Math 31, Fall 2014

Mathematics 31, Fall 2014

Calculus II

Lectures:

Section 7: Mondays, Tuesdays, Thursdays, and Fridays, 8-8:50am
Room 218, Brighton Hall

Section 8: Mondays, Wednesdays, Thursdays, and Fridays, 9-9:50am
MWF lectures will be in Room 101, Brighton Hall,
Thursday lectures will be in Room 102, Eureka Hall

Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Tentative Office Hours:
10-11am, which may change based on demand. Also by appointment.

A description of the course: Math 31, Fall 2014 (pdf)

Drop Policy

Announcements:

Final Exam Schedule. Please take this into account when registering for classes:
Section 7 (8am class): Monday, December 15, 8-10am.
Section 8 (9am class): Wednesday, December 17, 8-10am.

PAL for Math 31. [Verbatim from the official flyer.] The Peer Assisted Learning Program improves student success in gateway courses! NSM 12F is a one-unit course, graded Cr/NCr, facilitated by a student who has successfully mastered the material in Math 31. Space is limited! You must sign up in person. Four sections of NSM 12F are open (class starts on 2nd day listed):

MW 2-2:50pm, BRH 113
TR 12-12:50pm, SQU 105 (1st class is Th)
TR 9-9:50am, SQU 128 (1st class is Th)
WF 11-11:50am, MND 4007.

Interested? Please show up this week!! Adds are first come/first served. Fall data for Math 30 (we don't yet have data for Math 31): 90.4% of students in a PAL passed Math 30 with a C or better. 73.7% of students NOT in a PAL passed Math 30 with a C or better.

Essay Project:

Help Setting Up LaTeX:
There are many different LaTeX editors; here is a comparison:
(wikipedia link)

The easiest seems to be the website writelatex.org
(writelatex.org)
which you can use without downloading any software.
But if you want something fancier, here are some links for downloading software:

If you have a Mac, here's one method: Go to the webpage (TUG webpage) and simply click on the MacTeX.pkg link, and follow the simple instructions.
If you have a PC, here's one method: Go to the webpage (webpage), and follow the instructions. I use WinEdt on my PC.
Once it's on your computer, you should be able to open the tex files of lecture notes found below. Feel free to modify the lecture notes, adding your own comments, etc.

Help Building Your Code:
If you have trouble building your code into a nice output file (and are getting error messages), read this:
(LaTeX code)
(pdf)

Deadlines:

Friday, October 10: Turn in a single page demonstrating that you have access to LaTeX and are able to use it. Write a few mathematical formulas. It is ok to be whimsical and irreverent.
Friday, October 31, or preferably earlier: Turn in a brief essay proposal, written using LaTeX, telling me your field of interest and briefly describing your concrete example of how calculus (preferably integration) is useful for your future plans. Also, please meet with me in person to briefly explain your project.
Monday, November 24: The first draft of your essay is due. It should be about 2-3 pages. It should be well-written and demonstrate mathematical knowledge. Focus on a well-defined, concrete calculus problem in your field of interest. It should be a problem that is interesting to YOU, and I'm hoping that this project is FUN!
Friday, December 5: The final draft of your essay is due.

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 Monday, September 8:
Section 5.5 (8, 18, 20, 28, 32, 40, 48, 54, 60, 66, 78, 86)

Homework 2, due Friday, September 12:
Section 6.1 (4, 8, 16, 20, 22, 28, 32, 52)
Section 6.2 (4, 6, 10, 12, 14)

Homework 3, due Friday, September 19:
There won't be a quiz on Friday. Instead, on Friday please turn in a written statement addressing: (1) what is the most challenging part of the class so far? (2) give an example of part (1), and explain in detail why you think it is challenging. I will grade it as if it were a quiz.
Section 6.2 (16, 18, 42, 50, 54, 56, 68)
Section 6.3 (4, 6, 8, 10, 14, 16, 22a, 38, 40, 42, 46)

Homework 4, due Monday, September 29:
Part One: Section 7.1 (4, 10, 12, 16, 24, 26, 30, 32, 34)
Part Two: Section 7.1 (38, 42, 52, 56, 62)
Please only use the "Table Method" to check your answer. You need to be able to use "u, dv" notation.

Homework 5, due Thursday, October 9:
Section 7.2 (2, 4, 6, 16, 24, 26, 32, 56)
Section 7.3 (2, 4, 6, 16, 20, 22, 24, 32)
Section 6.5 (2, 4, 9, 10, 14, 18, 20)

Homework 6, due Thursday, October 16:
Section 7.4 (8, 9, 12, 18, 19, 22, 23, 24, 26)

Homework 7, due Friday, October 24:
Section 7.7 (1, 5, 6, 10, 11, 14, 15, 19, 20, 21, 22)

Homework 8, due Friday, October 31:
Section 7.8 (6, 8, 10, 12, 14, 16, 18, 26, 30, 32, 34, 50)
Section 8.1 (8, 10, 12, 14, 16, 32)

Homework 9, due Friday, November 7:
Section 8.2 (6, 8, 10, 12)
Section 11.1 (4, 6, 8, 10, 12, 14, 16, 20, 22, 24, 26, 28, 30, 32, 34, 42)
Section 11.2 (8, 18, 20)

Homework 10, due Friday, November 14:
Section 11.2 (15, 22, 30, 32, 36, 44, 48, 56, 60)
Section 11.3 (4, 8, 12, 16, 20, 26)
Section 11.4 (4, 6, 8, 10)

Homework 11, due Thursday, December 4:
Section 11.4 (14, 16, 18, 20)
Section 11.5 (4, 6, 10, 12, 14, 20)
Section 11.6 (2, 4, 6, 8, 10, 12, 14)

Homework 12, due Thursday, December 11:
Section 11.6 (26)
Section 11.8 (4, 8, 12, 18)
Section 11.9 (4, 12, 16, 26, 34)
Section 11.10 (2, 6, 10, 14, 16)

Exams:

Exams and Solutions are posted on Sac CT.

Lecture Schedule

If my lecture is essentially the same as the book, please understand if I don't type up lecture notes.

Date	Topics	Book	Notes	Code	Project
1. T-W 9/2-3	Introduction, Review of Integration.	§ 5.1-5.4	(pdf)	(tex)
2. R 9/4	The Substitution Rule.	§ 5.5	(pdf)	(tex)
3. F 9/5	The Substitution Rule, Areas Between Curves.	§ 5.5, 6.1	(pdf)	(tex)
4. M 9/8	Areas Between Curves, cont'd.	§ 6.1	(pdf)	(tex)
5. T-W 9/9-10	Volumes, I.	§ 6.2	(pdf)	(tex)
6. R 9/11	Volumes, II.	§ 6.2	(pdf)	(tex)
7. F 9/12	Volumes, III.	§ 6.3	(pdf)	(tex)
8. M 9/15	Volumes, IV.	§ 6.3	(pdf)	(tex)
9. T-W 9/16-17	Volumes, V.	§ 6.3	(pdf)	(tex)
10. R 9/18	Review. (We will come back to Avg Value later.)		(pdf)	(tex)
11. F 9/19	Review.		(pdf)	(tex)
M 9/22	MIDTERM 1
12. T-W 9/23-24	Integration by Parts, I.	§ 7.1	(pdf)	(tex)
13. R 9/25	Integration by Parts, II.	§ 7.1	(pdf)	(tex)
14. F 9/26	Trigonometric Integrals.	§ 7.2	(pdf)	(tex)
15. M 9/29	Trig. Substitution, I.	§ 7.3	(pdf)	(tex)
16. T-W 9/30-10/1	Trig. Substitution, II.	§ 7.3	(pdf)	(tex)
17. R 10/2	Trig. Substitution, III.	§ 7.3	(pdf)	(tex)
18. F 10/3	Average Value, Exp/Log Review.	§ 6.5	(pdf)	(tex)
19. M 10/6	Homework in Class.
20. T-W 10/7-8	HW questions, Finish Exp/Log review		See Lecture 18 Notes.
21. R 10/9	Rational Functions, I.	§ 7.4
22. F 10/10	Rational Functions, II.	§ 7.4
23. M 10/13	Rational Functions, III.	§ 7.4
24. T-W 10/14-15	Review.	§ 7.1-7.4
R 10/16	MIDTERM 2
25. F 10/17	Approximate Integration, I.	§ 7.7	(pdf)	(tex)
26. M 10/20	Approximate Integration, II.	§ 7.7	(pdf)	(tex)
27. T-W 10/21-22	Approximate Integration, III.	§ 7.7	(pdf)	(tex)
28. R 10/23	Improper Integrals.	§ 7.8	(pdf)	(tex)
29. F 10/24	Arclength.	§ 8.1
30. M 10/27	Area of a Surface of Revolution, I.	§ 8.2	(pdf)	(tex)
31. T-W 10/28-29	Area of a Surface of Revolution, II.	§ 8.2
32. R 10/30	Sequences.	§ 11.1	(pdf)	(tex)
33. F 10/31	Sequences, II.	§ 11.1			Proposal
34. M 11/3	Series, I.	§ 11.2
35. T-W 11/4-5	Series, II.	§ 11.2
36. R 11/6	The Integral Test, I.	§ 11.3
37. F 11/7	The Integral Test, II.	§ 11.3
38. M 11/10	The Comparison Test.	§ 11.4
T 11/11	NO CLASS (Veteran's Day)
39. W-R 11/12-13	Review.
F 11/14	MIDTERM 3
40. M 11/17	Review, Went over the Exam.
41. T-W 11/18-19	Review, Answered Questions.
42. R 11/20	Make-Up Quiz, Limit Comparison Test.	§ 11.4
43. F 11/21	Alternating Series Test.	§ 11.5
44. M 11/24	Absolute Convergence, Conditional Convergence.	§ 11.6			First Draft
45. T-W 11/25-26	Ratio Test and Root Test.	§ 11.6
R-F 11/27-28	NO CLASS (Thanksgiving)
46. M 12/1	Power Series, I.	§ 11.8
47. T-W 12/2-3	Power Series, II.	§ 11.8
48. R 12/4	Power Series, III.	§ 11.8
49. F 12/5	Representations of Functions as Power Series.	§ 11.9
50. M 12/8	Taylor Series, I.	§ 11.10			Final Draft
51. T-W 12/9-10	Taylor Series, II.	§ 11.10	(pdf)	(tex)
52. R 12/11	Review.
53. F 12/12	Review.


	FINAL EXAM: 12/15, 8-10am (8am class), 12/17, 8-10am (9am class)