Thomas' Calculus, 15th edition

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

per month

monthly payments or pay one-time

Purchasing Instructions

This form contains two groups of radio buttons, one for Exam Pack purchasing options, and one for standard purchasing options. Only one option can be chosen for purchase. Any option that is selected will deselect any previously selected purchase option.

eTextbook + Study Prep

ISBN-13: 9780137616077 (2022 update)

eTextbook

ISBN-13: 9780137616077 (2022 update)

  • Find it fast

    Quickly navigate your eTextbook with search

  • Stay organized

    Access all your eTextbooks in one place

  • Easily continue access

    Keep learning with auto-renew

  • Study well

Now in its 15th Edition, Thomas’ Calculus is the calculus textbook that generations of STEM students have learned from. Authors Joel Hass, Christopher Heil, and Przemyslaw Bogacki guide you to a level of mathematical proficiency, with support as needed through clear and intuitive explanations, current applications, and generalized concepts.

This textbook will help you move past memorized procedures to genuine understanding of calculus, beginning with foundational topics—such as integrals, transcendental functions, techniques of integration, limits and continuity, and derivatives and their applications—and then moving to advanced topics—including vectors, partial derivatives, multiple integrals, vector calculus, infinite sequences and series, and parametric equations and polar coordinates. Carefully paced examples and exercise sets will help you generalize concepts from single-variable to multivariable calculus.

The 15th Edition adds exercises, updates many applications, and revises figures and language for clarity. New online chapters cover complex functions, Fourier series, and wavelets.

Published by Pearson (December 29th 2022) - Copyright © 2023

ISBN-13: 9780137616077

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
  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 Derivatives of Inverse Functions and Logarithms
    • 3.9 Related Rates
    • 3.10 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

Appendix A

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

Appendix B (online)

  • B.1 Determinants
  • B.2 Extreme Values and Saddle Points for Functions of More than Two Variables
  • B.3 The Method of Gradient Descent

Answers to Odd-Numbered Exercises

Applications Index

Subject Index

A Brief Table of Integrals

Credits