product title: Calculus: A Complete course, 10th edition

Format types

MyLab with eText = Access to the blended learning platform, merging digital content with complementary homework, tutorials, and assessments. Includes the accompanying eText.

This classic text has earned a reputation for excellent accuracy and mathematical rigour

The 10th edition continues in the pattern of the 8th and 9th editions, adding important, but overlooked, topics while clarifying old ones, and building on the solid core emplaced in prior editions.

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.

The 10th edition is suitable for a semester course in differential equations, in addition to the existing standard material suitable for four semesters of calculus. Not only can it be used to deliver five standard courses of conventional material, it can do much more through some of the unique topics and approaches, which can be added or overlooked by the instructor without penalty. It explores computers and mathematics through Maple and now Python, as well as important applications from information theory to Levy distributions.

New to this edition

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.

Table of contents

• 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
• 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