Interactive Calculus, Early Transcendentals, 1st edition

Published by Pearson (June 1, 2024) © 2025

  • Jason Gregersen Michigan Technological University
  • Marc Renault Shippensburg University
  • Rachel Vincent-Finley Southern University
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Watch. Explore. Practice. Interactive Calculus: Early Transcendentals, 1st Edition is a unique, carefully crafted, customizable set of complete resources designed to support you in your single-variable calculus course. 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 from Pearson. Videos cover everything in Thomas' Calculus and beyond.

  • 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

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