# SM223 — Calculus III with Optimization

## Fall 2012, Sections 5025 and 6025

#### Asst. Prof. Nelson Uhan

### Announcements

**Dec 5**The final exam is on Monday, December 17, 1330 - 1630. See below for information.**Nov 26**Exam 4 is on Monday, December 3. See below for information and review problems.**Oct 28**Due to USNA's closure, Exam 3 is now on Wednesday, October 31.**Oct 22**Exam 3 is on Monday, October 29. See below for information and review problems.**Oct 19**Homeworks 35 - 38 have been changed:- Homework 35 (due M 10/22): none (review day)
- Homework 36 (due W 10/23): 14.8: 3, 4, 5, 6, 7, 8*, 9
- Homework 37 (due R 10/24): 14.8: 10, 13, 15, 16, 19, 20
- Homework 38 (due F 10/25): 14.8: 29, 30*, 31, 32, 33, 35, 37

**Oct 17**Homeworks 33 and 34 have been changed:- Homework 33: 14.7: 39, 40*, 41, 42, 43, 45, 47
- Homework 34: 14.7: 31, 35, 48, 50, 51

**Sep 26**Exam 2 is on Wednesday, October 3. See below for information and review problems.**Sep 12**I have made some changes to my EI policy. See the course policy statement (now revised) below.**Sep 4**Exam 1 is on Monday, September 10. See below for information and review problems.**Aug 29**A small adjustment to Homeworks 6 and 8:- Homework 6: remove 12.5.12
- Homework 8: add 12.5.12

**Aug 20**Make sure you are able to access WebAssign as soon as possible. Use the class key e-mailed to you. If you are having trouble, take a look at this tutorial.The homework assignments are on the syllabus. Note that there is a homework assignment due Wednesday (Aug 22). Remember that homework is always due at the beginning of the next class; the due dates are also on WebAssign.

### General information

### Lesson notes

- 1. 3D coordinate systems (Aug 20)
- 2. Vectors (Aug 22)
- 3. The dot product (Aug 23)
- 4. The dot product, cont. (Aug 24)
- 5. The cross product (Aug 27)
- 6. Equations of lines in 3D (Aug 29)
- 7. Equations of planes in 3D (Aug 30)
- 8. Equations of planes in 3D, cylinders (Aug 31)
- 9. Quadric surfaces (Sep 4)
- 10. Vector functions and space curves (Sep 5)
- 11. Derivatives and integrals of vector functions (Sep 6)
- 12. Review (Sep 7)
- 13. Exam 1 (Sep 10)
- 14. Velocity and acceleration (Sep 12)
- 15. Projectile motion (Sep 13) [filled notes]
- 16. Projectile motion, continued (Sep 14)
- 17. Projectile motion, continued (Sep 17) [filled notes]
- 18. Multivariable functions (Sep 19)
- 19. Level curves (Sep 20)
- 20. Partial derivatives (Sep 21)
- 21. Partial derivatives, continued (Sep 24) [solutions]
- 22. Tangent planes and linear approximations (Sep 26)
- 23. Differentials (Sep 27)
- 24. The chain rule (Sep 28)
- 25. Review (Oct 1)
- 26. Exam 2 (Oct 3)
- 27. The gradient vector and directional derivatives (Oct 4)
- 28. Maximizing the directional derivatives (Oct 5)
- 29. Tangent planes and normal lines (Oct 10)
- 30. Introduction to operations research and optimization (Oct 11)
- 31. Local minima and maxima (Oct 12)
- 32. Local minima and maxima, cont. (Oct 15)
- 33. Constrained optimization (Oct 17) [filled notes]
- 34. Constrained optimization, cont. (Oct 18)
- 35. Constrained optimization, cont. (Oct 19)
- 36. Lagrange multipliers (Oct 22)
- 37. Lagrange multipliers, cont. (Oct 24)
- 38. Lagrange multipliers, cont. (Oct 25)
- 39. Review (Oct 26)
- 40. Exam 3 (Oct 31)
- 41. Double integrals over rectangles (Nov 1)
- 42. Iterated integrals (Nov 2)
- 43. Double integrals over general regions (Nov 5)
- 44. Double integrals over general regions, cont. (Nov 7)
- 44a. Double integrals over general regions, cont. (Nov 8)
- 45. Polar coordinates (Nov 9)
- 46. Double integrals in polar coordinates (Nov 14)
- 47. Applications: mass and center of mass (Nov 15) [filled notes]
- 48. Triple integrals (Nov 16)
- 49. Triple integrals, cont. (Nov 19)
- 50. Triple integrals, cont. (Nov 21)
- 51. Mass and center of mass, revisited (Nov 26) [filled notes]
- 52. Triple integrals in cylindrical coordinates (Nov 28)
- 53. Triple integrals in cylindrical coordinates, cont. (Nov 29)

### Solutions to quizzes

Note: Now that the semester is over, I have taken down these solutions.

- 1. Aug 23
- 2. Aug 24 - see solutions to 12.3.26 below
- 3. Aug 30
- 4. Sep 4
- 5. Sep 5
- 6. Sep 12 - "not really a quiz"
- 7. Sep 19
- 8. Sep 20
- 9. Sep 26
- 10. Sep 27
- 11. Oct 10
- 12. Oct 11
- 13. Oct 19
- 14. Oct 24
- 15. Oct 25
- 16. Nov 2
- 17. Nov 7
- 18. Nov 8
- 19. Nov 15
- 20. Nov 21
- 21. Nov 28
- 22. Nov 29
- 23. Dec 5
- 24. Dec 6 - A
- 25. Dec 6 - B

### Solutions to homework problems not on WebAssign

Note: Now that the semester is over, I have taken down these solutions.

- 1. 12.1: 39
- 2. 12.2: 39
- 3. 12.3: 12, 26
- 4. 12.3: 39, 56
- 5. 12.4: 30
- 6. 12.5: 12 (moved to Homework 8)
- 7. 12.5: 23, 26, 29, 30
- 8. 12.5: 67
- 10. 13.1: 8, 10, 17
- 11. 13.2: 1; 13.3: 7, 15
- 14. 13.4: 2, 9
- 17. 13.4: 28, 30
- 18. 14.1: 8
- 19. 14.1: 34, 46
- 20. 14.3: 4, 22
- 21. 14.3: 74
- 22. 14.4: 1, 4, 19, 20
- 27. 14.6: 1, 9, 12
- 28. 14.6: 18, 26, 28
- 29. 14.6: 37, 38, 43
- 30. 14.6: 51, 56
- 31. 14.7: 1, 5, 6, 7, 8, 9
- 32. 14.7: 10
- 33. 14.7: 40
- 36. 14.8: 8
- 38. 14.8: 30
- 41. 15.1: 5
- 42. 15.2: 16, 26
- 43. 15.3: 14
- 44. 15.3: 41, 46, 62
- 45. 10.3: 10, 16, 17, 21, 22, 29, 46
- 46. 15.4: 7, 8, 10
- 47. 15.5: 1, 3, 8, 15
- 49. 15.7: 20, 21, 22, 23
- 50. 15.7: 32, 36
- 51. 15.7: 49ab
- 52. 15.8: 18

### Exams

Note: Now that the semester is over, I have taken down the solutions to the exams and review problems.

- Exam 1 (Sep 10)
- Information and review problems
- Solutions
- Exam 2 (Oct 3)
- Information and review problems
- Solutions to review problems
- Solutions
- Exam 3 (Oct 29)
- Information and review problems
- Solutions to review problems
- Solutions
- Exam 4 (Dec 3)
- Information and review problems
- Solutions to review problems
- Solutions
- Final Exam (Dec 17)