MAT2500-02 homework and class log

Your homework will appear here each day as it is assigned, with occasional links to some MAPLE worksheets when helpful to illustrate some points where technology can be useful. [There are 56 days in the semester, numbered consecutively below and  labeled by the day of the week.] Usually it will be summarized on the white board in class, but if not, it is your responsibility to check it here. You are responsible for any hyperlinked material here as well as requesting any handouts or returned tests or quizzes from classes you missed.

  1. GETTING STARTED STUFF Monday, January 14. By Wednesday January 16, e-mail me [robert.jantzen@villanova.edu] from your OFFICIAL Villanova e-mail account (which identifies you with your full name) with the EXACT (case-sensitive) subject heading "[MAT2500-02]" telling about your last math courses, your comfort level with graphing calculators and computers and math itself, how much experience you have with MAPLE (and Mathcad if appropriate) so far, why you chose your major, etc.
    Login to the Villanova home page and check out our My Classrooms classroom site, and visit the link to my course homepage from it
    [ http://www.homepage.villanova.edu/robert.jantzen/courses/ma2500/mat2500w.htm ],
    and read the on-line links describing aspects of the course (no need yet to look at the
    MAPLE command worksheet or examples or tutorial). Fill out your paper schedule form (get  a copy in class) to return in class Tuesday or (if you forget)  drop it by my office St Aug 370 (third floor, Mendel side, by side stairwell) Tuesday and see where you can find me in the future when you need to.

    In class: explore technology support... netscape class stuff [login to VU homepage, go to our classroom], open maple 7.
    [Note the textbook appendices A,B,C,D for review of precalculus foundations if you find yourself a bit rusty. Also recall some rules of algebra.]

    Homework: 12.1: 1, 2, 3, 5, 11, 13, 15, 19a, 21a, 23, 31, 35;
    [problem 12.1.42 in class is just to tie the course back to calc2 and illustrate problem solving approach and documentation].
  2. T: 12.2: 1, 2, 5, 7, 11, 13, 15, 19, 25, 29, 31, 33.
  3. W: 12.2: 23, 25, 35 (tension result given in units of force; vertical component balances downward gravitational force F = mg, g = 9.8 N/kg, where m = 0.8kg);
    12.3: 1, 3, 5, 9, 11, 15, 21 (enough to find just one angle), 23, 27, 33.
  4. F:  handout on resolving a vector;
    12.3: 39, 46 [ans: b_perp = orth_a b = 1/10*<11,33>], 49;
    optional fun problem: 57.
  5. M: Q1 (through day 3); handout on course rules, syllabus;
    12.4: 1, 5, 8, 9, 11 (move u right so initial points coincide), 15, 17, 23 (find 2 edge vectors from mutual corner first), 27, 29, 31, 33 (zero triple scalar product => zero volume => coplanar), 35 (first redo diagram with same initial points for F and D).
  6. T: 10.1: 1, [optional: 3], 5, 9, 11, 17, 19, 23 (by hand);
    in class review of MAPLE worksheets, creating sections for each problem (put "restart" a beginning of each section), dotprod and crossprod commands loaded by "with(linalg)";
    10.1.23*; read MAPLE commands for vector geometry so far, then do with MAPLE:  12.3.41* (also find orthog component "b_perp"; see projection section of previous worksheet link), 12.4.33*.
  7. W: handout on lines and planes;
    12.5: 1 (draw a quick sketch to understand each statement), 3, 5, 9 (parametric only), 11, 14 [ans: a: x=5+2t, y=1-t, z=t, b: (5,1,0), (0,7/2,-5/2),(7,0,1)], 17;
    19, 21, 25, 27, 35, 43, 45.
  8. F: handout on distances between points, lines and planes;
    12.5: 49 (also find angle between planes: 78º), 53, 61 (find pt on plane, project the 2 point difference vector along the normal), 63 (find pt on each plane, project their difference vector along the normal) [do not use formulas: this is practice in vector projection geometry]];
    optional problem if extra time and bored: 68 [ans: D = 2].
  9. M: classlist handout; Test 1 Friday Feb 8;
    13.1: 1, 3, 5, 7-12, 13, 15, 17, 21, 27* [refer back to 21: what is z-sqrt(x^2+y^2)? plot the spacecurve and the surface together as in the template], 31 [eliminate z first by setting: z^2 = z^2 and solve for y, use x to express y and then in turn z, let x be t], read 35.
  10. T: Maple12.mws due Feb 4-6 [see below];
    13.2: 1, 2, 3, 7 [recall: exp(-2t) = (exp(t))^(-2)], 9, 13, 15, 19, 21, 29,  27a (by hand), 27b*. 
  11. W: Q2 thru 12.5;
    TEST 1:  Friday Feb 8, Problem session:  Wednesday Feb 6, 5:00pm MLRC;
    13.2:  22, 31 [angle between tangent vectors], 35, 39, 45, 47;
    13.3: 3 (note the input of the sqrt in the integrand is a perfect square in this problem).
  12. F: mandatory 5 minute office visit by end of Thursday, Feb 7 (read email);
    13.3: 7, 11, 19, 21 [do not use formula 11: instead use parametrized curve form r = [t,t^3,0] ], 33, 35.
  13. M: 13.4: 1, 2, 5, 13 [recall v = exp(t)+exp(-t) since v^2 is a perfect square], 17, 17b*, 31;
    maple12.mws due today-W.
  14. T: 13.4: 29 [note that v^2 = 3^2(1+t^2)^2 is a perfect square];
    Problems Plus (p.870): 2. [Note b) has answer 52 ft/sec = 36 mph];
    13.R (p.868): 9 [angle between tangent vectors], 14a [use parametrized curve r = [t,t^4-t^2,0], evaluate T'(0) before simplifying derivative to find N(0) easily, find osc circle: x^2 + (y+1/2)^2 = 1/4], 14b*;
    maple12.mws worksheet on diskette prepared as described below due today through W.
  15. W:  Wednesday Feb 6, 5:00pm MLRC test 1 problem session;
    (for monday) 14.1: 1, 3, 7, 9, 11, 13, 19, 25, 29, 31, 37, 43, 49*, 67a (read only b,c).
  16. F: Test 1 thru 13.2.
  17. M: 14.2:  1, 2, 5, 7, 15, 17, 21*[toolbar plot option: contour, or "style=contour"], 23, 27, 31 [optional 3; use the maple spreadsheet in the link worksheet, just redefine f , select and re-execute, then plot it to see the result much easier].
  18. T: 14.3: 1, 3, 7, 11, 13, 23, 27, 33, 43 [in class if time: 16, 18, 35, 36].
  19. W:  14.3: 39, 41; 45, 47, 51, 55, 57.
  20. F: Quiz 3 thru 14.3 first HW set;
    14.3:     65, 67, 75 [use implicit differentiation of the equation] , 76, 81; 9*.
  21. TEST 2:  Friday,  March 1, MLRC Monday that week?;
    maple13.mws due M-W;
    M: 14.4:     1, 5, 7, 7*[calc by hand, then: > plot3d({f(x,y),L(x,y)},x=-5...5,y=-5..5); (choose appropriate ranges, then zoom in as instructed, check that they agree)],
    [optional 9*], 11, 15, 21.
  22. T: 14.4: 17, 19, 23, 25, 27 [simpler to first use: ln(A^(1/2))=(1/2)ln A], 29, 33, 37 [remember 14.3.75].
  23. W: 14.5: 1, 7, 11, 13, 15, 19, 29, 33, 37a, 45, optional: 49 [maple, pdf].
  24. F: Q4 thru 14.4;
    14.6 (thru top p.932): 1, 3, 5, 7, 9, 11, 13, 15, 19.
  25. M: MLRC problem session 5pm;
    14.6: 21, 25, 27b, 31, 36, 43 (first part by hand), 43*, 45, 51.
  26. T: handout on 2D and 3D derivatives;
    14.R (some done in class):  3, 5, 13, 16, 19, 23, 25, 29, 31, 32a (now units DO matter), 35, 37, 38, 40a, 43, 45, 46.
  27. W: 14.7: 7 (due M after Spring Break)
  28. F: Test 2 thru first part of 14.6 (day 24);
    Spring Break
  29. M: 14.7: 1, 3, 5, 13 [divide thru before differentiating!], 15, 17, 19 (do first by hand, including second derivative test and evaluation of f at critical points); 19*.
  30. T: 14.7: boundaries, word problems: 27, 37 (minimize square of distance);
    41,     45, 47, 50, read 51.
  31. W: 14.R: 62 (assume the package has length plus girth equal to 84 for the largest box, intuititively obvious; answer: V=5488 in^3);
    You must build a rectangular shipping crate with a volume of 60 ft^3. Its sides cost $1/ft^2, its top costs $2/ft, and its bottom costs $3/ft. What dimensions would minimize the total cost of the box?
  32. F: takehome Q5 thru 14.7 due M;
     15.1: 1, 3, 3b* [do this before next class: repeat this problem using MAPLE for (m,n)=(2,3), then (20,30), then (200,300), evaluating the average value (= average height of solid) as in the template worksheet as well: copy and paste 3 times then edit, deleting sequence listing after the first time; guess what the exact integral value is on the basis of this, respond with comment answer],
    5, 6 [midpoint sampling: (m,n)=(2,3), x along 20 ft side, y along 30 ft side: answer = 3600], 7, 9.
  33. M: 15.2: 1, 3, 7, 11 [factor the exponential first: exp(2x) exp(-y)], 18 [ans: e-2], 21, 27, 31*;
    maple14.mws due next M-W.
  34. T: 15.3: 1, 5, 9, 15, 17, 19, 25; 31*, 35, 39, 43, 47.
  35. W: 15.7: 1, 3, 5, 9, 11 (like example 2), 19, 23, 27, 29, 31;
    [we'll return to this section after a detour];
  36. F: Q6 thru 15.3;
    15.7: 17, 30; make sure you go over the previous 15.3,15,7 HW.
  37. M: handout exercise on cartesian multiple integrals; maple14.mws due M-W;
    review polar coordinate trig; (handout on polar coordinate integration);
    10.4 pp.660-665 (stop midpage): 1, 3, 5, 7, 9, 11, 15, 17, 21, 23, 29, 31, 35, 71* [starting at 0 how far does theta have to go for the sine to undergo one full cycle? this is the plotting interval];
    keep in mind that our most important curves for later use are circles centered at the origin or passing through the origin with a center on one of the coordinate axes, and vertical and horizontal lines, and lines passing through the origin.
  38. T: 15.4: 1, 3, 5, 7, 9, 19, 21 [double volume under hemisphere z=sqrt(a^2-x^2-y^2) above circle x^2+y^2<=a^2], 23.
  39. W: 15.4: 27, 29, 31 [what is the average depth? (integral of depth divided by area of region)], 32 [ans: a): 2*Pi*(1-(1+R)*exp(-R))], 33:
    Easter break.
  40. T: 12.7: 1, 2, 3, 5, 9, 15, 19, 21, 23, 27, 31, 33, 37, 39.
  41. W: 3 handouts on cylindrical and spherical coordinates, using them to describe regions of space or surfaces and then doing triple integrals; 12.7: 55, 61; 15.8: 1, 3, 5, 6, 7, 9, 17, 21.
  42. F: Q7 thru 15.4;
    15.8:     24 [ans: 8 sqrt(2) Pi/3], 31 [set up integral by hand], 31*, 33, 35.
  43. M: MLRC problem session for Test  3 at 5pm T;
    centroids etc:15.5: 5, 7, 11 [see example 3]; 15.7: 15 [see example 3]; 15.8: 25.
  44. T: probability(reread section 8.5 p.571 if necessary for 1D case): 15.5:  23, 26a [P(x<=1000,y<=1000)=.3996], 26b [P(x+y<=1000)=.2642].
  45. W: handout summary on 2D 3D integration regions;
    in class problems:
    15.R: 7, 9, 13, 25 (use polar coords), 27, 31, 37a, 41, 42 [ans: Pi/14], 47.
  46. F: Test 3 thru 15.8 (including center of mass) takehome but start in class. Due next F.
  47. M: 16.1: 1, 5, 9, 11-14, 15-18, 19*, 21, 25;
    maple15.mws due next M-W.
  48. T: 16.2 (f ds integrals only: pp.1047-1050, 1051 midpage, 1153): 1, 3, 4, 9
  49. W: 16.2: (F · dr integrals):  19, 21, 23, 25a;
    <F1,F2,F3> · <dx,dy,dz> integrals:     7, 17, 31, 37, 43;
    handout on line integrals.
  50. F: test 3 due;
     16.3: 3, 5, 11, 15 (same procedure as example 4), 19, 21, 33.
  51. M: 16.4: 1, 2; 17; maple15.mws due M-W.
  52. T: 16.5: 1, 5, 9, 12, 15, 17, 31 [but read 35,36 and look at identities 23-29].
  53. W: catch up on HW. Go over Test 3:  Answers [MAPLE discussion].
  54. F: teaching evaluations;
    Q8 thru 16.4: verifying Green's Thm (you may use MAPLE for integral evaluation).
  55. M: 16.7: 19 (use r(u,v)=[u,v,4-u^2-v^2], ie u=x, v=y).
  56. W=F: final class;
    handout on surface integrals;
    Review problems 16.R: 1-23 (except 20), 37 (zero curl, find potential).
  57. Th: May 2, 12:00-2:00pm MLRC problem session for final exam;
    Final exam on Sat (see below).

     

current maple assignment:
maple15.mws due: M-W Apr 22-24 [from days: 32, 33, 34, 37, 42; problems: 15.1.3, 15.2.31, 15.3.31, 10.4.71, 15.8.31; check web instructions and templates for each]

maple14.mws due:  [from days: 15, 17, 20, 21, 21, 25, 29; problems: 14.1.49, 14.2.21, 14.3.9, 14.4.7, [optional: 14.4.9], 14.6.43, 14.7.19; check web instructions and templates for each]
maple13.mws due:  February 18-20 [from days: 9, 10, 13, 14 ; problems: 13.1.27, 13.2.27b, 13.4.17b, 13.R.14b; check web instructions and templates for each]
maple12.mws due:  M-W Feb 4-6  [from days: 6 ; problems: 10.1.23, 12.3.41, 12.4.33; check web instructions and templates for each]
maple16.mws due:  [from days: ; problems: ; check web instructions and templates for each]

[* means use MAPLE with a partner: save as a "MAPLE section" with a title labeling the problem on a diskette (disk owner's name, phone number on label, all partners' names inside worksheet with date, worksheet not in a folder but at top level) with a backup diskette or hard drive copy (each partner keeps a copy for safety) until requested to hand in the collection of problems as a diskette. Filename: maplex.mws, where x is the chapter number the problems are coming from in the Calculus textbook. You may and should work individually on any given problem if successful, but must meet, discuss and merge your work with a fixed partner for a given maple worksheet collection of assignments. [Everyone must work with a partner.] [Using MAPLE at Villanova.] Upgrades are encouraged for completed assignments: make an honest effort to correct your worksheet, then stop by bob's office for discussion.

Consult the command list worksheet for examples when necessary: cmdlist3.mws


TEST 1:  Friday Feb 8, Problem session:  Tuesday Feb 5, 5:00pm MLRC.
TEST 2:  7th week: Friday,  March 1, Problem session:  5:00pm  MLRC.
TEST 3:  11th week?, Problem session:  5:00pm  MLRC.

FINAL EXAM:  , Problem session  5:00pm MLRC.
2500-02 MWF 10:30:  Sat, May 4, 10:45 - 1:15
2500-03 MW   12:45:  Fri, May 10, 8:00 - 10:30
You may switch days with permission.

                          MAPLE CHECKING ALLOWED FOR EXAMS
but you must have learned how to use it sufficiently for this to be any help

30-apr-2002 [course homepage]