1. iClicker Quiz (1) I have completed at least 50% of the reading and study-guide assignments associated with lecture 1-4, as indicated on the course schedule. a) Trueb) False

2. Calculus is the art of cutting things up into little pieces! Summing the pieces is called “integration”. Taking ratios of pieces is called “differentiation”. Use your imagination. But in any given situation, one type of cut will usually be more convenient that others.

4. Let f(x) and g(x) be functions of x Sum rule Quotient rule Chain rule Product rule Constant rule

6. Definite integral Average Indefinite integral

7. Circular area

8. Spherical Coordinates

9. Spherical Area r z  

10. spherical patchwork tomato slices cones orange slices a z  

11. Spherical Volume spherical patchwork cones orange slices tomato slices r z  dr

12. iClicker Quiz Which of the following area differentials will yield the surface area of a sphere of radius a?

13. Conical Volume ???

14. Conical Area ???

15. iClicker Quiz The charge density of a disc of radius a is described by the function  = Cr 3. The best differential area to use in this case is:

16. Uniform Density dA dx  C/m   C/m 2   C/m 3 dV

17. Non-uniform Density dA dx dV

18. Key concept When integrating a density to obtain a complete total (e.g. total mass or total charge), you must choose a differential over which the density is constant!

19. iClicker Quiz The charge density of a disc of radius a is described by the function  = Cr 3. The best differential area to use in this case is: