## Homework for Math 309A, Autumn 2016

There will be weekly homework assignments, usually due on Fridays. (Holidays in November will necessitate some variations.) Seven of the assignments will be collected and scored for 10 points. Typically two problems will be graded for three points each, and the remaining four points will be for completing the rest of the assignment (which will not be checked for correctness). After a homework assignment is graded, more details about the grading will be given with the assignment below.

HW 1, Week 1 will not be collected or graded.
To prepare for the worksheet on Monday 10/3, be sure you know how to compute determinants, and review using row reduction to solve systems of linear equations.
Also do the following problems. §7.1: #2,3,6; §7.2: 1,4,8,10,14,16. You can check the answers to these in the back of the book.

HW 2, Week 2, due Friday 10/7. §7.2: #13,17,24; §7.3: 6,7,8,17,18,23,25.
Optional problems on theory: good to read, work on if interested, don't turn in. For this week, the optional problems are §7.3: 31,34.
Grading: §7.3, #8 & 18 three points each, remaining four points for turning in the rest of the assignment.

HW 3, Week 3, due Friday 10/14, is given in this pdf.

HW 4, Week 4, due Friday 10/21. §7.5: #24(ab),26(ab); §7.6: #2,3,4,7; §7.8: #2,4,5,6,7 - (a) only in 7.
For this and later assignments, direction fields, trajectories, and phase portraits may be drawn by computer or by hand.
Optional theory problems: §7.5: #29 (connects our methods to what you learned about 2nd order equations in Math 307); §7.8: Read paragraph at end of p. 437 and do #18 & 19, then see me to discuss.
Grading: §7.6, #2, & §7.8, #4, three points each, remaining four points for turning in the rest of the assignment.

HW 5, Week 5, due Friday 10/28. §7.6: #13,17; §7.7:#3,11; §7.9: #1,4,5. (Not 7.8, as posted earlier)
In the §7.9 problems, if the matrix A is the same as in an earlier homework problem (either earlier in this assignment or in an earlier assignment), you may mention the earlier problem and state its solution; you don't have to do the work of finding it again.
Grading: §7.6, #17, & §7.9, #1, three points each, remaining four points for turning in the rest of the assignment.

HW 6, Week 6, will not be collected or graded. All problems in this assignment are in the student solutions manual.
Do these by 11/9 to get started thinking seriously about chapter 10. §10.1: #3,14,18; and
§10.5:#3,5,8 - for these problems, read §10.5 only up through equation (18) on p. 627.

Week 7: No homework, because of Friday holiday! Homework 7 and 8 will be due on Wednesdays, Nov. 16 and 23.
Office hours will added on Tuesdays for those two weeks. Note that Nov. 23 is the day before Thanksgiving.

HW 7, Week 8, due on Wednesday, 11/16.
§10.5: #1,6,7 - for these problems, you only need §10.5 up through equation (18) on p. 627.
§10.2:#1,2,6.
Fourier Series Homework handout: Problems 1(a)&(c) (don't forget the graphs) and 3(a)&(c). Recommended: start optional problem 2.
A CORRECTION has been made to the handout: in the very last line, it now say "h(x) = g(x - 3)" (not "g(x - π)" as in the original).
Grading: §10.5, #7, & Handout, #1a, three points each, remaining four points for turning in the rest of the assignment.

HW 8, Week 9, due on Wednesday, 11/23.
CAUTION: Be sure to read the instructions for each problem, which may be given earlier on the page, before a set of problems.
Fourier Series Homework handout (link above): #1(d),3(bde). Be sure to add the result of 1(d) to your table of series.
§10.4:#9,10,17,18; §10.5: #9.
Grading: Handout #3(e), four points; §10.5 #9, two points; remaining four points for turning in the rest of the assignment.

HW 9, Week 10, due on Friday, 12/2.
Additional Fourier Series Homework handout: do both problems. (Hard copy available in class on 11/28.)
§10.5: #11; §10.6: #9ab - in 9b just sketch instead of calculating for intermediate times,
#10ab, 12ab, 23 - in 23 you may leave the coefficients for w(t) expressed as integrals and skip the graphs.
Grading: §10.6 #10ab & 23, three points each,; remaining four points for turning in the rest of the assignment.

Additional reading on Fourier series for those who are interested.
For both more applications and more theory, try Fourier Analysis and Its Applications, by G. B. Folland. The Math library has three copies, one on reserve, two circulating.
For an interesting article on Fourier and how Fourier Series changed mathematics, see "Connections in Mathematical Analysis: the Case of Fourier Series," by E. Gonzalez-Velasco, American Mathematical Monthly, May 1992 (vol. 99, #5), pp. 427-441. You can access it online via UW Library e-journals list.

HW 10, Week 11, will not be collected or graded but should be done to prepare for the final exam.
§10.6: #15 with additions: Find the coefficients if L = π and f(x) = 5; or if f(x) = x.
(You can use the table if you consider the symmetry of the sine functions found in 15 on the interval (0, 2π).)
§10.7: #1a, 4a with L = 4, 5a, 8a with L = 4. What if the initial conditions were f(x) from #1 and g(x) from #8?
§10.8: #1ab, 2, 3a, 12ab, 14a. Note #16 gives an application to engineering/geophysics.

HOMEWORK FORMAT AND DEADLINES.

• Write your name, the class (e.g., Math 309A), the homework number, and the due date in the upper right corner of at least the front page of your homework.
• Don't be stingy with space. Leave at least one blank line between problems. If your writing shows through the paper, use only one side of the paper.
• Label every problem clearly.
• Show your work and/or reasoning. No credit will be given if all you show is the final answer given in the back of the book. More details about how much work to show are given below.
• STAPLE your pages together. The "fold and tear" method of fastening pages is not acceptable.
• Homework is due in class on the due date. It may also be turned in to the grader's mailbox, #13, in PDL C136*, up until 3:20 on the due date. After that time no late homework will be accepted. If you believe this policy is not reasonable for you because of special circumstances, please see the instructor to discuss it.
*The grader mailboxes are in PDL C136, which is next to the Math Department Office on the first floor and also contains a photocopier. (The Department Office is one floor above Math Advising.) There's a list on the end of the boxes, directly in front of the door, listing which box is for which class. The numbers are under the boxes.)

HOW MUCH CALCULATION DO YOU HAVE TO SHOW?

• When computing a determinant or the roots of a polynomial, show clearly any work you did by hand (steps in multiplying, factoring or quadratic formula, etc.). If you use a calculator or program, state the start and finish of each calculation, and indicate the technology used. For instance, write down the matrix you need to take the determinant of, write down the resulting polynomial, write down the roots, and state the technology and/or program used.
• When solving a system of linear equations by row reduction, you do not have to reduce completely but may stop when the solutions are clear. For example, see the solution provided for Autumn 2011 Quiz 1, problem 1: the solutions are immediately clear without zeroing out the redundant line of each matrix or dividing to get leading coefficient = 1. You do not have to write down labels for every step of row reduction (e.g. "R2 -> R2 - 2 R1") if you are sure it is very obvious what you did. But if you do several kinds of steps at once, make it easy for the grader to follow your work and say what you did. It might be a good idea to look over your work several hours later or the next day, to see how obvious your steps are. If you have to think hard to remember what you did in a step, you probably should give the grader more information.
• If you use a calculator or computer to do row reduction, show the initial matrix and the final matrix and say what technology and/or program you used to get the result.
• If you use calculator or computer to do homework problems, be sure you understand how to do, e.g., row reduction, "by hand" for the quizzes and tests.

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Most recently updated on December 4, 2016.