Published by Pearson (March 6, 2025) © 2025
Elizabeth Donovan | Jason Gregersen | Herb Kunze | Marc Renault | Rachel Vincent-FinleyProduct Information
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