Interactive Calculus, Early Transcendentals, 1st edition

  • Jason Gregersen
  • , Marc Renault
  • , Rachel Vincent-Finley

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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.

Published by Pearson (November 24th 2023) - Copyright © 2024

ISBN-13: 9780138059057

Subject: Calculus

Category: Calculus

  • 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