Math 41 Autumn 2012 |
|
|
|
Problems from the textbook and other handouts will serve one of two purposes in Math 41: as uncollected Daily Discussion Problems
or as graded Weekly Homework.
Each is handled in a different way and has a different purpose.
About Daily Discussion Problems (Quick Jump to List):
Each time we cover a topic, we will list below the corresponding text section and also some "discussion problems" that will help direct the discussion in the upcoming Tuesday/Thursday section meetings. Some may be similar to problems from weekly homework assignments, and problems from prior years' exams will give you an idea of the level of exam questions. You should try working these discussion problems immediately after reading the book section(s) being covered in lecture. For complete understanding of the course material, be sure that you understand both the discussion problems and the weekly homework problems, in addition to all examples from the readings. (Work on daily discussion problems will not be collected.)
About Weekly Homework (Quick Jump to List):
Completing homework assignments is an essential part of this course. Problems are designed to reinforce concepts covered in lecture as well as to encourage students to explore implications of the results discussed in class. Very few students will be able to go through the entire course without struggling on many problems, so do not be discouraged if you do not immediately know how to solve a problem. In confronting difficult questions you should consider how the problem at hand connects to topics, definitions and/or theorems discussed in class.
When you have worked on a problem for a while and remain stuck, you are encouraged to ask for hints from your instructor or TA. Students may also discuss problems with one another, but must write solutions on their own. In particular if you have taken notes while discussing homework problems with friends or instructors, you must put these notes away when writing your solution. The Honor Code applies to this and all other written aspects of the course. Be warned: watching someone else solve a problem will not make homework a good preparation for tests. Don't get caught in the trap of relying on others to get through homework assignments.
- Students are expected to take care in writing their assignments. For instance,
- assignments should be written neatly;
- assignments should contain clear, complete solutions;
- solutions sets which contain multiple pages should be stapled; and
- never forget to put your name, your section number and your TA's name on the top of your work.
- For a guide to solution completeness, see this handout of sample writeups for homework and exam problems.
Partial progress toward solutions on problems will be awarded partial credit, but simply writing answers down without justification will receive zero credit. Please note that usually only a portion of each week's problems will be scored; the selection of problems chosen to be graded will not be announced in advance.
Logistics for Weekly Homework:
Assignments must be turned in to your TA -- you will not receive credit for work turned into another section leader.
(If you're unable to turn in your homework in section, slide it under your TA's office door.)
The deadline is 3:30 p.m. on the given due date, and no late homework will be accepted under any circumstances. (This is as much a courtesy to the grader as an incentive to stay current with the course and not fall behind.)
To accommodate exceptional situations such as a serious illness, your lowest two homework scores will be dropped at the end of the quarter.
Solutions will be posted on this page by the following morning.
|
- Getting started:
- Read the Section Assignments to determine which discussion section you should attend starting Tuesday. Note: you cannot use Axess to sign up for a discussion section, only a lecture. You must use CourseWork to make your discussion section choice -- and the chart on the page linked above will show you the options for times.
- Look at the Course Schedule. Make sure you know when the three exams are (not during the lecture time
or in the regular classroom; locations TBA) and when the weekly homeworks are due. If you have a conflict with one of the two midterm exam times,
as soon as you know about it. (The final exam's date and time cannot be changed.)
- Look over the course web page and get to know what information is
there. Read all the General Information on the home page
(including the section "About this class") and
the About homework section above so you know the course policies and logistics.
- Look at the links at the very bottom of the course home page and follow the suggestions there about reading those pages.
- Read sections 1.1 through 1.3 -- this is probably old familiar stuff, but we won't cover it all in lecture, so make sure you've seen it all.
- Section 1.1:
- #1, 7, 41, 43, 61, 63, 73
- Section 1.2:
- Section 1.3:
- #1, 3, 19, 27, 35, 43, 47, 51
- More first-week information:
- Section 1.5:
- #1, 4, 13, 19, 23, 29, 35 (graphing calculator portions optional)
- Note: For answers to all even-numbered problems listed as Daily Discussion Problems, click here.
- Section 1.6:
- Section 2.2:
- Section 2.3:
- Appendix D:
- Section 2.4:
- Section 2.5:
- #3, 19, 21, 23, 27, 33, 47, 49
- Fall 2008 Exam 1 #1b,c; 3b,c
- Fall 2006 Exam 1 #1b,c; 2b; 4
- Handout from Wednesday's lecture (10/3):
- Section 2.6:
- #7, 11, 17, 37, 43ab, 45, 47, 53
- Note: For now, use only the methods of these sections, not differentiation shortcuts you might have seen elsewhere.
- Fall 2007 Exam 1 #9
- Fall 2009 Exam 1 #6
- Section 2.7:
- #3, 7, 27, 35, 41, 49b
- Note: For now, use only the methods of these sections, not differentiation shortcuts you might have seen elsewhere.
- Fall 2006 Exam 1 #5, 6, 7
- Fall 2010 Exam 1 #5, 9a
- Fall 2009 Exam 1 #3, 4b
- Section 2.8:
- Section 3.1:
- Section 3.2:
- Section 3.3:
- Section 3.4:
- #1, 13, 19, 21, 27, 31, 49, 53
- Notes: In reading Section 3.4, skip the sub-section called "Tangents to Parametric Curves," which starts after Example 9 and ends on page 204.
- Section 3.5:
- #11, 23, 27, 31
- Additional problem: At what points does the curve in problem 23 have a horizontal tangent? (Answer: at (-1,2) and (1,-2).)
- Section 3.6:
- Section 3.7:
- Section 3.9:
- Section 4.1:
- Handout from Monday's lecture: Related Rates problem-solving tips
- #11, 12, 13, 14, 19, 25, 29, 35, 41
- Note: For answers to even-numbered problems listed above, click here.
- Note: Full solutions to problems 11-14 will made available and handed out in section, but there is no substitute for first working these practice problems yourself. Solutions to 11-14
- Section 4.5:
- #1, 13, 19, 27, 31, 37, 41, 53, 65
- Note: For #53, find the asymptotes only; after we cover Section 4.3, you should try graphing the function by hand.
- Section 4.2:
- #1, 3, 11, 33, 35, 43, 47, 55
- Section 4.3: (except for Mean Value Theorem, which we'll cover later)
- #5, 7, 29, 33, 39
- Now graph the function of Section 4.5 #53.
- Section 4.6:
- #3, 11, 19, 23, 25, 31, 45, 53, 57, 59a
- Exercises Page 326: #63c, 65a
- Notes: Recall that Chapter Review problems (like those on page 326) have full solutions available here [and also see Solutions to 11, 19, 23, plus comments] -- but you should be thinking carefully about all these problems on your own before consulting solutions.
- Handouts from lecture: Absolute Extrema for Optimization and Solutions to 4.6 #11, 19, 23, plus comments
- Keep in mind that some topics on prior-year second midterms, such as the Mean Value Theorem, Newton's Method, and Antidifferentiation, are not going to be covered on this week's exam (they'll be on our final exam instead).
- Section 4.3: (Mean Value Theorem topic, p272-3)
- Section 4.7:
- Section 4.8:
- Section 5.1:
- #1, 3, 15, 21
- Note: We will use sigma notation throughout the next three weeks; see Appendix F for a review.
- Section 5.2:
- #5, 7, 9, 17, 21, 23, 27, 40, 47, 49, 51 (click here for answer to #40)
- Fall 2008 Final Exam #10; 11b,c; 12b
- Fall 2006 Final Exam #8
- Fall 2009 Final Exam #9a,b; 10a
- Section 5.3:
- #7, 17, 23, 29, 31, 39, 43, 51, 53, 59
- Fall 2006 Final Exam #3a, 9, 11
- Fall 2008 Final Exam #9, 11a, 12a, 13
- Fall 2009 Final Exam #11a,b; 14a
- Collection of "other problems" page 2, #4; page 3, #7-prime
- Section 5.4:
- Section 5.5:
- #11, 19, 27, 29, 31, 35, 47, 55, 57, 61
- Fall 2007 Final Exam #14
- Fall 2009 Final Exam #10b, 13c
- Fall 2006 Final Exam #3d
- Section 5.6:
- #5, 7, 17, 21, 23, 25, 39, 45
- Fall 2009 Final Exam #13d,e; 14b
- Fall 2008 Final Exam #12d,e
- Early next week, we'll post solutions to a "Mock Weekly Homework #10" (no actual due date, but recommended practice before the final exam), which covers the following problems:
|
List of Weekly Homework Assignments
Please see above for Weekly Homework policies.
- Due Tuesday, Oct. 2. Solutions (pdf)
- 1.1: #12, 32
- 1.2: #4, 16
- 1.3: #6, 24, 48, 62
- 1.5: #22
- 1.6: #16, 26, 56
- Page 88: #6, 11 (explain your answer without a calculator), 12(a)
- Due Tuesday, Oct. 9. Solutions (pdf)
- 2.2: #16
- 2.3: #18, 20, 22, 38, 46
- Appendix D: #9, 12, 16
- 2.4: #40, 53
- 2.5: #8, 20, 36, 38c, 42 (skip the graphing calculator portions; all asymptotes should be justified with limit calculations)
- Due Tuesday, Oct. 16. Solutions (pdf)
- 2.6: #10ab, 50, 54 (use only the methods of this chapter, not differentiation shortcuts from Chapter 3)
- 2.7: #26, 36 (use only the methods of this chapter, not differentiation shortcuts from Chapter 3)
- 2.8: #16, 24, 32
- 3.1: #18, 48, 54 (skip the graphing calculator part)
- 3.2: #46, 57
- 3.3: #8, 22
- Due Tuesday, Oct. 23. Solutions (pdf)
- 3.4: #32, 56, 64, 92
- 3.5: #12, 30 (skip part c), 32
- 3.7: #32, 34, 44
- Due Tuesday, Oct. 30. Solutions (pdf)
- 3.6: #26, 40
- 3.9: #18, 22, 32, 36
- 4.1: #20, 28, 34, 40
- 4.5: #4, 12, 36, 38, 46
- Due Tuesday, Nov. 6. Solutions (pdf)
- 4.2: #32, 36, 52
- 4.3: #24, 28, 60
- 4.5: #52 (see special instructions just below)
- 4.6: #14, 28, 34, 56
- Note: for 4.5 #52, complete the following steps:
(a) find the vertical and horizontal asymptotes,
(b) find the intervals of increase or decrease,
(c) find the coordinates of all local extrema,
(d) find the intervals of concavity and the coordinates of all inflection points,
(e) use information from (a)-(d) to sketch the graph.
- Due Thursday, Nov. 15. Solutions (pdf)
- 4.3: #64, 66
- 4.7: #4, 24, 28, 30
- 4.8: #8, 28, 34, 38, 52, 55, 56
- Tip for 4.8 #56: Treat "downward" as the positive direction.
- Notes: For 4.7 #24b, 28, and 30, you'll need a calculator.
- Due Thursday, Nov. 29. Solutions (pdf)
- 5.1: #20
- 5.2: #8, 22, 28, 32, 38, 48, 54
- 5.3: #24, 26, 28, 50, 54, 62, 72
- Note: Do not use the Evaluation Theorem (Fundamental Theorem of Calculus) to solve problems in section 5.2; use only the area and limit properties of the definite integral introduced in that section.
- Due Tuesday, Dec. 4. Solutions (pdf)
- 5.4: #12, 20, 22, 30
- 5.5: #10, 22, 30, 50, 60, 68
- No due date (but try these before the final exam). Solutions (pdf)
|
|