Single Variable Calculus: Early Transcendentals / Edition 2

by William Briggs

Overview

For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics.

The most successful new calculus text in the last two decades

The much-anticipated 3rd Edition of Briggs’ Calculus Series retains its hallmark features while introducing important advances and refinements. Briggs, Cochran, Gillett, and Schulz build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor. Examples are stepped out and thoughtfully annotated, and figures are designed to teach rather than simply supplement the narrative. The groundbreaking eBook contains approximately 700 Interactive Figures that can be manipulated to shed light on key concepts.

For the 3rd Edition, the authors synthesized feedback on the text and MyLab™ Math content from over 140 instructors and an Engineering Review Panel. This thorough and extensive review process, paired with the authors’ own teaching experiences, helped create a text that was designed for today’s calculus instructors and students.

Also available with MyLab Math

MyLab Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student.

Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

If you would like to purchase both the physical text and MyLab Math, search for:

0134996712 / 9780134996714 Single Variable Calculus: Early Transcendentals and MyLab Math with Pearson eText - Title-Specific Access Card Package, 3/e
Package consists of:

• 0134766857 / 9780134766850 Calculus: Early Transcendentals, Single Variable
• 0134856929 / 9780134856926 MyLab Math with Pearson eText - Standalone Access Card - for Calculus: Early Transcendentals, Single Variable

Product Details

ISBN-13:	2900321954236
Publisher:	Pearson Education
Publication date:	12/24/2013
Edition description:	Older Edition
Pages:	888
Product dimensions:	8.60(w) x 10.80(h) x 1.20(d)

About the Author

About our authors

William Briggs has been on the mathematics faculty at the University of Colorado at Denver for 23 years. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard University. He teaches undergraduate and graduate courses throughout the mathematics curriculum, with a special interest in mathematical modeling and differential equations as it applies to problems in the biosciences. He has written a quantitative reasoning textbook, Using and Understanding Mathematics; an undergraduate problem solving book, Ants, Bikes, and Clocks; and two tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform. He is the Society for Industrial and Applied Mathematics (SIAM) Vice President for Education, a University of Colorado President's Teaching Scholar, a recipient of the Outstanding Teacher Award of the Rocky Mountain Section of the Mathematical Association of America (MAA), and the recipient of a Fulbright Fellowship to Ireland.

Lyle Cochran is a professor of mathematics at Whitworth University in Spokane, Washington. He holds BS degrees in mathematics and mathematics education from Oregon State University and a MS and PhD in mathematics from Washington State University. He has taught a wide variety of undergraduate mathematics courses at Washington State University, Fresno Pacific University, and since 1995 at Whitworth University. His expertise is in mathematical analysis, and he has a special interest in the integration of technology and mathematics education. He has written technology materials for leading calculus and linear algebra textbooks including the Instructor's Mathematica Manual for Linear Algebra and Its Applications by David C. Lay and the Mathematica Technology Resource Manual for Thomas' Calculus. He is a member of the MAA and a former chair of the Department of Mathematics and Computer Science at Whitworth University.

Bernard Gillett is a Senior Instructor at the University of Colorado at Boulder; his primary focus is undergraduate education. He has taught a wide variety of mathematics courses over a 20-year career, receiving 5 teaching awards in that time. Bernard authored a software package for algebra, trigonometry, and precalculus; the Student's Guide and Solutions Manual and the Instructor's Guide and Solutions Manual for Using and Understanding Mathematics by Briggs and Bennett; and the Instructor's Resource Guide and Test Bank for Calculus and Calculus: Early Transcendentals by Briggs, Cochran and Gillett. Bernard is also an avid rock climber and has published 4 climbing guides for the mountains in and surrounding Rocky Mountain National Park.

Eric Schulz has been teaching mathematics at Walla Walla Community College since 1989 and began his work with Mathematica in 1992. He has an undergraduate degree in mathematics from Seattle Pacific University and a graduate degree in mathematics from the University of Washington. Eric loves working with students and is passionate about their success. His interest in innovative and effective uses of technology in teaching mathematics has remained strong throughout his career. He is the developer of the Basic Math Assistant, Classroom Assistant, and Writing Assistant palettes that ship in Mathematica worldwide. He is an author on multiple textbooks: Calculus and Calculus: Early Transcendentals with Briggs, Cochran and Gillett, and Precalculus with Sachs and Briggs, where he writes, codes and creates dynamic eTexts combining narrative, videos and Interactive Figures using Mathematica and CDF technology.

Table of Contents

1. Functions

1.1 Review of Functions

1.2 Representing Functions

1.3 Inverse, Exponential, and Logarithmic Functions

1.4 Trigonometric Functions and Their Inverses

Review Exercises

2. Limits

2.1 The Idea of Limits

2.2 Definitions of Limits

2.3 Techniques for Computing Limits

2.4 Infinite Limits

2.5 Limits at Infinity

2.6 Continuity

2.7 Precise Definitions of Limits

Review Exercises

3. Derivatives

3.1 Introducing the Derivative

3.2 The Derivative as a Function

3.3 Rules of Differentiation

3.4 The Product and Quotient Rules

3.5 Derivatives of Trigonometric Functions

3.6 Derivatives as Rates of Change

3.7 The Chain Rule

3.8 Implicit Differentiation

3.9 Derivatives of Logarithmic and Exponential Functions

3.10 Derivatives of Inverse Trigonometric Functions

3.11 Related Rates

Review Exercises

4. Applications of the Derivative

4.1 Maxima and Minima

4.2 Mean Value Theorem

4.3 What Derivatives Tell Us

4.4 Graphing Functions

4.5 Optimization Problems

4.6 Linear Approximation and Differentials

4.7 L'Hôpital's Rule

4.8 Newton's Method

4.9 Antiderivatives

Review Exercises

5. Integration

5.1 Approximating Areas under Curves

5.2 Definite Integrals

5.3 Fundamental Theorem of Calculus

5.4 Working with Integrals

5.5 Substitution Rule

Review Exercises

6. Applications of Integration

6.1 Velocity and Net Change

6.2 Regions Between Curves

6.3 Volume by Slicing

6.4 Volume by Shells

6.5 Length of Curves

6.6 Surface Area

6.7 Physical Applications

Review Exercises

7. Logarithmic, Exponential, and Hyperbolic Functions

7.1 Logarithmic and Exponential Functions Revisited

7.2 Exponential Models

7.3 Hyperbolic Functions

Review Exercises

8. Integration Techniques

8.1 Basic Approaches

8.2 Integration by Parts

8.3 Trigonometric Integrals

8.4 Trigonometric Substitutions

8.5 Partial Fractions

8.6 Integration Strategies

8.7 Other Methods of Integration

8.8 Numerical Integration

8.9 Improper Integrals

Review Exercises

9. Differential Equations

9.1 Basic Ideas

9.2 Direction Fields and Euler's Method

9.3 Separable Differential Equations

9.4 Special First-Order Linear Differential Equations

9.5 Modeling with Differential Equations

Review Exercises

10. Sequences and Infinite Series

10.1 An Overview

10.2 Sequences

10.3 Infinite Series

10.4 The Divergence and Integral Tests

10.5 Comparison Tests

10.6 Alternating Series

10.7 The Ratio and Root Tests

10.8 Choosing a Convergence Test

Review Exercises

11. Power Series

11.1 Approximating Functions with Polynomials

11.2 Properties of Power Series

11.3 Taylor Series

11.4 Working with Taylor Series

Review Exercises

12. Parametric and Polar Curves

12.1 Parametric Equations

12.2 Polar Coordinates

12.3 Calculus in Polar Coordinates

12.4 Conic Sections

Review Exercises

Appendix A. Proofs of Selected Theorems

Appendix B. Algebra Review ONLINE

Appendix C. Complex Numbers ONLINE

Answers

Index

Table of Integrals