1. Sequence, Series, and Power Series
2. Vectors and Coordinate Geometry in 3-Space
3. Arc length, Metric Spaces, and Applications
4. Vector Functions and Curves
5. Partial Differentiation
6. Applications of Partial Derivatives
7. Multiple Integration
8. Vector Fields
9. Vector Calculus
10. Differential Forms and Exterior Calculus
11. Ordinary Differential Equations
12. 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

• 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.

• 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.

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.