I'm a student
I'm an educator
Request full copy

Thomas' Calculus, 15th edition

Published by Pearson (May 5, 2022) © 2023

  • Joel R. Hass University of California, Davis
  • Christopher E. Heil Georgia Institute of Technology
  • Maurice D. Weir Naval Postgraduate School
  • Przemyslaw Bogacki Old Dominion University

eTextbook

C$67.99

  • Easy-to-use search and navigation
  • Add notes and highlights
  • Flashcards help streamline study sessions

MyLab

fromC$87.49

  • Reach every student with personalized support
  • Customize courses with ease
  • Optimize learning with dynamic study tools

For 3-semester or 4-quarter courses in Calculus for students majoring in mathematics, engineering or science.

Clarity and precision

Thomas' Calculus goes beyond memorizing formulas and routine procedures to help students develop deeper understanding. It guides students to a level of mathematical proficiency and maturity needed for the course, with support for those who require it through its balance of clear and intuitive explanations, current applications and generalized concepts. The 15th Edition meets the needs of students with increasingly varied levels of readiness for the calculus sequence. This revision also adds exercises, revises figures and narrative for clarity, and updates many applications with modern topics.

Hallmark features of this title

  • Key topics are presented both informally and formally.
  • Results are carefully stated and proved throughout, and proofs are clearly explained and motivated.
  • Strong exercise sets feature a wide range from skills problems to applied and theoretical problems.
  • Writing exercises ask students to explore and explain various concepts and applications. A list of questions at the end of each chapter asks them to review and summarize what they have learned.
  • Technology exercises in each section ask students to use the calculator or computer when solving the problems. Computer Explorations offer exercises requiring a computer algebra system such as Maple or Mathematica.
  • Annotations within examples guide students through the problem solution and emphasize that each step in a mathematical argument is justified.

New and updated features of this title

  • Many narrative clarifications and revisions have been made throughout the text.
  • A new appendix on Determinants and Gradient Descent has been added, covering many topics relevant to students interested in Machine Learning and Neural Networks.
  • Many updated graphics and figures have been enhanced to bring out clear visualization and mathematical correctness.
  • Many exercise instructions have been clarified, such as suggesting where the use of a calculator may be needed.
  • Notation of inverse trig functions has been changed throughout the text to favor arcsin notation over sin^{-1}, etc.
  • New advanced online chapters and sections are offered on Complex Functions, Fourier Series and Wavelets in the eText and MyLab Math course.

Features of MyLab Math for the 15th Edition

  • 100 additional Setup & Solve exercises have been selected by author Przemyslaw Bogacki. These exercises focus students on the process of problem solving by requiring them to set up their equations before moving on to the solution.
  • Integrated Review quizzes and personalized homework are now built into all MyLab Math courses. No separate Integrated Review course is required.
  • New online chapters and sections on Complex Functions, Fourier Series and Wavelets offer exercises, as requested by many users. These are also available in the standalone eText.
  • All Interactive Figures have been updated for accessibility to meet WCAG standards. The 180 figures can be used in lecture and by students independently.
    • Figures are editable using the free GeoGebra software; they were created by Marc Renault (Shippensburg University), Kevin Hopkins (Southwest Baptist University), Steve Phelps (University of Cincinnati), and Tim Brzezinzki (Southington High School, CT).
  • GeoGebra Exercises are gradable graphing and computational exercises that help students demonstrate their understanding, enabling them to interact directly with the graph in a manner that reflects how they would graph on paper.

Features of Pearson eText for the 15th Edition

  • New advanced online chapters and sections are offered on Complex Functions, Fourier Series and Wavelets.
  • A new appendix on Determinants and Gradient Descent covers many topics relevant to students interested in Machine Learning and Neural Networks.
  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

About our authors

Joel Hass received his PhD from the University of California - Berkeley. He is currently a professor of mathematics at the University of California - Davis. He has coauthored widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass's current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.

Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil's current areas of research include redundant representations, operator theory, and applied harmonic analysis. In his spare time, Heil pursues his hobby of astronomy.

The late Maurice D. Weir of the the Naval Postgraduate School in Monterey, California was Professor Emeritus as a member of the Department of Applied Mathematics. He held a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. Weir was awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He co-authored eight books, including University Calculus and Thomas' Calculus.

Przemyslaw Bogacki is an Associate Professor of Mathematics and Statistics and a University Professor at Old Dominion University. He received his PhD in 1990 from Southern Methodist University. He is also the author of a text on linear algebra, which appeared in 2019. He is actively involved in applications of technology in collegiate mathematics. His areas of research include computer aided geometric design and numerical solution of initial value problems for ordinary differential equations.

Need help? Get in touch

MyLab

Customize your course to teach your way. MyLab® is a flexible platform merging world-class content with dynamic study tools. It takes a personalized approach designed to ignite each student's unique potential. And, with the freedom it affords to adapt your pedagogy, you can reinforce select concepts and guide students to real results.

Pearson+

All in one place. Pearson+ offers instant access to eTextbooks, videos and study tools in one intuitive interface. Students choose how they learn best with enhanced search, audio and flashcards. The Pearson+ app lets them read where life takes them, no wi-fi needed. Students can access Pearson+ through a subscription or their MyLab or Mastering course.

Video
Play
Privacy and cookies
By watching, you agree Pearson can share your viewership data for marketing and analytics for one year, revocable by deleting your cookies.

Video transcript (PDF | 25KB) 

Empower your students, in class and beyond

Meet students where they are with MyLab®, and capture their attention in every lecture, activity, and assignment using immersive content, customized tools, and interactive learning experiences in your discipline.