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Calculus: A Complete Course, 10th edition

Published by Pearson Canada (January 26, 2021) © 2022

  • Robert A. Adams Professor Emeritus at University of British Columbia
  • Christopher Essex University of Western Ontario

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For courses in Calculus.

Proven in North America and abroad, this classic text has earned a reputation for excellent accuracy and mathematical rigour. It remains the only mainstream textbook that covers sufficient conditions for maxima and minima in higher dimensions. In the classical curriculum, differentials are defined as linear combinations of other differentials. But then later they are also asserted to be products of differentials, without explanation. This edition clarifies, connecting these new objects as they arise. Metrics are a rather fuzzy topic in most texts, leaving the questions that arc length implies hanging. The exploration of these questions leads to new gateway topics, including spherical geometry (as in navigation), and special relativity, which both emerge rather effortlessly once the metric concept is properly in place.

Hallmark features of this title

A wide range of exercises and examples varying in difficulty and nature.

  • The plethora of exercises and problems will support your students' development and help them build a comfortable level to practice as their skills and knowledge grow.
  • Highlighted definitions, theorems, and examples throughout the text help your students consolidate their knowledge.

Reader-friendly content and structure supports your students' understanding.

  • With its reader-friendly language, the textbook holds a reputation for outstanding accuracy and mathematical rigour.
  • The Book structure is set to build up knowledge from one idea to the next as the chapters progress.
  • Chapter review at the end of the chapters presents key ideas and exercises to further support student learning.

Improvements and changes to the existing material throughout the book

  • Chapter 11 introduces a new concept of a metric space and its application to spherical trigonometry, including the concept of navigation on the surface of our spherical planet.
  • Chapter 11 also presents Einstein's theory of special relativity, the conclusions of which follow from the selection of a particular metric for measuring distance in four-dimensional space-time.
  • A new section on the introduction to the methods of the Calculus of Variations is included in Section 20.4.
  • A new introduction to the open-source programming language Python, in Appendix VI, which can replace Maple or Mathematica as a free computer algebra system.

Features of MyLab® Math for the 10th Edition

MyLab® is the teaching and learning platform that allows instructors to reach every student with powerful self-study material and assessments.

An online homework and tutorial environment for your students as part of their learning experience.
  • Teach your course your way: Whether you would like to build your own assignments or create your own questions, MyLab gives you the flexibility to easily create your course to fit your needs.
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  • Deliver trusted content: We partner with highly respected authors to develop interactive content and course-specific resources that you can trust — and keep your students engaged.
A series of exercises and assessments give your students the opportunity to self-test and consolidate their knowledge.
  • Exercises with immediate feedbackare based on the textbook exercises and regenerate algorithmically to give students an unlimited opportunity for practice and mastery.
  • Learning Catalytics® is an interactive classroom tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking.

Discover more about MyLab® Math.

Chapter P Preliminaries
  1. Limits and Continuity
  2. Differentiation
  3. Transcendental Functions
  4. More Applications of Differentiation
  5. Integration
  6. Techniques of Integration
  7. Applications of Integration
  8. Conics, Parametric Curves, and Polar Curves
  9. Sequence, Series, and Power Series
  10. Vectors and Coordinate Geometry in 3-Space
  11. Arc length, Metric Spaces, and Applications
  12. Vector Functions and Curves
  13. Partial Differentiation
  14. Applications of Partial Derivatives
  15. Multiple Integration
  16. Vector Fields
  17. Vector Calculus
  18. Differential Forms and Exterior Calculus
  19. Ordinary Differential Equations
  20. More Topics in Differential Equations

    21. Appendix 1 Complex Numbers

    Appendix 2 Complex Functions

    Appendix 3 Continuous Functions

    Appendix 4 The Riemann Integral

    Appendix 5 Doing Calculus with Maple

    Appendix 6 Doing Calculus with Python

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