MAT2500 08S [jantzen] homework and daily 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 class days in the semester, numbered consecutively below and  labeled by the (first initial of 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. Homework is understood to be done by the  next class meeting (unless that class is a test).


 Textbook technology: Red numbered homework problems have hints on your red TEC CD that comes inside your textbook [open the index.html file with internet explorer, go to homework hints in the Main Menu; if you like to play games, try the appropriate math modules when relevant to a section].  The green Video Skillbuilder CD has detailed video discussed examples from each section of the book as well as a video introduction by the author [click on the Start.html file to get the Main Menu]. There are also tutorials and on-line quizzes and web extras at the textbook website.

  1. M (January 14, 2008): GETTING STARTED STUFF. By Friday, August 25, e-mail me [robert.jantzen@villanova.edu] from your OFFICIAL Villanova e-mail account (which identifies you with your full name) with the subject heading "[MAT2500]", telling about your last math courses, your comfort level with graphing calculators and computers and math itself, [for sophomores only] how much experience you have with MAPLE (and Mathcad if appropriate) so far, why you chose your major, etc. Tell me what your previous math course was named (Mat1500 = Calc 1, Mat1505 = Calc 2, Mat2705 = DEwLA).
    [In ALL email to me, include the string "mat2500" somewhere in the subject heading if you want me to read it. I filter my email.]

    In class:
    1) Log on     to your computer and open Internet Explorer. (IE allows you to open MAPLE files linked to web pages automatically if MAPLE is already open or if it is available through the Start Menu Program listing under Math Applications, in Netscape you must save the file locally and then open in it MAPLE using the File Open task.)
    2)     Log on to the Villanova home page in Internet Explorer (click on the upper right "login" icon and use your standard VU email username and password) and check out our My Courses classroom site, and visit the link to my course homepage from it
    [ http://www.homepage.villanova.edu/robert.jantzen/courses/mat2705/ ],
    3) Open     Maple 11 Standard (red not yellow icon) from the Windows Start Menu Program listing under Math Applications
    [or click on this maple file link: cmdlist3.mw]
    4)         bob will quickly show you the computer environment supporting our class.
    5) afterclass: log on to MyWebCT and look at the Grade book: you will find all your Quiz, Test and Maple grades here during the semester.
     [This is the only part of WebCT we will use this semester.]

    After class: check out the on-line links describing aspects of the course (no need yet to look at the MAPLE stuff). Fill out your paper schedule form (get  a copy in class to fill out or print it out back-to-back earlier to fill out in advance and bring to your first class already done) to return in class Thursday.
    [You can     drop by my office St Aug 370 (third floor, Mendel side, by side stairwell) to talk with me about the course if you wish and to see where you can find me in the future when you need to.]

    Read computer classroom etiquette. Then read the first paper handout: algebra/calc background sheet.

    Handouts:
    student schedule sheet sections 02 [you can print these double-sided to fill out in advance]
    [use the 3 letter dorm abbreviations]

    Homework Problems: 12.1: 1, 2, 3, 5 (short list so you can check out our class website and read about the course rules, advice, bob FAQ, etc, respond with your email; freshmen who do not yet have the book: handouts/stewart5e-12-1.pdf). It is important that you read the section in the book from which homework problems have been selected before attempting them. Here is an example of a PDF problem solution: Stewart 12.1.42 [Okay, I cheated and looked at the answer manual to see how to get started. Then I made a nice Maple worksheet of the problem.]
     
  2. T: Return your schedule forms at the beginning of class;
    REMEMBER DIFFERENT TIME ON TUESDAYS!
    algebra/calc background sheet;
    12.1:  11, 13, 15, 19a [hint: show the distance from P1 to M is the same as from P2 to M and equal to half the total distance; this is the hard way with points and not vectors], 21a, 23, 31, 33, 35;
    12.2: 1, 2, 5, 7, 11, 13, 15, 19, 25. 
  3. W: don't forget the 1st day email assignment!
    12.2: 29, 31, 33 (tension result given in units of force; vertical component balances downward gravitational force F = mg, g = 9.8 N/kg, where m = 0.8kg), 37.
  4. F: 12.3: 1, 3, 5, 9, 11, 15, 21 (it is enough to find just one angle), 23, 29;
    optional fun problems if you like math: 51 (geometry [pdf,.mw]), 53 (chemical geometry [.mw]).

    WEEK 2 [-1]: textbook section scans for those without textbook: 12.2, 12.3, 12.4
  5. T: handout on course rules, syllabus;
    handout on resolving a vector [using Maple]
    12.3: 35, 42 [ans: b_perp = orth_a b = <-3.6,1.8>], 45.
     
  6. W: 12.4: 1, 5, 8, 9, 11 (move u right so initial points coincide),
    15    , 17, 23 (find 2 edge vectors from a mutual corner first),
    27(Maple example), 29, 31, 33 (zero triple scalar product => zero volume => coplanar),
    35 (first redo diagram with same initial points for F and r).

     > <2,1,1>·(<1,-1,2> × <0,-2,3>)   [boldface times sign and boldface centered dot from Common Symbols palette]
         > <2,1,1>·<2,1,1>     then take sqrt (Expressions palette) to get length [example worksheet]
     
  7. F: Quiz thru 12.2;
    it is not very useful to try to draw parametrized curves based on what the graphs of x and y look like: technology is meant for visualizing math!;
    10.1: 1, 9, 13, 17, 19, 21, 28 [it does not hurt to use technology if you cannot guess them all]
    [textbook example curves][curve tutorial];
    try to save these files locally on your C: drive or N: drive and then open citrix maple and then open them and execute them by hitting the !!! icon on the toolbar.

    > plot([t3-2 t, t2-t, t=-2..2])
    plots the first two expressions for x and y as a parametrized curve in the xy plane
    > plot([t3-2 t, t2-t],t=-2..2,color=[red,blue])
    plots the first two expressions versus t as two graphs, the color option helps distinguish them

    WEEK 3 [-1]:
     Weeks 3, 4 and 5 (better early than late but NEVER TOO LATE!): come by and find me in my office, tell me how things are going. This is a required visit. Only takes 5 minutes or less.
     
  8. M: handout on lines and planes;
    never use the symmetric equations of a line: they are useless for all practical purposes!;
    12.5: 1 (draw a quick sketch to understand each statement),
    3, 5, 9 (parametric only),
    13, 16 [ans: a) x = 5+2t, y = 1-t, z = t ; b) (5,1,0), (0,7/2,-5/2),(7,0,1)],
    17, 19;  23, 25, 31, 39, 45, 49.
     
  9. T: Read about mandatory office visit at beginning of week above;
    Maple lab, read the Maple Tips and  Maple FAQ on our home page before coming to class (or afterwards if not before!);
    bring your laptop if you want to make sure you can access citrix maple on it;
    HOMEWORK: play a little bit with Standard Maple, do the "10 minute tour" and then "symbolic and numerical calculations" from the HELP menu, look at the mathematical dictionary link there if you wish. Download the quiz answer key worksheet, execute it and look at how the work was documented and set up.
     
  10. W: on-line handout on geometry of lines and planes (distances between);
    12.5: 53 (also find angle between planes: 78º),
    57    , 65 (find pt on plane, project the 2 point difference vector along the normal),
    67 (find pt on each plane, project their difference vector along the normal---do not just plug into a formula: this is practice in vector projection geometry];
    optional problem if extra time and bored with routine problems: 72 [ans: D = 2].
     
  11. F: Quiz 2 on cross-products (thru HW due wednesday);
    Maple assignments start: note asterisks;
    13.1: 1, 3, 5, 7, 11, 13, 19-24 (quickly, note technology is not necessary here to distinguish the different formulas),
    25    , 31* [refer back to similar problem 25: what is z2 - (x2+y2)? plot the spacecurve and the surface together as in the template, adjust the ranges for the surface so it is just contains the curve and it not a lot bigger],
    35 [eliminate z first by setting: z2 (for cone) = z2 (for plane) and solve for y in terms of x, then use x to express y and then in turn z, finally let x be t],
    read 41;
    12.5.53*: using the answer in the back of the book and the example in the command list cmdlist3.mw file at our website in the section "visualizing lines and planes: subsection unparametrized planes" (you need > with(plots): for the spacecurve and display commands), plot the two planes and the line of intersection and confirm that visually it looks right. Adjust your plot to be pleasing, i.e., so the line segment is roughly a bit bigger than the intersecting planes.

    WEEK 4 [-1]:
  12. M: Test 1 date decided;
    notify bob orally in class if you have not been able to identify one or two partners for Maple assignments;
    13.2: 1, 2, 3, 7 [recall: exp(3t) = (exp(t))3], 9, 13, 15, 19, 21, 29,  27a (by hand), 27b* (graph your results using this template; make a comment about how it looks). 

    > with(Student[VectorCalculus]):
    > <1,2,-3> × <1,1,1>
                     5 ex - 4 ey - ez              
     [this is just new notation for the unit vectors i, j, k;  > BasisFormat(false): returns to column notation]
    > F := t → <t, t2 , t3> : F(t)
     > F '(t)
     >  ∫  F(t) dt
     > with(plots):
         > spacecurve(F (t), t=0..1, axes=boxed)
     
  13. T: 13.2:  22, 31 [angle between tangent vectors],
    35 [use technology to do the integrals, then repeat using u-substitution on each simple integral and compare results],
    39    , 45, 47 [use cross product differentiation rule 5 on page 859].
  14. W: 13.3: 3 (note the input of the sqrt in the integrand is a perfect square in this problem);
    do 7 instead by numerical integration either with your graphing calculator or Maple (right-click on output, choose approximate);
    11, 13, 21, 23 [do not use formula 11: instead use the parametrized curve form r = <t,t3,0> ];
    [on-line reminder of  dot and cross products and  length, area, volume];
    handouts on geometry of spacecurves (page 1 for 13,3) and space curve curvature and acceleration (pages 2-4 for 13.4)
    [[osculating circle][plane curve]].
  15. F: Quiz 3 through 13.2;
    13.3: 39 [perfect square!], 41;
    > with(Student[VectorCalculus]):
       SpaceCurveTutor(<t,t2,0>,t=-1..1)          from the Tools Menu, Tutors, Vector Calculus, Space Curves [choose animate osculating circles]
    parabola osculating circle zoom.

    WEEK 5[-1]:
  16. M: 13.4: 1, 2 [avg velocity = vector displacement / time interval],
    5, 11  [recall v = exp(t)+exp(-t) since v2 is a perfect square],
    17, 17b*[pick an appropriate time interval starting at 0, use the spacecurve command as in the 13.1 hw],
    31 [note that v2 = 32(1+t2)2 is a perfect square],
    35 [also perfect square, see 11] .
  17. T: on-line handout only: projections revisited just for those who like vector geometry;
    13.4: 19 (minimize function when its derivative is zero!);
    13.R (p.882):
    14a [use parametrized curve r = [t,t^4-t^2,0], evaluate T '(0) before simplifying derivative (i.e., set t = 0 before simplifying the expressions after differentiating) to find N(0) easily, find osc circle: x^2 + (y+1/2)^2 = 1/4],
    14b*: edit the template with your hand results including comments and also do the zoom plot to see the close match of the circle to the curve];
    This is the most interesting HW problem: Problems Plus (p.884): 2. [Note b) has answer 52 ft/sec = 37 mph]. [solution]
  18. W: 14.1: 1, 3, 7, 9, 11, 13, 19, 25, 29, 31, 35, 43;
    |maple14.mw problems begin:
    51*, just do a single appropriate plot3d and contourplot after loading plots and defining the maple function f(x,y)],
    71a (read only b,c; if you are interested to see how the data is fit see example 3);
    after finishing the preceding, for fun look at 53-58 and try to first match contour plots with the 3d plots (not all are so easy!) and then think about which formulas might go with which pairs [see plots].

    Th: MLRC 5:30 delayed to 5:45 (date with wife at haircutters)
    Test 1 voluntary problem session. Happy Valentine's Day:
  19. F: Test 1. No need to memorize many formulas, you just have to be able to project vectors along and orthogonal to a given direction, find the direction unit vector of any given nonzero vector, evaluate cross products, dot products, triple scalar products, and of course use vectors produced from a parametrized curve position vector by differentiation in these various vector processes (you should remember that ds/dt = |r'(t)| of course, and how to write equations for lines and planes!).

    WEEK 6[-1]:  maple13.mw is due this week M-F Feb 18-22 [earlier submission means better chance of immediate feedback]
  20. M:  14.2:  1, 2, 5, 7, 11, 15, 17, 21*[toolbar plot option: contour, or "style=patchcontour" or  right-click style patch+contour, explain in comment], 23, 27, 35 (does a 3d plot of the expression support your conclusion? you conclusion drawn before looking at the back of the book obviously).

    Test 1 Answer key is now online.
     
  21. T: 14.3: 1, 3, 5, 13, 15, 17, 25, 29, 35, 45 [in class if time: 18, 20, 37, 38].
  22. W: 14.3: (implicit differentiation!) 41, 43; 47, 49, 53, 57, 59; 65 [just average the adjacent secant line slopes on either side of the point where the partial derivative is to be evaluated, as in the opening example: pdf], 77, 78.
     
  23. F: SNOW DAY.

    WEEK 7[-1]:
  24. M: Quiz 4 thru 14.3 first HW; check your WebCT grades against the numbers on your test and quizzes; Test 1 back---check answer key;
    14.4: (tangent planes, linear approximation: plain, fancy; differentiability illustrated): 1, 3, 7, 11, 15, 21.
    7*[calculate by hand, then do two plots: first > plot3d( [f(x,y),L(x,y)],x = a...b, y = c..d); (choose appropriate ranges to show a good part of the surface behavior with the plane), then zoom in by choosing a smaller window about the point of tangency as instructed by the textbook, check that they agree, make a comment)],
    [optional 9*].
  25. T:14.4 (differentials): 17, 19; 23, 25, 27 [simpler to first use: ln(A1/2)=(1/2) ln A (yes!)], 29, 33, 37 [remember partials from 14.3.77].
  26. W: 14.5: 1, 7, 11, 15, 17, 21, 31, 35, 39a, 47;
    optional: 51 [use answer only to check work after an honest try: maple, pdf; note this "coordinate transformation" of this second order derivative expression is extremely important for gravitational, electromagnetic, quantum mechanical and heat transfer problems, among many others].
  27. F: Leap Day!
    Quiz 5 thru 14.4 (explicit and implicit partial diff; linear approximation);
    14.5: 43[pdf].

    Spring Break. enjoy and be safe.

    WEEK 8[-]:
  28. M: if you did not take your Quiz 5, today/tomorrow is the day to make it up; see bob in before/after class;
    midterm grades due in Wed noon: for Maple upgrades; current midterm grades without quiz 5 are posted in WebCT
    you can compute your own average dropping lowest quiz and see effect of 2/2 maple grade on your outcome using the link on our top level page;
    14.6 (thru p.946): 1, 3, 5, 7, 9, 11, 15, 19, 23, 29.
  29. T: handout on derivatives of 2d and 2d functions; 36;
    14.6: 27b, 31, 38, 45 (derive equations of plane and line by hand), 47, 53;
    45* [plot your results in an appropriate window, i.e., adjust windows of function, plane, line to be compatible, after doing problem by hand];
    head start in class with any partner? nope. f(x,y,z) = xy+yz+zx = 3 at (1,1,1) -> tan plane, normal line
  30. W: catch up on homework please.
  31. F: Quiz 6;
    14.7: 1, 3, 5, 7, 13, 15, 17, 19 (do by hand, including second derivative test and evaluation of f at critical points); 19* [template shows how to narrow down your search to find extrema by trial and error, record your tweaked image or images confirming your hand results, include commentary];
    optional: if you are interested in the more realistic case of example 4 where numerical root finding is required, read this worksheet.
    Today 3/14 is π-day! [and Einstein's birthday]

    WEEK 9[-1]:
  32. M: 14.7:  handout on  2D 2nd derivative test and multivariable derivative and differential notation;
    some on-line only notes if you are interested;
    boundaries, word problems    : 27 (or 29), 37 [minimize square of distance], 41, 45 (or 47) [except for different constants these 3 problems are the same!], 52 [use constraint to eliminate r, max resulting function of 2 variables, consider triangular boundary];
    read     53 [this explains least squares fitting of lines to data].
     
  33. T: quiz answer keys online, check them; determine TEST 2 date: W26;F28;M31?;
    14.R (review problems; note some of the highest numbered problems refer to 14.8, which we did not do): some in class if time: 1, 7, 17,  , 21, 25, 29, 33, 34a, 39, 53,
    14.7: 48 [ans: the height is 2.5 times the square base; obviously cost of materials is not the design factor in this case, no?];

     
  34. W: Maple Tools Menu, Select Calculus Multi-Variable, Approximate Integration Tutor (midpoint evaluation usually best)

    15.1: 1, 3 [do by hand first], 3 [after doing this by hand, before next class: repeat this problem using the MAPLE Approximate Integration Tutor (with midpoint evaluation for (m,n) = (2,2), then (20,20), then (200,200), comparing it with the exact value given by the Tutor],
    5, 6 [midpoint sampling: (m,n)=(2,3), x along 20 ft side, y along 30 ft side: answer = 3600], 7, 9;
    15* [note: (m,n) = (1,1), (2,2), (4,4), (8,8), (16,16), (32,32) = (2p,2p) for p = 0..5 is what the problem is asking for] .

    Easter Recess: 

    WEEK 9[+1]: Maple14.mw due this week
  35. T: 15.2: 1, 3, 7, 11 [factor the exponential first: exp(2x) exp(-y)], 19, 21, 27, 31*.
    Try to meet with Maple partners to complete maple14.mw.
     Begin class by opening Maple and entering from palette: ∫02  ∫0π y sin(x y) dy dx .
    [upper limits not quite typeset in right position, but you understand]

    step by step checking of multiple integration (worksheet):
    > x + y
    > ∫ % dx
    > eval(%,x=b) - eval(%,x=a)
    >  ∫ % dy
    > eval(%,y=d) - eval(%,y=c)
    > etc... if triple integral
     
  36. W: 15.3: handout on double integrals;
    1, 5, 9, 15, 17, 21, 23; 33*, 41, 43, 47, 51.

    Th:MLRC 5:30 problem session today for Test 2 thru Chapter 14.
  37. F: Quiz 7 thru 15.2;
    jump to 15.7: 1, 3, 5, 9, 11 [like example 2, but first write eqn of plane (result: x/a +y/b +z/c=1, where a,b,c are intercepts), then solve for z], 19, 25,
    29 [see handout setup: exercise in setting up triple integrals in Cartesian coordinates];
    31 [two projections onto coordinate planes are faces of the solid, the third has a border obtained by eliminating y from the two equations given in the figure to describe the condition on x and z for that edge];
    * use the standard maple expression palette icon for the definite integral to check at least one problem triple integral of your choice, then include in maple15 hw.*

    WEEK 10[+1]:
  38. M: Test 2 thru chapter 14.
     
  39. T:   April Fools' Day !
    review polar coordinate trig (no paper handout);
    handout on polar coordinates and polar coordinate integration (the integration is next time);
    10.3 pp.669-674 (stop midpage: tangents unnecessary in polar coords),
    last subsection midpage 676-677:
    10.3: 1, 3, 5, 7, 9, 11, 15, 17, 21, 25, 29, 31, 35,
    69* [Nephroid of Freeth: starting at θ = 0 how far does theta have to go for the sine to undergo one full cycle? i.e., θ/2 = 2 π ; 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, as in the handout examples.
     
  40. W: 15.4: (areas but no lengths): 1, 3, 5, 7, 9, 21, 23 [twice the volume under the hemisphere z = sqrt(a2 - x2 - y2) above the circle x2 + y2  ≤ a2], 25 [integrand is difference of z values from cone (below) to sphere (above) expressed as graphs of functions in polar coordinates].
     
  41. F: Quiz 8 on iterated integrals in Cartesian coordinates;
    Recall 15.7.ex3 and re-express outer double integral, inner limits of integration and integrand in polar coordinates: ∫ ∫ r<=2  [∫y= 0..x^2+z^2  x2+z2 dy] dA;
    15.4: 17 [at what acute angular values of theta does cos(3θ) =0? these are the starting and stopping values of θ for one loop],
    29, 31, 33 [what is the average depth? (integral of depth divided by area of region)], 34 [ans: a): 2π(1-(1+R) e-R)], 35;
    Optional: Read 36 [this enables one to sum the probability under a normal curve in statistics]

    WEEK 11[+1]:
  42. M: 12.7: 1, 2, 3, 5, 9, 15, 19, 21, 23, 27, 31, 33, 37, 39;
    3(!) handouts on cylindrical and spherical coordinates and using them to describe regions of space and bounding surfaces.
     
  43. T:  handout on triple integrals in cyl/sph coords and summarizing handout integration over 2D and 3D regions of the plane and space;
    12.7:  55, 61;
    15.8: 1, 3, 5, 6, 7, 11, 17, 23
     
  44. W: 15.8: 24 [ans: 8 sqrt(2) Pi/3], 31 [set up integral by hand], 31* (do this for class to check your answer), 33, 35; optional 37* (fun!).
     
  45. F: Quiz 9 on cylindrical coordinate integration;
    handout on distributions/density/center of stuff;
    15.5 (center of mass, centroids p.1014): 5, 7, 11 [see example 3];
    15.7: 15 [use cylindrical coordinates about the x axis, i.e., polar coordinates in the yz plane, see example 3];
    15.8: 29.

    WEEK 12[+1]: Maple15 due this week
  46. M: 15.5 (probability, recall section 8.5 of calc2 probability theory, read and understand as an application): 
    23    , 25, 26a [P(x<=1000,y<=1000) = .3996], 26b [P(x+y<=1000) = .2642]. [Maple is the right tool for this!]
     
  47. T: 15.R(eview): [PDF if you do not have your textbook in class]
    7, 9, 13, 25 (use cylindrical coords with polar coords in yz plane), 27,
    31    ; 37a,b [for b) see page 1028: Iz = ∫∫∫ (x2+y2) dV]; 41, 42 [ans: 64π/9]; 47.
     
  48. W: 16.1: 1, 5, 9; 21, 25;
    comparison shopping:
    11-14: <y, x>, <1, sin y>,  <x - 2, x + 1>, <y, 1/x> ;
    15-18, <1, 2, 3>, <1, 2, z>, <x, y, 3>, <x, y, z> ;
    29-32: xy, x2-y2, x2+y2, (x2+y2)1/2;
    19*; just try the template, no need to submit [check here for result, with bonus orblem 25 done as well].

    Th: MLRC voluntary problem session 5:30pm       :-(
     
  49. F: Take home Test 3 out in class;
    Do as much of the test this weekend as possible: DO NOT PROCRASTINATE.
    normal homework resumes monday

    WEEK 13[+1]: TAKE HOME TEST ONE WEEK to complete;
    due back Friday anytime (under door of office if not in class)
  50. M: on-line only: progress report: where we've been and where we're going (to end);
    handout on line integrals    ;
    16.2 (f ds scalar line integrals: pp.1062-1065 midpage): 1, 3, 9, 11 [vector eq of line, t=0..1]; 31;
    34 [ans: <4.60,0.14,-0.44>, worksheet compares with centroid]
     
  51. T: bob is sick today, have some pity please;
    16.2 (F • dr = F • (dr/dt) dt  vector line integrals):
    7     [ ∫C <xy,x-y>•<dx,dy>], 17, 19, 21, 23, 25a;
     41, 45;
    optional: 40 [ans: K(1/2-1/sqrt(30)],  44.
     
  52. W: handout on potential functions;
    16.3: 1, 3, 5, 11 (b: find potential function and take difference, or do straight line segment line integral), 15 (again); 23, 33.
     
  53. F: Take home test due; No Quiz; if an extension till Monday is necessary, you may ask for an extension (email bob);
    16.4: 1, 2 [ans: -2 π], 17 [do the line integral too], 18 [convert double integral to polar coordinates; ans: 12 π];
    optional: the line integral technique for integrating areas of regions of the plane is cute but we just don't have time for it.

    WEEK 14:
  54. M: handout on divergence and curl, Gauss and Stokes versions of Green's Theorem.
    16.5: 1, 5, 9, 11, 12, 15, 17, 31 [but read 35, 36 and look at identities 23-29].
     
  55. T:[F]: surface integral demo [not required for final exam];
    optional handouts explaining surface integrals, and working problem 16.7.19 on surface integrals, examples of Gauss and Stokes in 3D (look at summary 16.10 on p.1134);
    read 16.6-9 if interested when you have some time (summer break?).
     
  56. W:[M]: "solid angle" example (what is solid angle? how do we measure areas in the sky? how big is the moon? how many moons would cover the sky? [.mw]);
    final exam chat: chapters 15, 16; facebook class group photo;
    CATS forms.

    MLRC voluntary problem session T: May 6, time: 6:30pm

    FINAL EXAM W: May 7, 10:45-1:15, M G92.

Weeks 3, 4 and 5 (NEVER TOO LATE!): come by and find me in my office, tell me how things are going. This is a required visit. Only takes 5 minutes or less. [Well, now it IS  too late, learn to take advantage of your professors' time in the future.]

Current MAPLE file :
maple13.mws due:  Week 6
maple14.mws due:  Week 8
maple15..mws due:

*MAPLE homework log and instructions [asterisk "*" marked homework problems]

Test 1:  Week 5: ; MLRC 5:30 problem session .
Test 2:  Week 9: ;  MLRC 5:30 problem session  .
Test 3: Take home out ; in  ; MLRC problem session 

FINAL EXAM:
     11:30MWF/1:00T  Wed, May 7, 10:45-1:15
                          Graphing Calculator / Maple Checking ALLOWED FOR ALL QUIZZES/EXAMS
30-apr-2008 [course homepage] [log from last time taught]