Thomas' Calculus, 14th edition

  • Joel R. Hass, 
  • Christopher E. Heil, 
  • Maurice D. Weir

Choose the option that's right for you

$9.99 / mo

4-month term, pay monthly or pay $39.96

Enjoy these features

  • Up to 2 devices
  • Discounted tutor access
  • Exclusive offers

$14.99 / mo

4-month term, pay monthly or pay $59.96

Enjoy these features

  • Up to 2 devices
  • Discounted tutor access
  • Exclusive offers

Learn more, spend less

  • Watch and learn

    Videos & animations bring concepts to life

  • Learn anytime, anywhere

    Get the app to access your eTextbook whenever you need it

  • Make it your own

    Your notes. Your highlights. Your eTextbook

  • Find it fast

    Quickly navigate your eTextbook with search

  • Stay organized

    Access all your eTextbooks in one place

Overview

Through its balance of clear and intuitive explanations, current applications, and generalized concepts, Thomas' Calculus helps you reach a level of mathematical proficiency and maturity and provides support where needed. This revision introduces new co-author Christopher Heil.

Published by Pearson (January 1st 2021) - Copyright © 2018

ISBN-13: 9780137442997

Subject: Calculus

Category: Calculus

Table of contents

Table of Contents

  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
  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
  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 Related Rates
    • 3.9 Linearization and Differentials
  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 Applied Optimization
    • 4.6 Newton’S Method
    • 4.7 Antiderivatives
  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
  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
  7. Transcendental Functions
    • 7.1 Inverse Functions and Their Derivatives
    • 7.2 Natural Logarithms
    • 7.3 Exponential Functions
    • 7.4 Exponential Change and Separable Differential Equations
    • 7.5 Indeterminate Forms and L’Hôpital's Rule
    • 7.6 Inverse Trigonometric Functions
    • 7.7 Hyperbolic Functions
    • 7.8 Relative Rates of Growth
  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
  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
  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
  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
  12. Vectors and the Geometry of Space
    • 12.1 Three-Dimensional Coordinate Systems
    • 12.2 Vectors
    • 12.3 The Dot Product
    • 12.4 The Cross Product
    • 12.5 Lines and Planes in Space
    • 12.6 Cylinders and Quadric Surfaces
  13. Vector-Valued Functions and Motion in Space
    • 13.1 Curves in Space and Their Tangents
    • 13.2 Integrals of Vector Functions; Projectile Motion
    • 13.3 Arc Length in Space
    • 13.4 Curvature and Normal Vectors of a Curve
    • 13.5 Tangential and Normal Components of Acceleration
    • 13.6 Velocity and Acceleration in Polar Coordinates
  14. Partial Derivatives
    • 14.1 Functions of Several Variables
    • 14.2 Limits and Continuity in Higher Dimensions
    • 14.3 Partial Derivatives
    • 14.4 The Chain Rule
    • 14.5 Directional Derivatives and Gradient Vectors
    • 14.6 Tangent Planes and Differentials
    • 14.7 Extreme Values and Saddle Points
    • 14.8 Lagrange Multipliers
    • 14.9 Taylor’s Formula for Two Variables
    • 14.10 Partial Derivatives with Constrained Variables
  15. Multiple Integrals
    • 15.1 Double and Iterated Integrals over Rectangles
    • 15.2 Double Integrals over General Regions
    • 15.3 Area by Double Integration
    • 15.4 Double Integrals in Polar Form
    • 15.5 Triple Integrals in Rectangular Coordinates
    • 15.6 Applications
    • 15.7 Triple Integrals in Cylindrical and Spherical Coordinates
    • 15.8 Substitutions in Multiple Integrals
  16. Integrals and Vector Fields
    • 16.1 Line Integrals of Scalar Functions
    • 16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
    • 16.3 Path Independence, Conservative Fields, and Potential Functions
    • 16.4 Green’s Theorem in the Plane
    • 16.5 Surfaces and Area
    • 16.6 Surface Integrals
    • 16.7 Stokes' Theorem
    • 16.8 The Divergence Theorem and a Unified Theory
  17. Second-Order Differential Equations (Online at www.goo.gl/MgDXPY)
    • 17.1 Second-Order Linear Equations
    • 17.2 Nonhomogeneous Linear Equations
    • 17.3 Applications
    • 17.4 Euler Equations
    • 17.5 Power-Series Solutions

Appendices

  1. Real Numbers and the Real Line
  2. Mathematical Induction
  3. Lines, Circles, and Parabolas
  4. Proofs of Limit Theorems
  5. Commonly Occurring Limits
  6. Theory of the Real Numbers
  7. Complex Numbers
  8. The Distributive Law for Vector Cross Products
  9. The Mixed Derivative Theorem and the Increment Theorem

Your questions answered

Introducing Pearson+. Reimagined learning, designed for you. Choose from one eTextbook or over 1,500 eTextbooks and study tools, all in one place, for one low monthly subscription. A new way to buy books that fits your budget. Make the most of your study time with offline access, enhanced search, notes and flashcards — to get organized, get the work done quicker and get results. Plus, with the app, put textbooks in your pocket and learn wherever. It's time to upgrade the textbook and simplify learning, so you can have time to live too.

Pearson eTextbook is an easy-to-use digital textbook available from Pearson+. Make it your own by adding notes and highlights. Download the Pearson+ mobile app to learn on the go, even offline. Listen on the go with our new audiobook feature, available for most titles.

When you choose a plan, you're signing up for a 4-month 'term'. You can opt to make a one-time payment for the initial 4-month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4-month term has ended. You can turn on auto-renew in My account at any time to continue your subscription before your 4-month term has ended.

When you purchase a Pearson+ subscription, it will last 4 months. Before your initial 4-month term ends, you can extend your subscription by turning auto-renew on in My account.

If you turn auto-renew on, we’ll automatically renew your subscription and charge you every month until you turn off auto-renew. If you made a one-time payment for your initial 4-month term, you’ll now pay monthly.

To avoid the next payment charge, make sure you turn auto renewal off 1 day before the auto renewal date. You can subscribe again after auto-renew has been turned off by purchasing another Pearson+ subscription. We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details before your first monthly payment.

With a Multi Pearson+ subscription plan, you can download up to 10 titles on the Pearson+ app from My list on each of your authorized devices every month.

When you're using your Multi Pearson+ subscription plan in a browser, you can select and read from as many titles as you like.