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.
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A wide range of exercises and examples varying in difficulty and nature.
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Reader-friendly content and structure supports your students' understanding.
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.
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Chapter P Preliminaries
- Limits and Continuity
- Differentiation
- Transcendental Functions
- More Applications of Differentiation
- Integration
- Techniques of Integration
- Applications of Integration
- Conics, Parametric Curves, and Polar Curves
- Sequence, Series, and Power Series
- Vectors and Coordinate Geometry in 3-Space
- Arc length, Metric Spaces, and Applications
- Vector Functions and Curves
- Partial Differentiation
- Applications of Partial Derivatives
- Multiple Integration
- Vector Fields
- Vector Calculus
- Differential Forms and Exterior Calculus
- Ordinary Differential Equations
- More Topics in Differential Equations
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
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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