Homework for Math 326, Spring 2013

General rules:


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