Math 42 Homework

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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.

List of Daily Discussion Problems

• 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:
• Section 5.9:
• #1, 5, 17, 19, 33, 37
• Hint for #17: Don't bother trying to find the best possible value for K2, just find (and be prepared to justify) some number that definitely works; such a K2 should be found without a calculator.
• See also Problem 3 of 2010 Exam 1 and Problem 2 of 2009 Final Exam.
• 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.)
• 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
• 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.
• Trigonometric Integrals (Section 5.7 p389-91):
• 5.7 #1, 9, 16, 35.
• Partial Fraction Decomposition (Appendix G, plus Section 5.7 p391-3):
• Section 5.7 #19, 21, 27, 31, 33
• Appendix G #3, 31
• Section 6.1:
• In reading Section 6.1, skip "Areas Enclosed by Parametric Curves" at the end.
• #3, 7, 17, 27, 41
• Section 6.2:
• #5, 19, 29, 33, 35, 41
• Section 6.3:
• #1, 9, 15, 35
• Section 6.8
• #1, 7, 9, 11, 13, 14, 17
• Further advice: for another problem involving the normal distribution, see Problem 4 of 2010 final exam.
• Section 7.1
• #7, 11, 13
• Section 7.2
• #1, 3-6, 19, 23
• Section 7.3
• #3, 13, 21, 39, 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.
• 7.4: #10, 12, 14, 22
• 7.5: #4, 10, 18 (see notes)
• Note for 7.3 #40b: Be sure to use that x(0)=0 (which is stated in part a but intended for use in all parts).
• Note for 7.5 problems: You may cite (without solving) the explicit solution to a logistic equation (page 534) whenever you need it.
• 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".

List of Weekly Homework Assignments

Please see above for Weekly Homework policies.

Autumn 2014 -- Department of Mathematics, Stanford University