Syllabus for SM221 Calculus III

Fall Semester, 2004-2005

TEXT: CALCULUS, Concepts and Contexts 2nd Edition, by James Stewart

NOTES:

  1. Please see http://www.usna.navy.mil/MathDept/website/courses/fall2004-2005/sm221_fall_2004-2005.html . This site will have the most up to date information about the course, including this syllabus, practice exams, etc.

  2. Calculus III is very geometric in nature.  Almost every concept we will study has a corresponding visualization.  To help us in this regard, all students in this course are expected to have a calculator like the Voyage 200 with the capabilities to graph and do symbolic calculations.  There will be assignments that use such a calculator as well as questions on the common final exam for which it is expected that the student has such a calculator.  In addition, students will be expected to use the Maple software issued on their computers.  Use of Maple (or occasionally the Voyage 200) is expected on problems preceded by an M.  The underlined references (such as C3M# ) refer to chapter C3M# in Prof C.E. Moore’s Maple Notes for Calculus III which are also available on the web.

  3. If you would like help in the course, you should contact your instructor for extra-instruction.  If your instructor is not available, try the Math Lab.  It is staffed all six class periods every class day with instructors who should be able to answer your questions.  Also, hard copies of web page information will be kept there (syllabi, practice tests, etc.).  Also, the Midshipman Group Study Program (MGSP) will be available evenings from Sunday through Thursday.  Upper class midshipmen will be available to help as you work on Calculus III in groups.  More information will be given to you about the particulars of MGSP at the start of the semester.

  4. The final exam will contain a couple of questions for which the calculator will not be allowed.

 

LESSON SECTION & TOPIC PROBLEMS
1. 9.1 Three Dimensions p. 651: 3,6,8,11,13,23,24,26,27
2. 9.2 Vectors p. 659: 4,6,14,17,22,23,27
3. 9.3 Dot Product p. 666: 1,7,9,10,12,16,19,22,23,29
4. 9.4 Cross Product (omit vector triple products) p. 674: 1,2,4,14,15,17,19,20 Torque Wrench Lab
5. 9.5 Lines p. 683: 1,3,4,5,7,9,13,14
6. 9.5 Planes p. 684: 19,23,25,29,33,37,38,41,45,49
7. 9.6 Functions & Surfaces p. 692: 1,2,4,9,10,11,12,13
8. 9.6 Functions & Surfaces p. 692: 14,15,17,19,M28,M29 (C3M1 3,4)
9. 9.7 Cylindrical & Spherical p. 696: 3,6,7,10,11,12,13,15,16,21,28,,M33 (C3M2)
10. Review
11. Review
12. Test on Chapter 9
 
13. 10.1 Vector Functions & Space Curves p. 710: 1,4,5,6,7,8,9,10,11,15,19
14. 10.2 Derivatives & Integrals of Vector Functions p. 716: 1,6,11,17,M23,32,36
15. 10.3 Arc Length p. 723: 1,3,4,5,M6,
16. 10.4 Motion in Space thru p729 p. 733: 1,2,5,7,14,17
17. 10.4/10.5 Parametric Surfaces p. 733: 18,21,25 / p. 740: 1-4
18. 10.5 (continued) p. 740: 11,12,21,22,23,27,M30 (C3M4 1,3)
19. Review
20. 11.1 Functions of Several Variables p. 756: 1,2,6,9,12,16,23
21. 11.1/11.3 Partial Derivatives p. 756: 31-38   p. 776: 1,4,6
22. 11.3 (continued) p. 776: 14,22,29,36,46,53,60,61, Hill Web Lab
23. 11.4 Tangent Planes & Linear Approximations (omit differentials) p. 788: 1,4,M5,16,M34 (C3M5a)
24. 11.5 Chain Rule p. 796: 4,5,11,16,20,28
25. 11.5/11.6 Direction Derivative & the Gradient Vector p. 797: 29,34  p. 808: 1,4,9
26. 11.6 (continued) p. 809: 13,20,23,26,29,32,35. M40 (C3M5b)
27. Review
28. Test on Chapters 10 and 11
 
29. 12.1 Double Integrals over Rectangles p.847: 1,3,5,9
30. 12.2 Iterated Integrals p. 853: 6,8,11,16,17,M28
31. 12.3 Double Integrals over General Regions p.861: 2,5,7,11,17
32. 12.3 (continued) p.861:19,21,27,35,38
33. 12.4 Double Integrals in Polar Coordinates p.867: 3,4,10,12,15,17
34. 12.4/12.5  Center of Mass p. 867: 20,21,25 p. 877: 3,6,9
35. 12.6 Surface Area p. 881: 2,5,8,M18a,c,d,M20b,c
36. 12.7 Triple Integrals p. 890: 2,6,9,10,15
37. 12.7 (continued) p. 890: M19,29,33,38a
38. 12.8 Triple Integrals - Cylindrical Coordinates p. 898: 2,5,7,8
39. 12.8 Triple Integrals - Spherical Coordinates p. 898: 3,15,19,25,M28,33 (C3M12a)
40. Review
41. Test on Chapter 12
 
42. 13.1 Vector Fields p. 922: 2,6,7,11-14
43. 13.1 (continued) p. 922: 16,M19,21,25,M27 (fieldplot)
44. 13.2 Line Integrals p. 933: 1,4,6,8
45. 13.2 (continued) p. 933: 13,17,M24,31,37
46. 13.3 Fundamental Theorem for Line Integrals p. 943: 1,2,4,7,11
47. 13.3/13.4 Green's Theorem p. 943: 15,23 / p. 951: 4,8
48. 13.4 (continued) p. 951: 11,17,19
49. 13.5 Curl & Divergence p. 958: 1,5,7,9,!0,11,13,14
50. 13.5/13.6 Surface Integrals p. 958: 19,20   p.970: 1,6,7
51. 13.6 (continued) p. 970: 18,19,20,25
52. 13.8 Divergence Theorem p. 983: 1,2,7,12
53. 13.8 (continued) p. 983: 11,M15,17,22,23
54. Review
55. Test on Chapter 13
56. 13.7 Stokes' Theorem p.976: 1,2,5,7
57 13.7 (continued) p.976:9,M11,17
58. Review
59. Review

Created by Prof Penn, hlp@usna.edu
Last modified 8-17-2004.