Math 250: Calculus III

April 27, 2012

Test # 3 Review Topics

1. Double integrals over regions between curves

2. Interchanging the order of double integration

3. Derivation and definition of a triple integral

4. Iterated integrals and Fubini’s theorem for triple integrals

5. Triple integrals over general regions

6. Triple integrals over regions between surfaces

7. Changing the order of triple integration

8. Computing volumes with double and triple integration

9. Double integrals in polar coordinates

10. Triple integrals in cylindrical and spherical coordinates

11. Change of variables; jacobian

12. Vector fields in two and three dimensions

13. Line integrals of scalar fields; derivation and computation

14. Line integrals of vector fields; derivation and computation

15. Line integral as work

16. Conservative vector fields; gradient of potential function

17. Finding potential functions in two and three dimensions

18. Fundamental theorem for gradient vector fields; path independence

19. Circulation of a vector field

20. Theorems about conservative vector fields

21. Rotation (curl) of a vector field

22. Surface parametrization

23. Normal vectors of parametric surfaces; tangent planes

24. Surface area of parametric surfaces

25. Surface integrals of scalar functions

26. Surface integrals of vector fields

27. Flux of a vector field