

Chapter 12: Review

Ch 13: Vector Calculus

13.1 Vector Fields

13.1 Exercises

13.2 Line Integrals

13.2 Exercises

13.3 The Fundamental Theorem for Line Integrals

13.3 Exercises

13.4 Green’s Theorem

13.4 Exercises

13.5 Curl and Divergence

13.5 Exercises

13.6 Parametric Surfaces and Their Areas

13.6 Exercises

13.7 Surface Integrals

13.7 Exercises

13.8 Stokes’ Theorem

13.8 Exercises

13.9 The Divergence Theorem

13.9 Exercises

Chapter 13: Review

Appendixes

Appendix A: Trigonometry

Appendix B: Sigma Notation

Appendix C: The Logarithm Defined as an Integral

Appendix D: Proofs

Appendix E: Answers to Odd-Numbered Exercises

Index

* James Stewart *received the M.S. degree from Stanford University and the Ph.D. from the University of Toronto. After two years as a postdoctoral fellow at the University of London, he became Professor of

*at McMaster University. His research has been in harmonic analysis and functional analysis. Stewart’s books include a series of high school textbooks as well as a best-selling series of calculus textbooks. He is also co-author, with Lothar Redlin and Saleem Watson, of a series of college algebra and precalculus textbooks. Translations of his books include those in Spanish, Portuguese, French, Italian, Korean, Chinese, Greek, and Indonesian.*

**Mathematics**A talented violinst, Stewart was concertmaster of the McMaster Symphony Orchestra for many years and played professionally in the Hamilton Philharmonic Orchestra. Having explored connections between music and mathematics, Stewart has given more than 20 talks worldwide on Mathematics and Music and is planning to write a book that attempts to explain why mathematicians tend to be musical.

Stewart was named a Fellow of the Fields Institute in 2002 and was awarded an honorary D.Sc. in 2003 by McMaster University. The library of the Fields Institute is named after him. The James Stewart Mathematics Centre was opened in October, 2003, at McMaster University.

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