MAT1505 17F 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 days in the semester, numbered consecutively below and  labeled by the (first initial of the) day of the week.] 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. Red numbered problems have hints online.

It is your responsibility to check homework here. (Put a favorite in your browser to the class homepage.) 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, in which case the homework is due the following class meeting).

*asterisk marked problems are to be done with MAPLE as explained in the separate MAPLE homework log.

1. GETTING STARTED STUFF Wednesday August 23.
   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 "[MAT1505]"
    [always include this string in your subject heading if don't want your email to be lost in my overflowing mailbox]
   telling about your last math courses and how far you reached in your high school calc class (freshmen), your comfort level with graphing calculators and computers and math itself, why you chose your major, etc.
   
   In class open your favorite browser and log in to MyNova on the Villanova home page (use your standard VU email username and password) and check out our class photo roster, and visit the link to my course homepage from it by clicking on my home page URL under my photo and then on our class homepage, directly:classroom site linked to your list of courses at the center of the web page, and visit the link to my course homepage from it )open in a new tab or it won't work]
   [ http://www.homepage.villanova.edu/robert.jantzen/courses/mat1505/ ],
   and read the on-line links describing aspects of the course
   (no need yet to look at the MAPLE examples and tips yet: we will get around to Maple soon, but here is the worksheet bob used in class: document mode, worksheet mode; here is a sample worksheet report, exported animated GIF. we will return here later for volumes of revolution).
   If you have any questions, drop by my office St Aug 370 (third floor, Mendel side, by side stairwell) or just come to see where you can find me in the future when you need to; I welcome visitors.
   
   Homework (light first day assignment):
   Make sure you read my welcoming email sent on the weekend, and register with WebAssign.
   [If not already done: download Maple here. Then install it.]
   Explore the on-line resources. Browse the pages linked to our class home page.
   Read the online handout on functions and differentiation .
   Fill out the paper schedule form bob handed out in class. [see handouts];  use the 3 letter dorm abbreviations to return in class the next class day.
   
   Read 5.3. Do 5.3: 7, 9 using WebAssign, and the "Getting Started with WebAssign" assignment.
   [Hint: this is what your WebAssignment 5.3 should look like.]
   
   
2. F: hand in filled-in schedule sheets;
   check carefully your telephone number and dorm abbreviation on the signup sheet;
   Think about paper handout on algebra and differentiation rules;
   Velocity example of net change and the fundamental thm of calculus: s5-4-60.mw;
   5.4: 1, 5, 31, 33, 45, 50, 52, 59, 65;
   Take home Quiz 0 for practice, will be graded (practice for new grader) but will not count; due Monday in class; you need to be able to evaluate a definite integral exactly in Maple, and numerically approximate it, and solve an equation numerically (Maple or GC) to 6 decimal places.
   
   if you have a moment for reflection read:
   differentiation versus integration: notation and associated pictures
   
   WEEK 1[+2]:
   
3. M: bring your laptops today, with Maple installed; bob will help you adjust your palettes and show you the interface.
   Then open up this file: datafit-int.mw and read it with a partner, then do the final section exercise with this data from Stewart 5.4.74^* (convert to mile units at the end). Ask bob when you are confused about anything. Finish this as part of a first Maple assignment. Find a partner or two eventually to join with you in consolidating your work into a single group worksheet and do other problems from chapter 5 (Friday the class contact info will be available as well);
   syllabus handout with office hours.
   
   Quiz 0 [Lambert Big Pharma application]
   
   
4. T: chain rule for scaled integration variable in a function;
   5.5( "u-substitution"): 1, 3, 7, 13, 19, 21, 25, 45 [hint: separate into two integrals], 59 [express as a definite integral in u ; practice for Friday quiz];
   
   
5. W: bell curve example of change of integration variable [pdf, mw];
   5.5: [74], [79], 81, 83, 85, 86, 87, 91;
   square bracketed problems on this HW page are not on WebAssign;
   hit "read it" button on exercise problems to get an e-book, browse forward to the HW exercises, homework hints have an icon to the left of the problem number, and for more than the red numbered problems? check it out for me. My view gives this resource.
   [numerical parameters online change so you can't just enter the answer from the back of the book for odd numbered problems!]
   
   
6. F: Quiz 1 (u substitution, net change theorem);
   paper only classlist contact information handout (you don't want your cell numbers on the web!);
   5.R. Review problems [no review problems are on WebAssign]: 4, 7, 15, 23, 31, 39, 45, 53, 59, 61, 63, 64* [second Maple problem, use template [forget parts a,b, graph C, then C, S together on interval -10..10, solve the condition c) for the first positive solution showing the graph of C together with the constant function 0.7 on the interval 0..1 which contains it (click on gridlines) since there are an infinite number], 66 [Maple easily gives you the value of the limit, your task is to derive it].
   
   The Maple5.mw assignment is due anytime next week through the weekend, the earlier the better. You can use this template: lastname-lastname-maple5.mw to get started, with one section for each of the two Maple problems.
   
   WEEK 2[+1]: Weeks 3 and 4 or earlier: come by and find me in my office, spend 5 minutes, tell me how things are going. This is a required visit. Do not delay if you find yourself having trouble.
   
   Optional 5.Plus challenge problems which can eventually replace a low quiz grade, or if you just like a mathematical challenge.
   
   M: Labor Day.
   
7. T: 6.1: 1. 3. 9, 11, 15, 27, 31, 33, 49; 53 [see this approach],
   Read Applied Project "The Gini Index" on p.436 as the applied project following section 6.1 (inserted as a result of the lobbying of our very own Math&Stat Dept prof. Klaus Volpert);
   [If curious checkout this Gini index calculus application only using calculus you already know.]
   
   
8. W: 6.2: 1, 7, 9, 11, 33, 41, 47, 49. 
   
   
9. F: Quiz 2 area between two curves;
   derive volume formula for the Great Pyramid of Egypt and see if it works for the data you find;
   6.2:  53 [hint: look at video soln][challenge: can you repeat this for side lengths a, b, c?] , 55 [see Maple solution and plots], 57, 61, 64.
   
   if you have a moment for reflection read:
   regions of the plane: relationships between variables [areas, volumes of revolution].
   
   WEEK 3[+1]:
10. M: 6.4 work: 3, 7, 13, 23, 34 [keep maximum significant figures in part a) to obtain correct integer for part b).
    
    
11. T:  6.4: 21 , 24, [29], 30 [this problem is all about units!), [if curious, look at plots for 6.2.55: Maple plot];
    If you are curious about how bob used Maple on the pyramid problem, click here. Conical tank?
    
    If you like a challenge, try 6Plus.4a with hint.
    Serious Challenge with Prize: do the work calculation extension of this problem and get a 100 to replace your lowest test grade (provided you don't blow off any subsequent tests and do the work yourself). [first try r = 1, L = 4, for a concrete example if you have trouble with the symbolic calculations]
    
    Don't forget to come find my office, especially if you feel that you are having difficulties. Test 1 Tuesday in Week 5.
    
    
12. W: 6.5 [average value]: 1, 7, 9, [13], 17, 18, [first do by hand 23];
    6.5.23* [Do rest of problem with Maple]. See worksheet maple6.mw link on next line;
    Maple6.mw: 6.AppliedProject: Where to Sit at the Movies* (after 6.5): part 1 done in class together.
    
    
13. F: Quiz 3 on volumes of revolution and related work problems;
     6.R: 11, 18 a-b, 25, 26 [part b gives you the answer!], 29, 33 [remember Review problems are not on WebAssign];
    6.Plus.2 (no WebAssign either; hint: solve for point x = a of intersection in terms of the slope m of the line y =  m x; solve condition on m using Maple, remember I = sqrt(-1)!  [soln]
    
    end of Cassini [photos]
    
    WEEK 4[+1]:
14. M: online handout:  blood flow as an example of dimensionless variables (6.5.18);
    7.1: 3, 5, 9, 17, 39 [example of using Tutor], 45;  just for fun: [iteration example]; [change of variable example]
    
    
15. T: what is this good for?
    7.1: 57, [59, 65], 66, [67], 68 [dimensional discussion], [69], 71; (boldface problems worked in class?);
    optional minor challenge: 73 [this shows how one can manipulate integral formulas with u-sub and int by parts in combination]
    
    7:30 Tonight the Villanova One Book talk!
    
    
16. W: 7.6: bring laptops;  Integration using Tables of Integrals (no!) and Computer Algebra Systems (yes!):
    examples;
    online activity: 7.Plus Problems on WebAssign: use some mathematical thinking plus Maple (when helpful, which is usually) to solve at least one or more of the following problems beyond the four WebAssign problems:  WebAssign: 1, 3, 4, 11, [5, 12, 15] or any others that might appeal to you. These are challenging but doable. If you like math they are fun instead of the dreary homework problems you normally do to digest the concepts. You may collaborate. This is a way of testing your problem solving skills rather than redoing similar artificial one step problems. If you really get stumped on everything, you can email bob for a hint on a problem you have some luck in setting up. Here are some hints. Write up carefully your successful problems and I will look over your work if you wish. 7.7.11 solution.
    
    
17. F: Quiz 4 on integration by parts;
    7.7 (approximate integration):  2, 3, 7, 30, 35, 42 [You can use the ApproximateIntTutor, and the "Compare" button which gives all the approximations simultaneously---you can copy and paste each number you want to Notepad or Wordpad, whatever instead of writing them down before inserting in WebAssign];
    [Maple approach to these problems]
    
    Note: you can avoid wasting time while Maple tries to integrate something difficult exactly by selecting the integral and then from the "Format" menu, "Convert to", "Inert Form", and then numerically approximating the integral directly.
    
    WEEK 5[+1]: Test 1 through int by parts on Tuesday, MLRC voluntary problem session at 5:30pm Monday.
18. M: 7.7: (numerical error?): 21, [23* use template problem 24 here], 37;
    [Maple approach to these problems]
    
    5:30pm MLRC voluntary test 1 problem session.
    
19. T: Test 1 through int by parts.
    
    
20. W: 7.8 [improper integrals]: 1, 3, 5, 13, 21, 29, 30, 57.
    
    
21. F: [no quiz] 7.8: [62 in WebAssign but nothing how to enter, just do it, use the change of variables where the exponential is exp(-v^2/V^2) so do a change of variable from v to the dimensionless variable u = v/V], 66, 68,70;
    66*: Plot together on the same axes both the original density x(r) and the perceived density function y(r) setting R = 1   for 0 <= r <= 1 (equivalent to using the dimensionless variables u = r/R, S = s/R). Use Maple to evaluate the definite integral. [r and s both measure the same thing!];
    (comparison thm: limit comparison theorem translates directly into this thm for improper integrals): [47*], 49, [51], [55], [79,use Maple for antiderivative, neither integral alone converges so they have to cancel for large x, this determines C], 515XP, 529XP.
    
    WEEK 6[+1]:
22. M: handout on dimensionless integrals;
    7.R: 67 (consistent time units!), 69, 70 (answer in Liters), 71, 74 (use separate denominator u-subs, compare with Maple result), 78, 79, 80].
    
    
23. T:  8.1(arclength): 1, [3*] (use Maple), 7, 9 (simple u-sub), 13 (perfect square!), 15 (use tan^2 +1 =  sec^2 to simplify perfect square,then use technology for antiderivative), 23 (use Maple evalf of inert form of integral), 33 (solve for y, perfect square is a power function!, do one quadrant, multiply by 4).
    
    
24. W: 8.1: 35, [36*], 39, 43, 44 (you need to numerically solve for a in the interval a = 0..100);
    44* [plot the final profile over the given interval together with the ground line y = 0 and the line y = h where h is the height you found to hang the wire, and set equal units on both axes so that it looks like you would see it; also show your plot of the condition determining a and show the numerical solution].
    
    
25. F: Quiz 5 on arclength;
    
    FALL BREAK  :-) Enjoy. Be safe in your travels.
    
    WEEK [7+1]: (notice we skipped 2 sections)
26. M: 8.4 (read on-line blood flow and handout: cardiac output):  [15, 16 (basic financial literacy!), 17], 18,19, [20], 21, [22].
    
    
27. T: [grade averaging example to motivate weighted averages];
    handout on probability [see also changing the variable in a probability integral, mw];
    8.5 (probability): 1, 5, 10 (median value of x: probability half below x, half above x), normal distribution: 15, 17,
    [21* Use Maple to answer each part of the problem. Graph the distribution by setting a₀ = 1, equivalent to measuring length in units of that lengthscale. Find the exact radius of the maximum of the distribution in terms of a₀ , hint: use  a₀ = 1 throughout the problem and convert all your lengths back to real units by multiplying by  a₀] ;
    [4, prep for quiz 6].
    
    
28. W: 8.5: 2, 6, 16 [template], 19; [optional: 20 (standard deviation)];
    If you have a moment for reflection read:
    differentiation versus integration: notation and associated pictures
    regions of the plane: relationships between variables [areas, volumes of revolution].
    
    
29. F: Quiz 6 on semi-infinite probability distributions and improper definite integrals, change of variable in such integrals (keep 8.5.4, Q6 15F in mind);
    8.R: [9, 21, 22, 23];
    catch up on Maple7-8, due anytime in the next week or 10 days, roughly.
    
    Optional. Problems 8 Plus: 6 (what is true of the 3 sectors of the semicircle into which the two intersection points divide it?), 11 (12 continues 11) are interesting challenge problems if you like math. The quiz replacement offer stands for problems 6 and 12.
    
    WEEK 8[+1]:
    Test 2 [arclength, improper integrals, probability integrals] on Tuesday in Week 9.
30. M: 11.1 (sequences): 1, 5, 11, [17], 23, 25, 29, 33, 41 (l'Hopital's rule: ∞/∞), 49, [59* (use the template in this worksheet)], 65.
    
    > seq(f(n), n = 1..N)    this is how you generate sequences in Maple; use evalf(f(n)) if you want the decimal values
    
    
31. T: 11.2(series): 1, 3, 15, 17, 18, 22, 27, 31, 41, 43, 49, 51, 57, 69, 75. (short problems, I avoided tedious entry of numerical values of first n terms).
    
    
32. W: W: 11.3 (integral test):  [1], [2], 7, 8, 11, 14, 15, 27, 29, 35, 37 (use Maple integral test template), 39, [46].
    
    
33. F: Quiz 7 on sequences, series;
    complete Maple7-8; look at archived test 2.
    
    WEEK [9+1]:
34. M: MLRC voluntary problem session 5:30;
     11.4:  1, 2, 5, 7, 23, 27, 28, 29,  31, [33*, 35*];
    Quiz 7 answer key online.
    
    
35. T: Test 2 [arclength, improper integrals, probability integrals, expected value] .
    
    
36. W: 11.5 (alternating series): 1, 2, 3, 5, 7, 11, 17, 23, 32.
    
    
37. F: Please meet with your partner if you did not get 2/2 on Maple6 to fix and resubmit or if you have not yet submitted Maple7-8 finish this off;
    no class meeting today.
    
    WEEK [10+1]:
38. M: 11.6: 1, 2, 5, 7, 13, 17, 23, 25, 31, 37, 43,
    50* (this problem mentions William Gosper calculating 17 million digits of Pi! and shows dramatically how using an efficient series representation pays off; > Digits:=20 is needed for part b) which looks at accuracy in the teens of digits; Digits:=10: returns to the default, use Maple to evaluate the limit in the ratio test; if you want to be amazed, evaluate the first 10 terms of the series as in this worksheet).
    
    
39. T: for 18S, you can choose me or avoid me in MAT2500 (please don't publicize this info);
    we are skipping 11.7 since general series convergence tests are not as important for Taylor series, where "absolute convergence rules" and the absolute convergence ratio test plus p-series comparison is all that matters;
    11.8: 5, 7, 9, 15, 17, 19, 21, 27, 37.
    
    
40. W: 11.9 (tricks with power series): 3, 5, [9, to make this less painful, use the fact that (x-1)/(x+2) = 1 -3/(x+2)], 13 [see this worked example], 15, 25, 32 [use Maple worksheet].
    
    
41. F: Quiz 8  on absolute/conditional convergence (11.6), power series convergence (11.8, like problem 2 on 15F quiz 9);
    11.10 (Taylor series!): [2], 3, 4, [5, 7], 11, 17 [cosh' = sinh, sinh' = cosh, cosh(0) = 1,sinh(0) = 0 follow immediately from their definitions in terms of the exponential function], 21, 25, 39, 55.
    > taylor(exp(x),x = 1, 6) ;convert(%,polynom)        # up to 5th power, centered at 1
    
    WEEK 11[+1]:
42. M: 11.10 (binomial series): 31, 33, 37, 51, 55, 59, 63, 73,
    84 (plot it and zoom in on the origin, what are all the values of the function and its derivatives at the origin?). 
    
    
43. T: 11:10  (error: theory, practice)  [table of power series][exp,ln,trig,binom series] [tangent taylor series];
    11.8: [20], 11.10: 60, 62, 78 [look at 84];
    binary series convergence (11.11 has a similar example)
    
    
44. W: 11.11 (applications):
    [kinetic energy, Applied Project]
    11:11: [33], 35, [36], 37; (two problems not in WebAssign!);
    [use Maple > taylor(f(x),x=0,6) to get Taylor series you need in these problems].
    [36: factor out d from the radical to use binomial series in small ratio R/d, as in 33 for d/D]
    [37: the angle from the center in radians is so small that it can be approximated by its tangent L/R]
    
    maple worksheets: 33, 35,, 36, 37
    
    
45. F: Final Quiz 9;
    summary of main points about series;
    if time in class look over and ask bob if you would like input on any of these review problems:
    11.R: in 11-18 recognize how to quickly identify the large n behavior (except 18 which is telescoping, forget it), some diverge, consider absolute value when not a positive series etc; look at some of the following problems that seem reasonable; 40-44 you should be able to answer these (41); 47-54 use tricks by manipulating simple series; 56 and 59; you should be able to do 57 (don't worry, first few terms only); 60 is a great application.
    
    WEEK 12[-1]:
46. M: in class we do review problems together;
    Test 3 (takehome, no Taylor remainder problems) MLRC voluntary problem session at 5:30pm.
    
    
    
47. T: Read the test instructions before starting this takehome test, which is linked to the end of the instruction page. Remember Document, Document, Document! Support any claims or steps you make or take with a reasoned explanation using proper mathematical notation. You may use technology to check every step you take, BUT this test is not about reading off a screen for responses UNLESS explicitly requested. All work should be your own. No collaboration.
    Read the instruction page now. Tentative due date: Friday after T-day break, but if absolutely necessary, Monday after that. Don't leave it till the last minute!
    
    T-Day break.
    
    WEEK 13[-1]:
48. M: parametrized curves can be fun (tease)!; circle notes (semicircle video);
     10.1 (execute worksheet and look at many other examples):
    (use Maple to visualize curves [set parameters =1 to plot]! Google named curves if interested):
    [1] [evaluate start and stop points to see direction], 7 [where is t = 0? where is start, stop?],
    9, 11, 13,  [optional for fun only: 28], [useful: 31], 33, 41,
    [43: use identity cot^2+1=csc^2 to eliminate parameter, what continuous range of angle makes it a continuous curve?], 45 [display both animatecurves!], 46 [see how you can Explore the trajectories for all forward angles].
    
    HW due Wednesday so you can continue working on Test 3.
    
    
49. T: Test 3 in class work.
    
    
50. W: (tangents, areas, arclengths) 10.2: 7, 13, 17, 31, 48, [53, 55];
     [many Maple worked HW problems];
    [optional viewing: Project 10.1/2 running circles around circles: fun with cycloids].
    
    
    
51. F: Test 3 due in class unless you need the weekend to do a better job.
    If needed, ask bob for an extension via email;
    polar coordinates (trig refresher: trig,  inverse trig (online); polar coords);
    10.3: 3, 5, 11, 17, 19, 21, 25, 27, 30, 32, 37, [49, 62]
    
    
    WEEK 14[+1]:
52. M: 10.4 (areas in polar coords):  7 (for order of magnitude one could compare to a semicircle of radius 4 centered at [0,3]), 21, 31 (find intersection point, find area of one half a single region between the two curves, multiply by twice the number of such regions; what percent of area of the circle passing through the intersection points does this represent? Is that reasonable?), 44 (use numerical solution for angle of intersection).
    
    
53. T: 10.4 (arclengths in polar coords): 47, 50 51, 517.XP.
    [optional glance: Spaghetti curves? How an innocent math problem can  lead to crazy stuff.]
    
    
54. W: 9.1[be careful example]: Bring laptops please;
    7, 9, 10, 17;
    [when you take MAT2705 DEwLinAlg you might find my website useful, or not :-) ].
    
    
55. F: 10.R (plots): 19, 23, 25, 27, 28; 29 (with a = 1), 30; 31, 40.
    archived final exam.
    
    
56. M: Bring laptops to fill out online CATS forms
    [Click here to log into the online CATS system];
    final exam remarks: derivative (dy/dx etc) and integral (arclength, area) properties in parametrized curves and polar curves.
    

end of list! scroll up for current day assignment.

Weeks 3 and 4 or earlier: come by and find me in my office, spend 5 minutes, tell me how things are going. This is a required visit.

FINAL EXAM: voluntary MLRC problem session Wednesday: 5pm?
                       1505-003 MWF 10:30: Thur, Dec 14 11:30 - 2:00
                       1505-004 MWF 11:30:  Sat, Dec 16 10:45 - 1:15 switching times allowed with instructor permission
                       extra option: Tol 314A, 11:30-2:00 Monday Dec 18.

                          MAPLE CHECKING ALLOWED FOR Quizzes, EXAMS