M326 HW

Homework for Math 326, Spring 2013

General rules:

There will be weekly homework assignments due on Fridays. Hand in your assignment in class, or to the grader's mailbox, Box 29 (over the number) in PDL C-136 by 3 PM. Hand in whatever you can on time; some work is much better than nothing. Late homework usually will not be accepted; if you have exceptional circumstances that makes this policy a hardship for you, see me to discuss it.
Don't be stingy with space. Leave at least one blank line between problems, and leave margins on at least two and preferably all four edges of the page. If your writing shows through the paper, use only one side of the paper.
Label every problem clearly (page and/or section number as well as problem number).
Write your name, the class, the assignment number, and the due date in the upper right corner of at least the first page of your paper.
STAPLE your pages together. The "fold and tear" method of fastening pages is not acceptable.
Seven of the assignments will be collected and graded. Your total of homework points for the quarter will be rescaled to the appropriate number of course points: see the Grading Scheme for details.
Only some of the homework problems are graded for correctness. If a problem is marked "1/1", you got credit for doing it, but your work was not checked.
Some weeks, the grader will grade some problems and I will grade some. Usually, he grades in green ink and I grade in red.

Assignments:

Due:	Reading and Problems:
April 5	Read §§5.0(intro)-5.3. Exercises: p. 122, 5.1.2, 5.1.3, 5.1.4: in all three problems, draw a sketch of the set S, say if S is open, closed, or neither, and whether it is a region, and determine B(S) and the interior of S. p. 124, 5.2.1, 5.2.2; and p. 127, 5.3.3.
April 12	Read §§6.0(chapter intro)-6.2 & 6.4. Exercises: p. 124, follow instructions of 5.2.3 (not 5.1.3) for function in 5.2.4(b); p. 124, 5.2.7 - you may use polar coordinates, and skip showing the inequality book asks for. p. 127, 5.3.9; p.134, 6.1.2 & 6.1.3; p. 138, 6.2.3 & 6.2.6; p. 153, 6.4.5.
April 19	Read §§6.5, (6.51-6.53 optional), 6.3, 6.6. Exercises: p. 153, 6.4.2; Also the following problem: Let f(x,y) = (x³ - 3xy²) / (x² + y²) everywhere except at the origin, where f(0,0) = 0. Compute f₁(0,0) and f₂(0,0). Then follow instructions of 6.4.7(c) (using the f defined here). p. 160, In 6.5.2, let H represent the given relation of (u,v) to (x,y) [so (u,v) = H(x,y)]; do the problem using matrix notation for derivatives and matrix multiplication. pp. 160-161, 6.5.9 & 6.5.15. pp. 143-144, 6.3.2 & 6.3.14.
April 26	Midterm, no homework to hand in. Read §§6.6-8; before Monday, April 29, start reading Ch. 7. Recommended review/study problems: p. 127, 5.3.4; p. 143, 6.3.6 - also say where the extrema occur; p. 176, 6.6.1 (one formula only) & 6.6.6; p. 186, 6.8.1, 6.8.2, & 6.8.10(a). Sample test posted with homework solutions (link below). Test rules.
May 3	Homework as pdf with comments and hints on all the exercises. Also answers to 4/24 worksheet. For your convenience, here's the assignment without the hints: Read all of chapter 7 except §7.3. Exercises: pp. 161-162, 6.5.21 & 6.5.22; p. 199, 7.1.2; p. 201, 7.2.1; p. 210, 7.5.2 and 7.5.9.
May 10	Read Chapter 8. Exercises: p. 220, 7.6.1(a)&(d) & 7.6.4; and pp. 228-230, 8.2.3, 8.2.5, 8.2.7(bc), and 8.2.9(abc). Note answers in back are often only partial answers; be sure you answer all questions asked, and show reasoning to justify your answers. ALSO NOTE: If the conditions of the Implicit Function Theorem fail, you have no conclusion, and must look at the geometry of the solution set to determine if it can be written as a graph. This is a little tricky in 8.2.3, but give it a try. In 8.2.7(bc), you should be able to see the geometry clearly enough to do this.
May 17	Read 9.0-9.3. Exercises: p. 230, 8.2.18 & 8.2.20; p. 234-235, 8.3.1 & 8.3.2; pp. 251-252, 9.2.2 - also sketch R and R' in their separate planes, & 9.2.6 - also compute Jabobian determinant of the mapping and the inverse mapping, and show they satisfy (9.1-6) on p. 242.
May 24	Midterm, no homework to hand in. Recommended review/study problems: Any homework problem from chapters 7, 8, and 9 you didn't do before, or feel unsure about; pp. 161-162, 6.5.22 or 6.5.23 (whichever you didn't do before); p. 176, 6.6.6; p. 210, 7.5.4; p. 230, 8.2.19; p. 234, 8.3.3; p. 262, 9.5.1. Sample test + 2 additonal problems posted at M326 Catalyst Workspace and answers posted there also.
Monday June 3	Read 9.4-9.5, 15.32, & 15.62. Don't worry about details of proofs in Chapter 15; read any other part of Ch. 15 you find useful. Exercises: p. 251, revisit 9.2.2 to compute the areas of R and R', and explain why your results are consistent with Thm. II, p. 465. p. 262, 9.5.5 & 9.5.6. In 9.5.6: correction, y = sinu sinhv; in part (a), "sizes" means "values," consider generic values only (non-generic considered in (c)), and be careful of signs. p. 468, 15.32.3, 15.32.5, 15.32.9, and 15.32.11.

Selected solutions for past homework assignments.
Notes on Regular and Singular points.

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Most recently updated on May 26, 2013