Calculus: Early Transcendentals 3rd Edition © 2019

Calculus: Early Transcendentals, published by Pearson, brings clear, advanced thinking to courses teaching single-variable and multivariable calculus. Digital integration provides more resources that can be used both in class and at home.

  • Online Support with MyMathLab® for School from Pearson
  • Exercise sets revised based on instructor feedback
  • Figures improved to facilitate learning in new ways

Calculus Program with Digital Integration

Early Transcendentals offers a high school calculus program with robust resources and differentiation that empowers learners.

Improved Student Results

Lesson structures and online resources work with students where they are to help them better understand the material and perform at a higher level.

Trusted Content

Our team of highly respected authors improved the interactive elements and course-specific exercises to refine the successful aspects of this program.

Curricular Flexibility

MyMathLab® for School allows teachers to build their own assignments, teach multiple sections, and set prerequisites so the course best fits everyone’s needs.


Self-Reflection and Engagement

33 assessments including stress management, diagnosing poor performance, enhancing motivation, and time motivation help students know themselves and identify issues that cause them to struggle in class.

Calculus Teaching Solutions

  • Revised Textbook
  • Deliver Trusted Content
  • Empower Every Learner
  • Teach Your Course Your Way
  • Improved Comprehension
    The authors made changes to the textbook so students could better understand and work through the exercise sets.
  • Figure Annotations
    Annotations on the figures read like an instructor speaks. Ideas are presented more clearly and students learn in new ways.
  • Worked-out Examples
    Worked-out examples help guide students through the process of a solution. They emphasize the rigorous justification needed for each step in a mathematical argument.
  • Quick Check Questions
    Quick Check questions encourage students to do the calculus while they are reading about it the way a teacher might test their skills during a lecture.
  • Setup & Solve Exercises
    Setup & Solve Exercises require students to show how they prepare a problem and arrive at the solution. This structure reflects how students need to work through tests.
  • Conceptual Questions
    Written by faculty at Cornell University, additional Conceptual Questions focus on a deeper theoretical understanding of key ideas in calculus.
  • Additional Practice Problems
    Additional practice problems beyond those in the textbook have been added to selected sections in MyMathLab for School. Labeled EXTRA, they pair well with chapter reviews and practice tests.
  • Enhanced Interactive Figures
    Mathematically richer Enhanced Interactive Figures illustrate concepts that are difficult for students to visualize and connect to key themes of calculus.
  • Instructional Videos
    All new, full-lecture Instructional Videos combine Interactive Figures and easier navigation. Students can easily reach and grasp the content they need to know.
  • Enhanced Sample Assignments
    Section-level Enhanced Sample Assignments include just-in-time prerequisite review. Their spaced practice of key concepts keep skills fresh. Students work without study aids to check their understanding.
  • Integrated Review Version
    An Integrated Review version of the online course contains pre-made, assignable quizzes to assess the prerequisite skills needed for each chapter. Each student receives the personalized remediation they need for any skills gaps.
  • Guided Projects
    78 Guided Projects allow students to work in a directed, step-by-step fashion, with various objectives. They vividly demonstrate the breadth of calculus and provide a wealth of mathematical excursions beyond the typical class experience.
  • Learning Catalytics
    Learning Catalytics uses students’ smartphones, tablets, or laptops to interest them in more interactive tasks and thinking during lecture. It fosters engagement and peer-to-peer learning with real-time analytics.

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More About Calculus: Early Transcendentals

  • William Briggs Author Bio
    William Briggs has been on the mathematics faculty at the University of Colorado at Denver for twenty-three 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 Bio
    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 Author Bio
    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 twenty-year 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 Bio
    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, 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 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

    Appendix A. Proofs of Selected Theorems

    Appendix B. Algebra Review ONLINE

    Appendix C. Complex Numbers ONLINE



    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. Vector-Valued Functions
    15. Functions of Several Variables
    16. Multiple Integration
    17. Vector Calculus

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