# Math 42 Homework

 Home Schedule Section Assignments Office Hours Homework Exams

## Description and Policies

Problems from the textbook and other handouts will serve one of two purposes in Math 42: 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; and
• completed assignments which contain multiple pages should be stapled for easy grading -- one point will be deducted for not doing this.
• For a guide to solution completeness, see these sample writeups for homework and exam problems (using problems from Chapter 1 of your text).

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 (and the selection of problems chosen to be graded will not be announced in advance); as a result, be sure to look over the posted solutions to check your ungraded problems when your paper is returned.

Logistics for Weekly Homework: Assignments must be turned in to your TA (discussion section leader) -- 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; submission to TA mailboxes is not permissible.) The deadline is 3:15 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 homework score will be dropped at the end of the quarter. Solutions will be posted on this page by the following morning.

Students are encouraged to pick up their graded homework assignments promptly; please make arrangements with your TA to pick it up outside of class (or via electronic scan if absolutely necessary) if you cannot attend the discussion section on the day the homework is returned. It is ultimately your responsibility to look over your graded assignment while consulting the posted solutions, not only to check your understanding but also to find any grading errors or mis-typed entries in your CourseWork grade record. If you find an error in how an assignment was graded or recorded, please appeal to your section leader (who has final authority on all homework appeals). If more than a week has passed since an assignment was returned in section, your CourseWork score entry for that assignment can no longer be changed.

## List of Daily Discussion Problems

• First-day checklist:
• Read the Section Assignments and sign up for the appropriate section on CourseWork. (Discussion sections begin Tuesday, September 23.)
• Look at the Course Schedule. Make sure you know when the 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 exam times, as soon as you know about it. (The deadline is a week prior to the exam, but it makes everyone's life easier to take care of things earlier.)
• Look over the course web page and get to know what information is there. Read the General Information page (especially the section "About this class") and the About homework section above so you know the course policies and logistics.
• Section 5.2:
• #7, 9, 51
• Section 5.3:
• #17, 23, 43, 51
• Section 5.5:
• #11, 19, 21, 51, 57, 61
• Section 5.6:
• #5, 7, 13, 21, 27, 39
• Section 5.10:
• Appendix D, pg A30-33:
• #17, 19, 23
• Additional problem 1: Use Definition 4 to prove that ${\displaystyle \lim_{n\to\infty} e^n=\infty}$.
• Additional problem 2: Use Definition 2 to prove that ${\displaystyle \lim_{x\to\infty} \arctan(x)=\tfrac{\pi}{2}}$. Show how Definition 2 can be modified so that you can write a sentence (involving $N$, $\epsilon$, etc.) stating that ${\displaystyle \lim_{x\to -\infty} \arctan(x)=-\tfrac{\pi}{2}}$ (which you don't have to prove).
• Section 5.9:
• Section 8.1 (thru pg 560 only):
• #9, 57
• Section 8.2:
• #1, 11, 19, 23, 25, 31, 37, 41, 59
• Hint for #31: Use the fact that $\frac{2}{n^2-1}=\frac{1}{n-1}-\frac{1}{n+1}$.
• Section 8.3:
• #3, 5, 9, 15, 19, 21, 29, 33, 37
• Note: Be sure to include all your reasoning when stating and justifying your answer -- this may require a sentence or two in some cases. (Indicate clearly which tests you use and what conclusions you draw from them.)
• Section 8.4
• #5, 15, 23, 29, 31, 33, 37
• Note: Be sure to include all your reasoning when stating and justifying your answer -- this may require a sentence or two in some cases. (Indicate clearly which tests you use and what conclusions you draw from them.)
• Grab-bag questions on series convergence (8.2-8.4 combined)
• Section 8.5
• #5, 7, 11, 13, 19, 25
• Section 8.6
• #1, 3, 7, 11, 13, 31, 35a, 37
• Section 8.7
• #2, 3, 4, 7, 14, 29, 39, 47, 51, 59, 63 [Solutions to 2, 4, 14]
• In reading 8.7, skip "Multiplication and Division of Power Series" at the end.
• Recall that "Maclaurin series" means "Taylor series centered at 0."
• Section 8.8
• #13, 21, 23, 27
• In reading 8.8, skip "Applications to Physics" at the end.

## List of Weekly Homework Assignments

Please see above for Weekly Homework policies.
1. Due Tuesday, Sept. 30. Solutions (pdf)
2. Due Tuesday, Oct. 7. Solutions (pdf)
3. Due Tuesday, Oct. 14. Solutions (pdf)
4. Due Tuesday, Oct. 21.
• 8.5: #8, 20, 24, 26, 34
• 8.6: #6, 14, 30, 32 (see notes)
• Note for 8.6 #14: You can use the result of Example 7 as your starting point.
• Note on "decimal places" (8.6 #30, etc.): For the purposes of this assignment, the phrase "find X to k decimal places" means "find an approximation to X that consists of k digits after the decimal point and for which the absolute value of error is justifiably less than or equal to (10k)/2."

Autumn 2014 -- Department of Mathematics, Stanford University