§ 1. Review of Single Variable Differentiation

§ 2. Thick Derivatives

§ 3. Using Differentials to Compute Derivatives

§ 4. The Multivariable Differential

§ 5. Chain Rule

§ 6. Chain Rule via Tree Diagrams

§ 7. Chain Rule via Differential Tree Diagrams

§ 8. Optimization

§ 9. Second Derivative Test

§ 10. Curvature and the Second Derivative Test

§ 11. Applications of Chain Rule

§ 12. Rearranging Differentials

§ 13. Examples from Thermodynamics

§ 14. Things not to do with Differentials

§ 15. Change of Variables

§ 16. The Vector Differential

§ 17. Other Coordinate Systems

§ 18. Activity: Determining $d\rr$ in Cylindrical and Spherical Coordinates

§ 19. Wrap-Up: Coordinate Expressions for $d\rr$

§ 20. Gradient

§ 21. Properties of the Gradient

§ 22. Directional Derivatives

§ 23. The Gradient in Curvilinear Coordinates

§ 24. Independence of Path

§ 25. Conservative Vector Fields

§ 26. Finding Potential Functions

§ 27. Visualizing Conservative Vector Fields

§ 28. The Geometry of the Gradient

§ 29. Lagrange Multipliers

§ 30. Lagrange Multipliers using Differentials

§ 31. Lagrange Multipliers Revisited

§ 32. Divergence

§ 33. The Divergence Theorem

§ 34. The Divergence in Curvilinear Coordinates

§ 35. Curl

§ 36. Stokes' Theorem

§ 37. Visualizing Divergence and Curl

§ 38. The Geometry of Curl

§ 39. Product Rules

§ 40. Integration by parts

§ 41. Second derivatives

§ 42. The Laplacian

§ 43. Formulas for Div, Grad, Curl (see also Vector Derivatives)