This is the study guide developed from 1996–2007 for the traditional 10-week course on vector calculus (starting with gradient) taught at Oregon State University. It includes a gentle introduction to some of the ideas in our book, and may be useful to students in more traditional courses.

• INTRODUCTION
• NOTATION
• WARMUP: Vectors and Dot Product
• §1. Differentials
• §2. Vector Differentials
• §3. The Gradient
• §4. Vector Fields
• §5. Line Integrals
• §6. Independence of Path
• §7. Finding Potential Functions
• INTERLUDE: Cross Product
• §8. Surfaces
• §9. Surface Integrals
• §10. The Divergence Theorem
• §11. Green's Theorem
• §12. Stokes' Theorem
• §13. Curl and Divergence
• §14. Change of Variables
• REVIEW