• This is the outer limits of what might be covered in a semester. Instructors will provide the particular selection that is relevant for a class

1. 12.1 Three-dimensional coordinate systems

2. 12.2 Vectors

3. 12.3 The dot product

4. 12.4 The cross product

5. 12.5 Equations of lines and planes

6. 12.6 Cylinders and quadric surfaces

7. 13.1 Vectors and space curves

8. 13.2 Derivative and integrals of vector functions

9. 13.3 Arc Length and Curvature

10. 13.4 Motion in space: velocity and acceleration

11. 14.1 Functions of several variables

12. 14.2 Limits and continuity

13. 14.3 Partial derivatives

14. 14.4 Tangent planes and linear approximation

15. 14.5 The chain rule

16. 14.6 Directional derivatives and the gradient vector

17. 14.7 Maximum and minimum values

18. 14.8 Lagrange Multipliers

19. 15.1 Double integrals over rectangles

20. 15.2 Iterated integrals

21. 15.3 Double integrals over general regions

22. 15.4 Double integrals in polar coordinates

23. 15.5 Applications of double integrals

24. 15.6 Surface area

25. 15.7 Triple integrals

26. 15.8 Triple integrals in cylindrical coordinates

27. 15.9 Triple integrals in spherical coordinates

28. 15.10 Change of variables in multiple integrals

29. 16.1 Vector fields

30. 16.2 Line integrals

31. 16.3 The fundamental theorem for line integrals

32. 16.4 Greens Theorem

33. 16.5 Curl and divergence

34. 16.6 Parametric Surfaces

35. 16.7 Surface Integrals

36. 16.8 Stokes Theorem

37. 16.9 Divergence Theorem