Calculus: Early Transcendentals 3rd Edition © 2019
Calculus: Early Transcendentals, published by Pearson, brings clear, advanced thinking to courses teaching singlevariable and multivariable calculus. Digital integration provides more resources that can be used both in class and at home.
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More About Calculus: Early Transcendentals

William Briggs Author BioWilliam Briggs has been on the mathematics faculty at the University of Colorado at Denver for twentythree years. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard Univeristy. He teaches undergraduate and graduate courses throughout the mathematics curriculum with a special interest in mathematical modeling and differential equations ans 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 Author BioLyle 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 Author BioBernard 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 twentyyear career, receiving five 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 four climbing guides for the mountains in and surrounding Rocky Mountain National Park.

Eric Schulz Author BioEric 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, Gillett, and Precalculus with Sachs, 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 FirstOrder 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. VectorValued Functions
 14.1 VectorValued Functions
 14.2 Calculus of VectorValued 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 SecondOrder 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
Appendix A. Proofs of Selected Theorems
Appendix B. Algebra Review ONLINE
Appendix C. Complex Numbers ONLINE
Answers
Index
Table of Integrals
1. Functions
2. Limits
3. Derivatives
4. Applications of the Derivative
5. Integration
6. Applications of Integration
7. Logarithmic, Exponential, and Hyperbolic Functions
8. Integration Techniques
9. Differential Equations
10. Sequences and Infinite Series
11. Power Series
12. Parametric and Polar Curves
13. Vectors and the Geometry of Space
14. VectorValued Functions
15. Functions of Several Variables
16. Multiple Integration
17. Vector Calculus
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