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Interactive Calculus, Early Transcendentals, 1st edition

Published by Pearson (July 18, 2023) © 2024

  • Jason Gregersen Michigan Technological University
  • Marc Renault Shippensburg University
  • Rachel Vincent-Finley Southern University

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For 3-semester or 4-quarter courses in Calculus for students majoring in mathematics, engineering or science. The first release is Single Variable for Calculus 1, 2 and will be complemented by Multivariable in 2024.

Watch. Explore. Practice.

Interactive Calculus: Early Transcendentals, 1st Edition is a fully curated, highly customizable set of complete resources designed to support instructors and students in single-variable and multivariable calculus courses. A team of 5 expert authors created hundreds of short videos that explain concepts and work out examples for every topic in calculus. Presenters offer additional content on proofs and less-common topics.

Material is based on the content structure of the acclaimed Thomas' Calculus text by Pearson. Videos cover everything in Thomas' Calculus and beyond.

Features of MyLab Math for the 1st Edition

Interactive elements and immediate feedback

  • Project-specific, author-created GeoGebra interactive figures are used in the videos AND by students immediately following each video.
  • Practice exercises that also follow the videos utilize the top-notch learning aids and ADA accessibility of MyLab® Math.
  • Interactive Assignments offer a new assignment format of MyLab Math.

Customization for instructor preference and industry-leading prerequisite help

  • Instructors can easily edit the order of content or add their own videos, interactives or exercises.
  • Content can be sequential or open to students as a learning experience.
  • Over 10,000 assignable exercises are available in MyLab Math in addition to the library of prebuilt assignments and prerequisite support resources.
  • 1. Functions
  • 1.1 Functions and Their Graphs
  • 1.2 Combining Functions; Shifting and Scaling Graphs
  • 1.3 Trigonometric Functions
  • 1.4 Graphing with Software
  • 1.5 Exponential Functions
  • 1.6 Inverse Functions and Logarithms
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
  • 2. Limits and Continuity
  • 2.1 Rates of Change and Tangent Lines to Curves
  • 2.2 Limit of a Function and Limit Laws
  • 2.3 The Precise Definition of a Limit
  • 2.4 One-Sided Limits
  • 2.5 Continuity
  • 2.6 Limits Involving Infinity; Asymptotes of Graphs
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
  • 3. Derivatives
  • 3.1 Tangent Lines and the Derivative at a Point
  • 3.2 The Derivative as a Function
  • 3.3 Differentiation Rules
  • 3.4 The Derivative as a Rate of Change
  • 3.5 Derivatives of Trigonometric Functions
  • 3.6 The Chain Rule
  • 3.7 Implicit Differentiation
  • 3.8 Derivatives of Inverse Functions and Logarithms
  • 3.9 Inverse Trigonometric Functions
  • 3.10 Related Rates
  • 3.11 Linearization and Differentials
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
  • 4. Applications of Derivatives
  • 4.1 Extreme Values of Functions on Closed Intervals
  • 4.2 The Mean Value Theorem
  • 4.3 Monotonic Functions and the First Derivative Test
  • 4.4 Concavity and Curve Sketching
  • 4.5 Indeterminate Forms and L'Hôpital's Rule
  • 4.6 Applied Optimization
  • 4.7 Newton's Method
  • 4.8 Antiderivatives
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
  • 5. Integrals
  • 5.1 Area and Estimating with Finite Sums
  • 5.2 Sigma Notation and Limits of Finite Sums
  • 5.3 The Definite Integral
  • 5.4 The Fundamental Theorem of Calculus
  • 5.5 Indefinite Integrals and the Substitution Method
  • 5.6 Definite Integral Substitutions and the Area Between Curves
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
  • 6. Applications of Definite Integrals
  • 6.1 Volumes Using Cross-Sections
  • 6.2 Volumes Using Cylindrical Shells
  • 6.3 Arc Length
  • 6.4 Areas of Surfaces of Revolution
  • 6.5 Work and Fluid Forces
  • 6.6 Moments and Centers of Mass
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
  • 7. Integrals and Transcendental Functions
  • 7.1 The Logarithm Defined as an Integral
  • 7.2 Exponential Change and Separable Differential Equations
  • 7.3 Hyperbolic Functions
  • 7.4 Relative Rates of Growth
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • 8. Techniques of Integration
  • 8.1 Using Basic Integration Formulas
  • 8.2 Integration by Parts
  • 8.3 Trigonometric Integrals
  • 8.4 Trigonometric Substitutions
  • 8.5 Integration of Rational Functions by Partial Fractions
  • 8.6 Integral Tables and Computer Algebra Systems
  • 8.7 Numerical Integration
  • 8.8 Improper Integrals
  • 8.9 Probability
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
  • 9. First-Order Differential Equations
  • 9.1 Solutions, Slope Fields, and Euler's Method
  • 9.2 First-Order Linear Equations
  • 9.3 Applications
  • 9.4 Graphical Solutions of Autonomous Equations
  • 9.5 Systems of Equations and Phase Planes
  • Questions to Guide Your Review
  • Practice Exercises
  • Technology Application Projects
  • 10. Infinite Sequences and Series
  • 10.1 Sequences
  • 10.2 Infinite Series
  • 10.3 The Integral Test
  • 10.4 Comparison Tests
  • 10.5 Absolute Convergence; The Ratio and Root Tests
  • 10.6 Alternating Series and Conditional Convergence
  • 10.7 Power Series
  • 10.8 Taylor and Maclaurin Series
  • 10.9 Convergence of Taylor Series
  • 10.10 Applications of Taylor Series
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
  • 11. Parametric Equations and Polar Coordinates
  • 11.1 Parametrizations of Plane Curves
  • 11.2 Calculus with Parametric Curves
  • 11.3 Polar Coordinates
  • 11.4 Graphing Polar Coordinate Equations
  • 11.5 Areas and Lengths in Polar Coordinates
  • 11.6 Conic Sections
  • 11.7 Conics in Polar Coordinates
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects

About our authors

Jason Gregersen received a bachelor's degree in Mathematics Education from Northern Michigan University in 2009, and a master's degree in Applied Mathematics from Michigan Technological University in 2011. Since 2011 he has been teaching at Michigan Technological University, where he is currently an Associate Teaching Professor primarily teaching calculus, linear algebra, and differential equations. His primary area of interest is in finding new ways to integrate technology into education, to increase student engagement and add authentic applications into the curriculum.

Marc Renault attended Wake Forest University where he received his bachelor's and master's degrees (1994, 1996) in Mathematics. In 2002 he received his Ph.D. in mathematics at Temple University. Since 2002 he has been at Shippensburg University in Pennsylvania, where he teaches a wide variety of courses. His research interests lie in combinatorics and number theory, but he also enjoys creating interactive figures with GeoGebra, always trying to construct the next great demonstration that will spark student curiosity in calculus.

Rachel Vincent-Finley earned a bachelor's degree in Mathematics from Bryn Mawr College and master's and doctoral degrees in Computational and Applied Mathematics from Rice University. She joined the faculty at Southern University and A&M College in 2009 and now serves as the Associate Dean for Academic Affairs in the College of Sciences and Engineering. Her service to the state of Louisiana includes appointments on the Louisiana Optical Network Infrastructure (LONI) Management Council and the LaSTEM Advisory Council. Her general research interests include numerical analysis with applications to molecular biophysics and materials science. Dr. Vincent-Finley's education and outreach efforts include broadening participation in STEM and enhancing the connections between higher education and industry through workforce development partnerships.

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