Thomas' Calculus, SI Units, 15th edition

Published by Pearson (July 18, 2023) © 2023

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

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Title overview

For three-semester or four-quarter courses in Calculus

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Thomas' Calculus goes beyond memorising formulas and routine procedures to help you develop deeper understanding. It guides you to a level of mathematical proficiency, with additional support if needed through its clear and intuitive explanations, current applications and generalised concepts. Technology exercises in every section use the calculator or computer for solving problems, and Computer Explorations offer exercises requiring a computer algebra system like Maple or Mathematica. The 15th Edition adds exercises, revises figures and language for clarity, and updates many applications; new online chapters cover Complex Functions, Fourier Series and Wavelets.

Key features

  • 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 summarise 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 emphasise that each step in a mathematical argument is justified.

New to this edition

  • 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 visualisation 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.
  • New advanced online chapters and sections are offered on Complex Functions, Fourier Series and Wavelets in the eText and MyLab Math course.

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Table of contents

  • 1. Functions
  • 2. Limits and Continuity
  • 3. Derivatives
  • 4. Applications of Derivatives
  • 5. Integrals
  • 6. Applications of Definite Integrals
  • 7. Transcendental Functions
  • 8. Techniques of Integration
  • 9. Infinite Sequences and Series
  • 10. Parametric Equations and Polar Coordinates
  • 11. Vectors and the Geometry of Space
  • 12. Vector-Valued Functions and Motion in Space
  • 13. Partial Derivatives
  • 14. Multiple Integrals
  • 15. Integrals and Vector Fields
  • 16. First-Order Differential Equations
  • 17. Second-Order Differential Equations (online)
  • 18. Complex Functions (online)
  • 19. Fourier Series and Wavelets (online)
  • 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 Probability
  • A.8 The Distributive Law for Vector Cross Products
  • A.9 The Mixed Derivative Theorem and the Increment Theorem
  • Answers to Odd-Numbered Exercises
  • Applications Index
  • Subject Index
  • Credits
  • A Brief Table of Integrals

Author bios

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. 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. 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. 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.

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