Mathematics 32, Spring 2015

Calculus III

Lectures:

Section 1: Mondays, Tuesdays, Wednesdays, and Fridays, 8-8:50am
Room 214, Brighton Hall

Section 2: Mondays, Wednesdays, and Fridays, 10-10:50am, in Room 148, Alpine Hall
and Tuesdays, 10:30-11:20am, in Room 156, Alpine Hall



Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Office Hours:
MWF 9-9:50am, and Thursdays 10:30-11:30am. Also by appointment.


A description of the course: Math 32, Spring 2015 (pdf)

Drop Policy


Extra Notes:

Notes on Triple Integrals in Cylindrical and Spherical Coordinates.

Notes on Line Integrals.

One of you pointed out this youtube video, on 3D graphing in Minecraft:
3D Graphing in Minecraft




Announcements:

We will be using the following FREE textbook:
APEX Calculus

We will start with Chapter 10 and will come back to Chapter 9 as needed.
At the end of the semester, we will cover the following topics from "vector calculus" that are NOT in the free textbook: scalar and vector fields, divergence and curl, line integrals, conservative fields and their application to physics, Green's Theorem, Stokes' Theorem, the Divergence Theorem. You can find this material in many books, for example Stewart or Marsden/Weinstein; the latter can be found here:
Marsden/Weinstein, Volume III



Final Exam Schedule. Please take this into account when registering for classes:
Section 1 (8am class): Monday, May 18, 8-10am.
Section 2 (10am class): Friday, May 22, 8-10am.




Homework:

Homework will not be collected; instead, on the ``due date'' there will be an in-class quiz with problems taken from the homework. This will prepare you for the testing environment and will show you my grading style.

Homework 1, due Friday, January 30:
Section 10.1 (8, 10, 12, 16, 18, 20, 24, 28, 32)
Section 10.2 (8, 10, 12, 18)

Homework 2, due Friday, February 6:
Section 10.2 (20, 24, 26)
Section 10.3 (8, 14, 16, 18, 20, 22, 26, 28, 32)
Section 10.4 (6, 8, 10, 12)

Homework 3, due Friday, February 13:
Section 10.4 (20, 22, 32, 34)
Section 10.5 (6, 10, 12, 16, 22, 24, 30)
Section 10.6 (4, 8, 10)

Homework 4, due Friday, February 27:
Section 11.1 (14, 26, 30)
Section 11.2 (6, 10, 14, 22, 28, 30, 36, 38, 40)
Section 11.3 (26, 28, 34, 36)

Homework 5, due Friday, March 6:
Section 11.4 (10, 12, 16, 18, 22, 24)
Section 11.5 (10, 12, 14, 16, 24, 32)

Homework 6, due Friday, March 20:
Section 12.2 (16, 18)
Section 12.3 (6, 8, 10, 12, 14, 18)
Section 12.4 (6, 8, 10, 12, 20)

Homework 7, due Friday, April 3:
Section 12.5 (8, 12, 14, 18, 22, 24)
(In problems 12 and 18, draw the picture; it's similar to the example we did in class of "figure 8's in a hilly landscape.")

Homework 8, due Friday, April 10:
Section 12.6 (8, 10, 14, 16, 20, 22, 26)


Homework 9, due Friday, April 17:
Section 12.7 (8, 12, 20, 24)
Section 12.8 (6, 8, 10, 12, 14, 18)


Homework 10, due Friday, April 24 (the day of Exam 3):
Section 13.1 (6, 8, 12, 16, 18, 20)
Section 13.2 (6, 10, 12, 18, 20)


Homework 11, due Friday, May 1:
Section 13.3 (4, 6, 8, 10, 12, 14, 15, 16)


Homework 12, due Friday, May 8:
Section 13.6 (6, 10, 12, 14, 16, 18, 20)



Exams:

Exams and Solutions are posted on Sac CT.




Lecture Schedule

DateTopicsBook
1. M 1/26 Introduction; Cartesian Coordinates in Space. § 10.1
2. T 1/27 Surfaces; Intro to Vectors § 10.1, 10.2
3. W 1/28 Intro to Vectors, II § 10.2
4. F 1/30 The Dot Product, I § 10.3
5. M 2/2 The Dot Product, II § 10.3
6. T 2/3 The Cross Product, I § 10.4
7. W 2/4 The Cross Product, II § 10.4
8. F 2/6 The Cross Product, III § 10.4
9. M 2/9 Lines in Space § 10.5
10. T 2/10 Lines, Projections, Distances § 10.5
11. W 2/11 Planes § 10.6
12. F 2/13 Planes intersecting things § 10.6
13. M 2/16 EXAM 1 for Section 2, § 11.1 (Vector-Val. Functions) for Section 1
13. T 2/17 EXAM 1 for Section 1, § 11.1 (Vector-Val. Functions) for Section 2
14. W 2/18 Calculus with Vector-Valued Functions, I § 11.2
15. F 2/20 Calculus with Vector-Valued Functions, II § 11.2
16. M 2/23 Averages; Arclength § 11.2, 11.3
17. T 2/24 Physics examples; Unit Tangent, Normal, Binormal Vectors § 11.3, 11.4
18. W 2/25 Parametrizing with Respect to Arclength; Curvature § 11.5
19. F 2/27 Curvature, cont'd § 11.5
20. M 3/2 Curvature, cont'd; Functions of Several Variables § 11.5, 12.1
21. T 3/3 Functions of Several Variables, cont'd § 12.1
22. W 3/4 Level Curves; Level Surfaces § 12.1
23. F 3/6 Limits of Multivariable Functions § 12.2
24. M 3/9 Review
25. T 3/10 Review
W 3/11 EXAM 2
26. F 3/13 Partial Derivatives, I § 12.3
27. M 3/16 Partial Derivatives, II § 12.3
28. T 3/17 Tangent Planes and Linear Approximations, I § 12.3
29. W 3/18 Tangent Planes and Linear Approximations, II § 12.3
30. F 3/20 Differentiability of Multivariable Functions § 12.4
M-F 3/23-27 NO CLASS (Spring Break)
31. M 3/30 the Multivariable Chain Rule § 12.5
T 3/31 NO CLASS (Cesar Chavez Day)
32. W 4/1 Chain Rule, cont'd; Implicit Differentiation § 12.5
33. F 4/3 Directional Derivatives, I § 12.6
34. M 4/6 Directional Derivatives, II § 12.6
35. T 4/7 Directional Derivatives, III § 12.6, 12.7
36. W 4/8 Directional Derivatives, IV § 12.6, 12.7
37. F 4/10 Directional Derivatives, V § 12.7
38. M 4/13 Extreme Values, I § 12.8
39. T 4/14 Extreme Values, II § 12.8
40. W 4/15 Extreme Values, III § 12.8
41. F 4/17 Double Integrals, I § 13.1, 13.2
42. M 4/20 Double Integrals, II § 13.1, 13.2
43. T 4/21 Double Integrals, III § 13.1, 13.2
44. W 4/22 Review
F 4/24 EXAM 3
45. M 4/27 Double Integrals in Polar Coordinates, I. § 9.4, 13.3
46. T 4/28 Double Integrals in Polar Coordinates, II. § 13.3
47. W 4/29 Double Integrals in Polar Coordinates, III. § 13.3
48. F 5/1 Triple Integrals, I. § 13.6
M 5/4 NO CLASS
49. T 5/5 Triple Integrals, II. § 13.6
50. W 5/6 Cylindrical and Spherical Coordinates Typed Notes.
51. F 5/8 Spherical Coordinates Typed Notes.
52. M 5/11 Line Integrals, I. Typed Notes.
53. T 5/12 Line Integrals, II. Typed Notes.
54. W 5/13 Review, I.
55. F 5/15 Review, II.
FINAL EXAM: 5/18, 8-10am (8am class), 5/22, 8-10am (10am class)