SM223 — Calculus III with Optimization

• 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
  The assignments and due dates have been updated on WebAssign.

• 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
  The assignments have been updated on WebAssign.

• 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.

• Syllabus
• Course policy statement
• WebAssign

• 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)

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

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

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)
• Information