Calculus, 3rd edition

William L. Briggs University of Colorado Denver
Lyle Cochran Whitworth University
Bernard Gillett University of Colorado Boulder
Eric Schulz Walla Walla Community College

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

Designed for today's calculus instructors and students

The much-anticipated 3rd Edition of Calculus 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.

Hallmark features of this title

Figures have been carefully crafted and reviewed. Whenever possible, the authors let the figures communicate essential ideas with annotations that echo an instructor's voice.
Annotated Examples:
- Worked-out examples have annotations in blue type to guide students through the process of a solution and to emphasize that each step in a mathematical argument is rigorously justified.
- These annotations echo how instructors talk through examples in lecture. They also help students who may struggle with the algebra and trigonometry steps in the solution process.
Quick Check questions encourage students to do the calculus as they are reading about it. These questions resemble the kinds of questions instructors pose in class.

New and updated features of this title

The exercise sets are a major focus of the revision. In response to reviewer and instructor feedback, the authors implemented some significant changes to the exercise sets by rearranging and relabeling exercises, modifying some exercises, and adding many new ones.
Of the approximately 10,400 exercises appearing in this edition, 18% are new and many of the exercises from second edition were revised for this edition.
A simplified exercise set structure went from 5 parts to 3: Getting Started, Practice Exercises, and Explorations and Challenges.
Chapter Review exercises received a major revamp to provide more exercises, particularly intermediate-level problems, and more opportunities for students to choose a strategy of solution. More than 26% of the Chapter Review exercises are new.

Highlights of the DIGITAL UPDATE for MyLab Math; available April 2023

Instructors, contact your sales rep to ensure you have the most recent version of the course.  

Nearly 500 new exercises added from the textbook to the MyLab
A new set of 3D printable versions of the interactive figures
New Math in the Real World animated videos
More example videos, with new videos providing alternate presentations of many key examples in calculus
Author review of Learning Aids and solutions for accuracy and fidelity with the text methods

Features of MyLab Math for the 3rd Edition

All interactive figures, interactive eTextbook, and any exercises that use Interactive Figures are now run on Wolfram Cloud instead of the Wolfram CDF Player.

Features of Pearson+ eTextbook for the 3rd Edition; available April 2023

The interactive eTextbook is now run on Wolfram Cloud instead of the Wolfram CDF Player.

1. Functions

1.1 Review of Functions
1.2 Representing Functions
1.3 Trigonometric Functions
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 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 and Exponential Functions

7.1 Inverse Functions
7.2 The Natural Logarithmic and Exponential Functions
7.3 Logarithmic and Exponential Functions with Other Bases
7.4 Exponential Models
7.5 Inverse Trigonometric Functions
7.6 L' Hôpital's Rule and Growth Rates of Functions
7.7 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

13. Vectors and the Geometry of Space

13.1 Vectors in the Plane
13.2 Vectors in Three Dimensions
13.3 Dot Products
13.4 Cross Products
13.5 Lines and Planes in Space
13.6 Cylinders and Quadric Surfaces
Review Exercises

14. Vector-Valued Functions

14.1 Vector-Valued Functions
14.2 Calculus of Vector-Valued Functions
14.3 Motion in Space
14.4 Length of Curves
14.5 Curvature and Normal Vectors
Review Exercises

15. Functions of Several Variables

15.1 Graphs and Level Curves
15.2 Limits and Continuity
15.3 Partial Derivatives
15.4 The Chain Rule
15.5 Directional Derivatives and the Gradient
15.6 Tangent Planes and Linear Approximation
15.7 Maximum/Minimum Problems
15.8 Lagrange Multipliers
Review Exercises

16. Multiple Integration

16.1 Double Integrals over Rectangular Regions
16.2 Double Integrals over General Regions
16.3 Double Integrals in Polar Coordinates
16.4 Triple Integrals
16.5 Triple Integrals in Cylindrical and Spherical Coordinates
16.6 Integrals for Mass Calculations
16.7 Change of Variables in Multiple Integrals
Review Exercises

17. Vector Calculus

17.1 Vector Fields
17.2 Line Integrals
17.3 Conservative Vector Fields
17.4 Green's Theorem
17.5 Divergence and Curl
17.6 Surface Integrals
17.7 Stokes' Theorem
17.8 Divergence Theorem
Review Exercises

D2 Second-Order Differential Equations ONLINE

D2.1 Basic Ideas
D2.2 Linear Homogeneous Equations
D2.3 Linear Nonhomogeneous Equations
D2.4 Applications
D2.5 Complex Forcing Functions
Review Exercises

APPENDICES

A. Proofs of Selected Theorems
B. Algebra Review ONLINE
C. Complex Numbers ONLINE

Answers

Index

Table of Integrals

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.

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