Math 31, Fall 2017

Mathematics 31, Fall 2017

Calculus II

Lectures:

Section 7: Mondays, Tuesdays, Wednesdays, and Fridays, 8-8:50am
Room 126, Library

Section 8: Mondays, Wednesdays, and Fridays, 12-12:50pm, in Room 1004, Tahoe Hall
and Tuesdays, 12-12:50pm, in Room 231, Alpine Hall

Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Tentative Office Hours:
M 9-9:50am, T 9-10:15, and WF 11-11:50am. Also by appointment.

A description of the course: Math 31, Fall 2017 (pdf)

Drop Policy

Announcements:

Textbook. There is no required textbook, but all of the class material can be found in either of the following two textbooks:
1. The classic: Calculus (Early Transcendentals), by James Stewart
2. OpenStax Calculus, Volume 2.

PAL for Math 31. 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. Five sections of NSM 12F are open:

1 81279 NSM 12F 01 Peer-Assisted Learning MATH 31 DIS 1 8 1 7 0 0 TR 12:00P-12:50P EUR413C 20 Pigno V.
1 81323 NSM 12F 02 Peer-Assisted Learning MATH 31 DIS 1 8 0 8 0 0 MW 02:00P-02:50P MND3007 15 Pigno V.
1 81341 NSM 12F 03 Peer-Assisted Learning MATH 31 DIS 1 8 1 7 0 0 MW 03:00P-03:50P ALP205 20 Pigno V.
1 81342 NSM 12F 04 Peer-Assisted Learning MATH 31 DIS 1 8 1 7 0 0 TR 08:00A-08:50A LSN2300 28 Pigno V.
1 86670 NSM 12F 05 Peer-Assisted Learning MATH 31 DIS 1 8 1 7 0 0 TR 01:30P-02:20P EUR413C 20 Pigno V.

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.
Even if you do not enroll in NSM 12F, you may still go to the PAL facilitator office hours for help. Office hours of the PAL leaders are held in SQU 315 and the times will be announced when they become available. Times of office hours will also be posted outside Prof. Shanbrom's office and SQU 315.

Final Exam Schedule.
Section 7: Monday, December 11, 8-10am.
Section 8: Wednesday, December 13, 10:15am-12:15pm.

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 6: 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 27, 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 20: 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 1: 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.

Quiz 1 on Friday, September 1:
Section 1.5 (255, 259, 263, 271, 272, 274, 276, 279, 284, 292, 293, 294)
...and read the book.

Quiz 2 on Friday, September 8:
Section 2.1 (4, 8, 13, 14, 16, 19)
Section 2.2 (58, 64, 68, 75, 76, 82, 90, 91, 98)
...and read the book.
FOR QUIZ 1.5: Section 1.5 (265, 266, 269, 270, 281, 282, 297)

Additional problems to review for Exam 1 on Monday, September 18:
Section 2.2 (78, 80, 96)
Section 2.3 (120, 122, 130, 132, 140, 142)
Please continue to work on all previous homework assignments, and feel free to do even more problems for practice.
I will give you a practice exam next week that we will work on together.

Quiz 3 on Wednesday, September 27:
Section 3.1 (9, 10, 11, 12, 16, 17, 24, 25, 36, 40, 42)

Quiz 4 on Tuesday, October 3:
Section 3.2 (78, 82, 83, 90, 91, 106, 107)
Section 3.3 (134, 136-139, 142, 146, 147)

Quiz 5 on Monday, October 9:
Section 3.4 (198, 199, 201, 202, 203, 207, 208, 211, 212)
and Exam 2 is on Wednesday, October 11.

Quiz 5.5 on Wednesday, October 18:
Integration by Parts problem---look over old homework.

Quiz 6 on Friday, October 20:
Section 3.7 (348-352, 362-367, 374-376)
Section 2.4 (166, 171-174, 176-177)

Quiz 7 on Friday, October 27:
Section 2.4 (166, 171-174, 176-177) (since I didn't quiz you on it last week)
Section 2.4 (191, 192, 193, 195, 196, 197, 207, 208)

Quiz 8 on Tuesday, October 31:
Section 5.1 (6, 8, 15, 16, 27, 28, 38, 40, 42)

Quiz 9 on Friday, November 3:
Section 5.2 (67, 68, 72, 73, 75, 76, 82, 86, 88, 89)
Remember that we have Exam 3 on Wednesday, November 8.

Quiz 10 on Wednesday, November 15:
Covering Sequences and Series. Here are some additional problems:
Section 5.1 (10, 14, 31, 32, 43, 48, 50, 51)
Section 5.2 (70, 80, 84, 87, 90, 91, 92, 93, 94, 95, 96)

Quiz 11 on Monday, November 27:
Section 5.3 (158, 160, 161, 169, 170)
Section 5.4 (196, 199, 201, 202, 211, 212)
Section 5.6 (Ratio Test) (320, 321, 322, 323, 324)

Quiz 12 on Friday, December 1:
Section 5.5 (250, 252, 255, 264, 294, 296, 298)
Section 6.1 (7, 10, 13, 14, 17, 20, 23, 24, 25, 26, 30, 35, 36, 37)

Quiz 13 on Friday, December 8:
Section 6.2 (70, 79, 80, 88, 90, 92, 96)
Section 6.3 (116, 140, 146, 150, 152, 154, 158)

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.
Also, I will incorporate parametric equations and polar coordinates, and the lecture schedule will be updated accordingly.

	Date	Topics	Stewart	OpenStax	Notes	Code	Project
	0. Prerequisites	The N Commandments			(pdf)	(tex)
Week 1	1. M 8/28	Introduction, Review of Integration.	§ 5.1-5.4	§ 1.1-1.4	(pdf)	(tex)
	2. T 8/29	The Substitution Rule.	§ 5.5	§ 1.5	(pdf)	(tex)
	3. W 8/30	The Substitution Rule, Areas Between Curves.	§ 6.1	§ 2.1	(pdf)	(tex)
	4. F 9/1	Areas Between Curves, cont'd.	§ 6.1	§ 2.1	(pdf)	(tex)
Week 2	M 9/4	NO CLASS (Labor Day)
	5. T 9/5	Volumes, I.	§ 6.2	§ 2.2	(pdf)	(tex)
	6. W 9/6	Volumes, II.	§ 6.2	§ 2.2	(pdf)	(tex)
	7. F 9/8	Volumes, III.	§ 6.3	§ 2.3	(pdf)	(tex)
Week 3	8. M 9/11	Volumes, IV.	§ 6.3	§ 2.3	(pdf)	(tex)
	9. T 9/12	Volumes, V.	§ 6.3	§ 2.3	(pdf)	(tex)
	10. W 9/13	Review. (We will come back to Avg Value later.)			(pdf)	(tex)
	11. F 9/15	Review.			(pdf)	(tex)
Week 4	M 9/18	EXAM 1
	12. T 9/19	Integration by Parts, I.	§ 7.1	§ 3.1	(pdf)	(tex)
	13. W 9/20	Integration by Parts, II.	§ 7.1	§ 3.1	(pdf)	(tex)
	14. F 9/22	Trigonometric Integrals.	§ 7.2	§ 3.2	(pdf)	(tex)
Week 5	15. M 9/25	Trig. Substitution, I.	§ 7.3	§ 3.3	(pdf)	(tex)
	16. T 9/26	Trig. Substitution, II.	§ 7.3	§ 3.3	(pdf)	(tex)
	17. W 9/27	Trig. Substitution, III.	§ 7.3	§ 3.3	(pdf)	(tex)
	18. F 9/29	Rational Functions, I.	§ 7.4	§ 3.4	(pdf)	(tex)
Week 6	19. M 10/2	Rational Functions, II.	§ 7.4	§ 3.4
	20. T 10/3	Rational Functions, III.	§ 7.4	§ 3.4	See Lecture 18 Notes.
	21. W 10/4	Homework in Class.
	22. F 10/6	Average Value, Exp/Log Review.	§ 6.5	§ 2.7			LaTeX Proof
Week 7	23. M 10/9	HW Questions, Finish Exp/Log Review.	§ 6.5	§ 2.7
	24. T 10/10	Review.	§
	W 10/11	EXAM 2
	25. F 10/13	Improper Integrals, I.	§ 7.8	§ 3.7
Week 8	26. M 10/16	Improper Integrals, II.	§ 7.8	§ 3.7
	27. T 10/17	Arclength, I.	§ 8.1	§ 2.4	(pdf)	(tex)
	28. W 10/18	Arclength, II.	§ 8.1	§ 2.4	(pdf)	(tex)
	29. F 10/20	Area of a Surface of Revolution, I.	§ 8.2	§ 2.4
Week 9	30. M 10/23	Area of a Surface of Revolution, II.	§ 8.2	§ 2.4	(pdf)	(tex)
	31. T 10/24	Sequences, I.	§ 11.1	§ 5.1
	32. W 10/25	Sequences, II.	§ 11.1	§ 5.1	(pdf)	(tex)
	33. F 10/27	Sequences, III.	§ 11.1	§ 5.1			Proposal
Week 10	34. M 10/30	Series, I.	§ 11.2	§ 5.2
	35. T 10/31	Series, II.	§ 11.2	§ 5.2
	36. W 11/1	Series, III.	§	§
	37. F 11/3	Series, IV.	§	§
Week 11	38. M 11/6	The Integral Test.	§ 11.3	§ 5.3
	39. T 11/7	Review.
	W 11/8	EXAM 3
	F 11/10	NO CLASS (Veteran's Day)
Week 12	40. M 11/13	The Comparison Test, I.	§ 11.4	§ 5.4
	41. T 11/14	The Comparison Test, II.	§ 11.4	§ 5.4
	42. W 11/15	The Ratio Test, I.	§ 11.6	§ 5.6
	43. F 11/17	The Ratio Test, II.	§ 11.6	§ 5.6
Week 13	44. M 11/20	The Root Test.	§ 11.6	§ 5.6			First Draft
	45. T 11/21	The Alternating Series Test.	§ 11.5	§ 5.5
	46. W 11/22	Absolute Convergence, Conditional Convergence.	§ 11.6	§
	R-F 11/23-24	NO CLASS (Thanksgiving)
Week 14	47. M 11/27	Power Series, I.	§ 11.8	§ 6.1
	48. T 11/28	Power Series, II.	§ 11.8	§ 6.1
	49. W 11/29	Power Series, III.	§ 11.8	§ 6.2
	50. F 12/1	Representations of Functions as Power Series.	§ 11.9	§ 6.3			Final Draft
Week 15	51. M 12/4	Taylor Series, I.	§ 11.10	§ 6.3
	52. T 12/5	Taylor Series, II.	§ 11.10	§ 6.3	(pdf)	(tex)
	53. W 12/6	Review.	§	§
	54. F 12/8	Review.

		FINAL EXAM: Section 7: Monday, 12/11, 8-10am

		FINAL EXAM: Section 8: Wednesday, 12/13, 10:15am-12:15pm