Math 31, Fall 2015

Mathematics 31, Fall 2015

Calculus II

Lectures:

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

Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Tentative Office Hours:
MTWRF 9-9:50am. Also by appointment.

A description of the course: Math 31, Fall 2015 (pdf)

Drop Policy

Announcements:

We will be using the following FREE textbook:
APEX Calculus
The bookstore is carrying Edition 2.0, but you might prefer to have the new Edition 3.0. I think they are the same except with small errors fixed in Edition 3.0.
Final Exam Schedule. Please take this into account when registering for classes:
Section 7: Monday, December 14, 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):

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 9: 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 30, 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.
Monday, November 23: 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!
Include citations/references: properly cite your sources (including for any figures you get from the internet). Do not plagiarize!
Friday, December 4: The final draft of your essay is due.
Turn in the first draft together with the final draft.

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, September 4. (The problem numbers correspond to the new Version 3.0!)
Section 5.1 (27)
Section 5.2 (6, 10)
Section 5.3 (16, 28)
Section 5.4 (6, 29)
Section 6.1 (4, 8, 12, 20, 24, 32, 62, 72, 76, 78)

Homework 2, "Due" Friday, September 11. (The problem numbers correspond to the new Version 3.0!)
Please get started over the weekend!
Section 7.1 (4, 8, 12, 14, 18, 20)
Section 7.2 (4, 6, 8, 12)

Homework 3, "Due" Monday, September 21---This is the day of Exam 1.
Section 7.2 (14, 16, 18)
Section 7.3 (6, 8, 10, 12, 14, 16, 18)
Again, you aren't turning this homework in, so I won't really know how much of the assignment you did. But keep in mind that the Exam will look a lot like the homework, so the more homework you do, the better you will do on the exam!

Homework 4, "Due" Friday, October 2. (The problem numbers correspond to the new Version 3.0.)
Please get started over the weekend!
Section 6.2 (6, 8, 24, 26, 34, 40, 46)
Section 6.3 (1, 2, 3, 8, 10, 18, 28, 32)

Homework 5, "Due" Friday, October 9. (The problem numbers correspond to the new Version 3.0.)
Please get started over the weekend!
Also remember that "LaTeX Proof" is due on Friday.
Section 6.4 (4, 6, 8, 16, 26, 28, 30, 32)
Section 6.5 (8, 10, 12, 16, 18, 26)

Homework 6, "Due" Friday, October 23. (The problem numbers correspond to the new Version 3.0.)
Please get started over the weekend!
Section 6.8 (6, 14, 16, 20, 22, 24, 26, 28, 30)
Section 7.4 (6, 8, 10, 18)

Homework 7, "Due" Friday, October 30. (The problem numbers correspond to the new Version 3.0.)
Please get started over the weekend!
Section 6.8 (32, 34)
Section 7.4 (12, 14, 16, 29, 30, 31, 32, 33)
Section 8.1 (6, 10, 12, 18, 20)

Homework 8, "Due" Friday, November 6. (The problem numbers correspond to the new Version 3.0.)
Section 8.1 (22, 26, 28, 36, 38)
Section 8.2 (2, 6, 8, 12, 20, 22, 24, 26, 32, 34, 36)

Homework 9, "Due" Thursday, November 12---the day of Exam 3
Section 8.2 (10, 14, 18, 28, 30, 38, 40, 42, 44)
The exam will cover Sections 6.8 (Improper Integrals), 7.4 (Arclength and Surface Area), 8.1 (Sequences), and 8.2 (Series)

Homework 10, "Due" Friday, November 20
Section 8.3 (6, 10, 12, 16, 18, 20, 22, 24, 28, 30)
Section 8.4 (8, 10, 12, 14)

Homework 11, "Due" Friday, December 5
Section 8.4 (18, 20, 22, 26, 28, 30)
Section 8.5 (1, 6, 8, 10, 12, 14, 23, 27)
Section 8.6 (6, 10, 12)

Homework 12: practice for the final exam
Section 8.6 (18, 20, 26, 28, 34, 36)
Section 8.7 (8, 12, 14, 16, 18, 20)
Section 8.8 (6, 20)

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
0. Prerequisites	The N Commandments		(pdf)	(tex)
1. M 8/31	Introduction, Review of Integration.	§ 5.1-5.4	(pdf)	(tex)
2. T 9/1	The Substitution Rule.	§ 6.1	(pdf)	(tex)
3. R 9/3	The Substitution Rule, Areas Between Curves.	§ 6.1, 7.1	(pdf)	(tex)
4. F 9/4	Areas Between Curves, cont'd.	§ 7.1	(pdf)	(tex)
M 9/7	NO CLASS (Labor Day)
5. T 9/8	Volumes, I.	§ 7.2	(pdf)	(tex)
6. R 9/10	Volumes, II.	§ 7.2	(pdf)	(tex)
7. F 9/11	Volumes, III.	§ 7.3	(pdf)	(tex)
8. M 9/14	Volumes, IV.	§ 7.3	(pdf)	(tex)
9. T 9/15	Volumes, V.	§ 7.3	(pdf)	(tex)
10. R 9/17	Review. (We will come back to Avg Value later.)		(pdf)	(tex)
11. F 9/18	Review.		(pdf)	(tex)
M 9/21	EXAM 1
12. T 9/22	Integration by Parts, I.	§ 6.2	(pdf)	(tex)
13. R 9/24	Integration by Parts, II.	§ 6.2	(pdf)	(tex)
14. F 9/25	Trigonometric Integrals.	§ 6.3	(pdf)	(tex)
15. M 9/28	Trig. Substitution, I.	§ 6.4	(pdf)	(tex)
16. T 9/29	Trig. Substitution, II.	§ 6.4	(pdf)	(tex)
17. R 10/1	Trig. Substitution, III.	§ 6.4	(pdf)	(tex)
18. F 10/2	Rational Functions, I.	§ 6.5
19. M 10/5	Rational Functions, II.	§ 6.5
20. T 10/6	Rational Functions, III.	§ 6.5
21. R 10/8	Homework in Class.
22. F 10/9	Average Value, Exp/Log Review.	§ 6.5	(pdf)	(tex)	LaTeX Proof
23. M 10/12	HW questions, Finish Exp/Log review		See Lecture 18 Notes.
24. T 10/13	Review.	§
R 10/15	EXAM 2
25. F 10/16	Improper Integrals, I.	§ 6.8	(pdf)	(tex)
26. M 10/19	Improper Integrals, II.	§ 6.8
27. T 10/20	Arclength, I.	§ 7.4
28. R 10/22	Arclength, II.	§ 7.4
29. F 10/23	Area of a Surface of Revolution, I.	§ 7.4	(pdf)	(tex)
30. M 10/26	Area of a Surface of Revolution, II.	§ 7.4
31. T 10/27	Sequences, I.	§ 8.1
32. R 10/29	Sequences, II.	§ 8.1	(pdf)	(tex)
33. F 10/30	Sequences, III.	§ 8.1			Proposal
34. M 11/2	Series, I.	§ 8.2
35. T 11/3	Series, II.	§ 8.2
36. R 11/5	Series, III.	§ 8.2
37. F 11/6	Series, IV.	§ 8.2
38. M 11/9	The Integral Test.	§ 8.3
39. T 11/10	Review.
W 11/11	NO CLASS (Veteran's Day)
R 11/12	EXAM 3
40. F 11/13	The Comparison Test, I.	§ 8.3
41. M 11/16	The Comparison Test, II.	§ 8.3
42. T 11/17	The Ratio Test, I.	§ 8.4
43. R 11/19	The Ratio Test, II.	§ 8.4
44. F 11/20	The Root Test.	§ 8.4
45. M 11/23	The Alternating Series Test.	§ 8.5			First Draft
46. T 11/24	Absolute Convergence, Conditional Convergence.	§ 8.5
R-F 11/26-27	NO CLASS (Thanksgiving)
47. M 11/30	Power Series, I.	§ 8.6
48. T 12/1	Power Series, II.	§ 8.6
49. R 12/3	Power Series, III.	§ 8.6
50. F 12/4	Representations of Functions as Power Series.	§ 8.6			Final Draft
51. M 12/7	Taylor Series, I.	§ 8.7, 8.8
52. T 12/8	Taylor Series, II.	§ 8.7, 8.8	(pdf)	(tex)
53. R 12/10	Review.
54. F 12/11	Review.


	FINAL EXAM: Monday, 12/14, 8-10am