Math 42 Homework
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 will be similar to problems from weekly homework assignments. For complete understanding of the course material, be sure that you understand both the discussion problems and the weekly homework problems. (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 (from Math 41 last quarter).
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 3:15 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 two homework scores will be dropped at the end of the quarter.
Solutions will be posted on this page by the following morning.
- For everyone:
- Read the Section Assignments and sign up
for the appropriate section on
CourseWork.
(Discussion sections begin Tuesday, January 10.)
- 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.)
- Especially for those who didn't take Math 41 in the fall (but
really for everyone else, as well):
- 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" if you didn't take Math 41) and
the About homework section above
so you know the course policies and logistics.
- Look at the links at the bottom of the course
home page and follow the suggestions there
about reading those pages.
- Section 5.2:
- Section 5.3:
- Section 5.5:
- Section 5.6:
- Section 5.7 (p389-91):
- Don't miss this important supplemental handout by Stewart.
- #1, 5, 7, 13, 15, 35; plus, evaluate the integral
- For the answer to the additional problem above, click here.
- Section 5.7 (p391-3):
- Section 5.9:
- Section 5.10:
- Rogawski reprint:
- Click here for information on electronic access during the quarter. (For example, if you haven't yet received the Rogawski reprint in class, or if you wish to view odd-numbered exercise answers, or see any section of the full text.)
- Rogawski Section 6.1:
- Rogawski Section 6.2 (p365-8 only):
- #5, 17, 21, 27, 31 [click for answers]
- Practice the problems below:
- Suppose the density of air located h meters above the earth's surface is some function f(h) kilograms per cubic meter. Write an integral involving f that represents the total mass of air in a cylindrical column 2 meters in diameter and 25 kilometers high, with base on the surface of the earth. [Click here for solutions to 1 and 2]
- The city of Circleboro is densely populated near its center, and its population density thins out towards the city limits. In fact, at a distance r miles from the center, the city's population density is 2000(3 – r)/π people per square mile. Assuming that the population density at the city limits is zero, what is the radius of the city? What is the total population of the city? [Click here for solutions to 1 and 2]
- Problem 9 of 2011 Exam 1. [solutions page]
- Rogawski Section 6.3:
- Rogawski Section 6.4:
- Rogawski Section 7.7:
- Section 8.1:
- Section 8.2:
- #1, 11, 19, 23, 25, 31, 41, 59
- Section 8.3:
- #3, 5, 9, 15, 19, 21, 29, 31, 33
- 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
- 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 [Solutions to 23, 27]
- In reading 8.8, skip "Applications to Physics" at the end.
- Section 7.1
- #7, 9, 11, 13
- Read this handout by M. Meckes on "What differential equations are all about," and do the problems on the last page.
- Section 7.2
- #1, 3-6, 19, 23 (Here's a scan of the direction field in #1: print & use if you like)
- Section 7.3
- #3, 13, 21, 39, 43, 47, 49
- In reading Section 7.3, skip "Orthogonal Trajectories," but do read "Mixing Problems" at the end.
- Hint for #49: Use the first two sentences to write a differential equation for m(t) alone, then use the product rule to find an expression for (mv)', and finally combine this with the information given to find a differential equation for v(t) alone.
- Section 7.4
- Section 7.5
- #1, 5, 9, 11, 15, 17
- Note: You may cite (without solving) the explicit solution to a logistic equation whenever you need it; its formula will also be provided on the exam. (For example, you can use a u-substitution technique to solve the equations of #15e and #17c by transforming them into logistic equations for u(t) and citing the solution.)
- Section 7.6
- Here are some additional problems (not to be collected) to try before the Final Exam; consider these as a never-due "Weekly Homework 10." [Solutions]
- 7.5: #4, 10, 18 (skip c)
- 7.6: #2, 4, 9 (skip graphing), 10
- Note: There is a misprint in #2a -- the expression for dy/dt should read "0.08y+0.00004xy".
Please see above for Weekly Homework policies.
- Due Tuesday, Jan. 17. Solutions (pdf)
- Due Tuesday, Jan. 24. Solutions (pdf)
- Due Tuesday, Jan. 31. Solutions (pdf)
- Due Tuesday, Feb. 7. Solutions (pdf)
- Due Tuesday, Feb. 14. Solutions (pdf)
- Due Tuesday, Feb. 21. Solutions (pdf)
- Due Thursday, Mar. 1. Solutions (pdf)
- 8.6: #6, 14, 30, 32 (For #14, you can use the result of Example 7 as your starting point.)
- 8.7: #18, 30, 54, 64
- 8.8: #12 (skip c), 14 (skip c), 20, 24, 26 (For #12, you can use your result from 8.7 #18.)
- Note on "decimal places": 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 (10–k)/2."
- Due Thursday, Mar. 8. Solutions (pdf)
- 7.1: #2, 8b,d, 10, 12
- 7.2: #2, 20, 22
- 7.3: #2, 8, 10, 14, 34, 40(b), 42
- Note for 7.2 #2, 20: If you prefer, you may download and print a scan of the direction fields here.
- Due Tuesday, Mar. 13. Solutions (pdf)
- 7.3: #44, 48, 50b, 53a (see note)
- 7.4: #10, 12, 14, 22
- Note for 7.3 #50b: Assume v0 is positive. (Find an expression for s(t), and determine what happens to s(t) as t approaches infinity.)
- Not collected: extra problems for practice before the Final Exam (see also Exams Page). Solutions (pdf)
- 7.5: #4, 10, 18 (skip c)
- 7.6: #2, 4, 9 (skip graphing), 10
- Note: There is a misprint in #2a -- the expression for dy/dt should read "0.08y+0.00004xy".
Back to the Math 42 home page.