Calculus with Precalculus, 3rd edition

Published by Pearson (February 4, 2025) © 2025

  • William L. Briggs University of Colorado Denver
  • Eric Schulz Walla Walla Community College

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For courses in Calculus.

Strengthen foundational calculus skills

The popular Calculus: Early Transcendentals, 3rd Edition by Briggs, Schulz, Gillett and Cochran is now reinforced with complete precalculus support to help students bridge potential skill gaps. Calculus with Precalculus: Early Transcendentals retains the proven features of the acclaimed calculus text while introducing expanded support content for courses where students may need a more in-depth refresh of prerequisite skills.

New features, additional content, and support resources have been added to the available MyLab® Math course and eTextbook to create an invaluable resource in supporting corequisite, drop down and slow calculus use cases; a new optional package is also available that is ideal for boot camp use cases.

Hallmark features of this title

Classic features of Briggs Calculus retained for Calculus with Precalculus:

  • 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.
  • Revised exercise sets are a major focus of the revision and include significant changes based on user feedback, including rearranging and relabeling exercises, modifying some exercises, and adding many new ones.
    • A simplified exercise set structure streamlines from 5 parts to 3: Getting Started, Practice Exercises, Explorations and Challenges.
    • Revamped Chapter Review exercises 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.
  • 720+ Interactive Figures save instructors time in class and to hold students accountable for deeper visual understanding. (Not available in print versions.)
  • Video Assignments are available for each section of the text. These editable assignments are perfect for any class format, including online, hybrid or flipped classroom.  (Not available in print versions.)

New and updated features of this title

Added precalculus support features in Calculus with Precalculus:

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

  • 30 new Progressive Worksheets for Calc I and Calc II take students from College Algebra to Precalculus to Calculus in the same worksheet. 
  • New Implementation Guides for Corequisite, Drop Down, Slow Calculus, and Boot Camp options: The Implementation Guides are written by experienced educators and include data based best practices and suggestions.
  • Expanded Integrated Review assignments give students even more practice for Basic, College Algebra and Precalculus objectives. MyLab Math then personalizes the assignments for each student’s needs.
  • New Readiness Check Quizzes for Calc I, Calc II, and Calc III are available.
  • New optional package includes Pearson's MyMathTest for an adaptive Boot Camp experience.  Contact your local Pearson representative for more information.

Highlights of MyLab Math for Calculus with Precalculus (available for Fall 2025 classes) 

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

  • New Video Assignments are available for each section of the text. These editable assignments are perfect for any class format, including online, hybrid or flipped classroom. 
  • 30 new Progressive Worksheets for Calc I and Calc II take students from College Algebra to Precalculus to Calculus in the same worksheet. 
  • New Implementation Guides for Corequisite, Drop Down, Slow Calculus, and Boot Camp options are written by experienced educators, and include data-based best practices and suggestions.
  • Expanded Integrated Review assignments give students even more practice for Basic, College Algebra and Precalculus objectives. MyLab Math then personalizes the assignments for each student’s needs.
  • New Readiness Check Quizzes for Calc I, Calc II, and Calc III are available.
  • New optional package includes Pearson's MyMathTest for an adaptive Boot Camp experience.  Contact your local Pearson representative for more information.

Features retained from MyLab Math for Briggs Calculus, 3rd Edition

  • All interactive figures, interactive eTextbook, and any exercises that use Interactive Figures are run on Wolfram Cloud instead of the Wolfram CDF Player.
  • Also included: 3D printable versions of the interactive figures, Math in the Real World animated videos, example videos, and author review of Learning Aids and solutions for accuracy and fidelity with the text methods.

Original Calculus Content

  • 1: Functions
    • Introduction
    • 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
    • Guided Projects
  • 2: Limits
    • Introduction
    • 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
    • Guided Projects
  • 3: Exponentials and Logarithms
    • Introduction
    • 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
    • Guided Projects
  • 4: Applications of the Derivative
    • Introduction
    • 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
    • Guided Projects
  • 5: Integration
    • Introduction
    • 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
    • Guided Projects
  • 6: Applications of Integration
    • Introduction
    • 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
    • Guided Projects
  • 7: Logarithmic, Exponential, and Hyperbolic Functions
    • Introduction
    • 7.1 Logarithmic and Exponential Functions Revisited
    • 7.2 Exponential Models
    • 7.3 Hyperbolic Functions
    • Review Exercises
    • Guided Projects
  • 8: Integration Techniques
    • Introduction
    • 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
    • Guided Projects
  • 9: Vectors
    • Introduction
    • 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
    • Guided Projects
  • 10: Sequences and Infinite Series
    • Introduction
    • 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
    • Guided Projects
  • 11: Power Series
    • Introduction
    • 11.1 Approximating Functions with Polynomials
    • 11.2 Properties of Power Series
    • 11.3 Taylor Series
    • 11.4 Working with Taylor Series
    • Review Exercises
    • Guided Projects
  • 12: Parametric and Polar Curves
    • Introduction
    • 12.1 Parametric Equations
    • 12.2 Polar Coordinates
    • 12.3 Calculus in Polar Coordinates
    • 12.4 Conic Sections
    • Review Exercises
    • Guided Projects
  • 13: Vectors and the Geometry of Space
    • Introduction
    • 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
    • Guided Projects
  • 14: Vector-Valued Functions
    • Introduction
    • 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
    • Guided Projects
  • 15: Functions of Several Variables
    • Introduction
    • 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
    • Guided Projects
  • 16: Multiple Integration
    • Introduction
    • 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
    • Guided Projects
  • 17: Vector Calculus
    • Introduction
    • 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
    • Guided Projects
  • Chapter D2: Second-order Differential Equations
    • D2 Introduction
    • D2.1 Basic Ideas
    • D2.2 Linear Homogenous Equations
    • D2.3 Linear Nonhomogenous Equations
    • D2.4 Applications
    • D2.5 Complex Forcing Functions
  • Appendices
    • A: Proof of Selected Theorems
    • B: Algebra; Set of Real Numbers; Absolute Value; Cartesian Coordinate System; Equation of Lines; Answers
    • C: Complex Numbers; Complex Arithmetic; Answers

Answers

Index

Index of Applications

Table of Integrals

Useful References

Precalculus Content

  • 1: Functions
    • 1.1 Introduction to Functions
    • 1.2 Graphs
    • 1.3 Linear Functions
    • 1.4 Combination of Functions
    • 1.5 Families of Functions
    • Summary and Review Exercises
  • 2: Polynomial and Rational Functions
    • 2.1 Quadratic Functions
    • 2.2 Polynomial Functions
    • 2.3 Real Roots and Factors of Polynomial Functions
    • 2.4 Complex Numbers
    • 2.5 Complex Roots of Polynomial Functions
    • 2.6 Rational Functions
    • 2.7 Inequalities
    • Summary and Review Exercises
  • 3: Exponentials and Logarithms
    • 3.1 Exponential Functions
    • 3.2 Inverse Functions
    • 3.3 Logarithmic Functions
    • 3.4 Logarithmic Identities
    • 3.5 Solving Exponential and Logarithmic Equations
    • Summary and Review Exercises
  • 4: Unit Circle Trigonometry
    • 4.1 Angles and their measures
    • 4.2 Unit Circle Definitions of Sine, Cosine, and Tangent
    • 4.3 Sine, Cosine, and Tangent Functions
    • 4.4 Secant, Cosecant, and Cotangent Functions
    • 4.5 Inverse Trigonometric Functions
    • Summary and Review Exercises
  • 5: Triangle Trigonometry
    • 5.1 Right Triangle Trigonometry
    • 5.2 Right Triangles and the Unit Circle
    • 5.3 Law of Sines
    • 5.4 Law of Cosines
    • 5.5 Application of Triangles
    • Summary and Review Exercises
  • 6: Trigonometric Identities
    • 6.1 Fundamental Identities
    • 6.2 Sum, Difference, and Double-Angle Identities
    • 6.3 Power-Reducing, Half-Angle, and Product-Sum Identities
    • 6.4 Solving Trigonometric Equations
    • Summary and Review Exercises
  • 7: Parametric and Polar Graphs
    • 7.1 Parametric Equations
    • 7.2 Polar Coordinates
    • 7.3 Polar Graphs
    • 7.4 Polar Form of Complex Numbers; DeMoivre's Theorem
    • Summary and Review Exercises
  • 8: Conic Sections
    • 8.1 Parabolas
    • 8.2 Ellipses and Circles
    • 8.3 Hyperbolas
    • 8.4 Eccentricity and Polar Equations of Conic Sections
    • Summary and Review Exercises
  • 9: Vectors
    • 9.1 Vectors in Two Dimensions
    • 9.2 Vectors in Three Dimensions
    • 9.3 Dot Product
    • 9.4 Cross Product
    • Summary and Review Exercises
  • 10: Systems of Equations and Matrices
    • 10.1 Systems of Equations and Inequalities
    • 10.2 Matrices
    • 10.3 Method of Partial Fractions
    • Summary and Review Exercises<
  • Appendices
    • A: Looking Forward to Calculus: Limits
    • B: Looking Forward to Calculus: Sequence and Series

Answers to Odd Exercises

Index

Application Index

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 2 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.

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.

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.

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.

Julianne Connell Sachs has undergraduate degrees in Mathematics and Spanish, and a graduate degree in Mathematics from Western Washington University. She taught math and physics in Guatemala for 1 year before joining the faculty at Walla Walla Community College in 2001. Julianne teaches courses ranging from beginning algebra through differential equations at WWCC. Through active learning and the strategic use of technology, she strives to guide students toward a deeper understanding of mathematics.

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