• §1. Vectors
• §2. The Dot Product
• §3. The Law of Cosines
• §4. Curvilinear Coordinates
• §5. Activity: Curvilinear Basis Vectors
• §6. Wrap-Up: Curvilinear Basis Vectors
• §7. Vector Fields
• §8. Differentials
• §9. The Vector Differential
• §10. Other Coordinate Systems
• §11. Activity: Determining $d\rr$ in Cylindrical and Spherical Coordinates
• §12. Wrap-Up: Coordinate Expressions for $d\rr$

Unit 2: Basics: The Gradient

Unit 3: Line Integrals

Unit 4: Surface Integrals

Unit 5: Vector Derivatives