Unit 1: Basics: Coordinates and Vectors

Unit 2: Basics: The Gradient

Unit 3: Line Integrals

Unit 4: Surface Integrals

• §1. Divergence
• §2. The Divergence Theorem
• §3. The Divergence in Curvilinear Coordinates
• §4. Curl
• §5. The Geometry of Curl
• §6. Formulas for Div, Grad, Curl
• §7. Stokes' Theorem
• §8. Visualizing Divergence and Curl
• §9. Product Rules
• §10. Integration by parts
• §11. Second derivatives
• §12. The Laplacian