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.

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Most recently updated on December 4, 2016.