MAT1505 23F homework and daily class log

Jump to current date! [where @ is located]

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.]

It is your responsibility to check homework here (not all problems are in WebAssign). 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). WebAssign "deadlines" are at 11:59pm of the day they are due, allowing you to complete problems you have trouble with after class discussion. [If Friday is quiz day, HW due Friday has a WebAssign deadline of midnight Monday.]  The WebAssign extension tool can be used to request more time or more attempts for a given homework assignment, so persistence can give any student 100 percent credit on the homework cumulative grade.

Read the textbook (w
atch embeded videos). Do the homework assignments on time to keep up. Use the Ask Your Instructor tool when you are stuck. Ask for extensions in due date and number of tries till you get 100 percent correct.

Textbook technology: WebAssign homework management/grading is required, giving you access to an incredible wealth of multimedia tools together with the online e-book textbook you can access from any internet connection. WebAssign deadlines are suggested to keep students on track, but extensions in time and number of tries are always granted.
Textbook problems
are labeled by chapter and section and problem number, and identify each WebAssign problem. Optional problems which are not available in WebAssign will be square bracketed [[...]] and are helpful for your learning. Check this homework page for hints and some linked Maple worksheet solutions. Use the Ask Your Instructor tool to get help on any problem for which you cannot get the correct answer. There is no reason for anyone not to get 100 percent credit for the homework assignments. This is the most important component of learning in this class, doing problems to digest the ideas.

Read what Villanova students say about the most important things you can do to succeed here.

If you have any questions, drop by my office St Aug 370 (third floor facing Mendel by side stairwell) or just come to see where you can find me in the future when you might need to. I welcome visitors.

  1. W: GETTING STARTED STUFF Wednesday August 23: Introduction and Overview
    We will access our e-textbook/HW WebAssign portal through BlackBoard with your laptop or phone.
    [ "Ask your Teacher" "Request Extension';]

    Lecture Notes: 5.0 Riemann definition of a definite integral etc the first minilecture!
        [ the first Maple Worksheet = MW file extension]

    Make sure you read my welcoming email sent before the first class, and register with WebAssign (immediately, if not already done) and by the weekend, reply to that email with your schedule attached as described there, including a bit of introduction of you to bob, as described in that email.

    Make sure you download Maple 2023 to your local computer, available by clicking here and install it when you get a chance (it takes about 15 minutes or less total), If you have any trouble, email me with an explanation of the errors. You are expected to be able to use Maple on your laptop when needed. We will develop the experience as we go. I will give one-on-one tours of Maple in office hours to those who are interested.
    No problem if you never used it before, as is the case for all entering freshmen.

    Explore the on-line resources. Browse the pages linked to our class home page.
    Read this online handout on functions and differentiation to see what background is assumed.

    Do the "Getting Started with WebAssign" assignment. Notice the "Ask Your Instructor" button!

  2. Th: Lecture Notes 5.3 Fundamental Theorem of Calculus, Review plus derivative/differential notation (pages 4-6) [summary]
    Read 5.3. Do 5.3: 7, 9, 13, 16, 29, 37, 41 in the WebAssign portal;
    see textbook section opening video examples in Maple when reading the section;
    think about these online handouts on rules of algebra and  rules of differentiation.

  3. F: Quiz 1 on 5.3 (take home open resource quiz but no collaboration, due Monday in class);
    when stuck on a quiz, email me your question);
    Lecture Notes 5.4 indefinite integration and net change (pages 3-4);
    velocity example of net change and the fundamental theorem of calculus:;
    5.4: 3, 7, 17, 39, 41, 53 [hint: separate into two integrals], 58, 60, 69,
    tabular data: 75 (consistent units! hrs, secs).

    WEEK 2[-1]:
  4. M: Lecture Notes 5.5a change variable in integral;
    summary online handout: "u-substitution";
    extending our short list of function derivatives: chain rule for scaled integration variable in a function;
    5.5 1, *, 7, 13, 19, 21, 25,
    51 [hint: separate into two integrals], 65 [express as a definite integral in u].

    Tuesday Drop Add period ends   [free phone app for great scans of quizzes: Adobe Scan]

  5. W: Lecture Notes 5.5b symmetry and transforming definite integrals;  [example: bell curves; page two]
     5.5:  87, 89, dimensionless variable discussion:
    91 (please read worksheet for comments, use palette to enter subscripted variable "C_0" in WebAssign, remember math is case sensitive),
    92, 93, 97

  6. Th: Review problems [no review problems are on WebAssign; see e-text: Review section, skip over true false and concept check]:
    4 (remember Riemann definition!), 7 (visualization is important), 15, 21, 23, 31, 41, 53, 59, 64, 65, 67, 69,
    72 [Maple gives you the value of the limit, your task is to derive it using the fundamental theorem of calculus; the worksheet explains why this limit is interesting for an optional read];

  7. F: paper class lists distributed; Office Hours midday serve nearly everone;
    Quiz 2 (posted online for after class, paper copy handed out in class);
    Lecture Notes 6.1 on Areas between Curves;
    6.1: 1. 3, 11, 13, 17, 25,  57, 58;
    61 [graphical integration]; numerical root necessary?;
    Income inequality is a serious problem today, made painfully clear by COVID.
    Read Applied Project "The Gini Index", the applied project following section 6.1 (inserted as a result of the lobbying of our very own Math&Stat Dept prof. Klaus Volpert) which is important in quantifying income and wealth inequality.
    [If curious checkout this Gini index calculus application only using calculus you already know, appearing as an Applied Project in the text after this section, inspired by our own Klaus Volpert in the Math/Stat Dept.]

    > plot([f(x),g(x)],x=a..b,color=[red,blue])    # plot 2 graphs together, or use drop second expression onto PlotBuilder plot of either one

    WEEK 3[-2]:  Monday is Labor Day!
  8. W: Check Quiz 1 answer key in archive; Quiz 2 due in class;
    Note Menu Maple Tools, Tutors, Calculus 1, Volumes of Revolution;
     Lecture Notes 6.2 on Volumes (of Revolution, etc); [example]
    6.2: 5. 6. 11, 51,
    59 [see how to set up problem in Maple worksheet],
    67 [elliptical version of example 7], 73 [circular cross-sections]; 
    online handout on regions of the plane: relationships between variables [areas, volumes of revolution].

  9. Th: Check Quiz 2 answer key in archive;
    in class group work 6.2.61 [cap of sphere set up], Example 9, 77 [set up], if time: 6.4.48 [frustrum];
    6.2: 64 diagram: [this called a trirectangular tetrahedron; use horizontal plane cross-sections, similar triangles or write equation of line in plane for side face projection!],
    65  [recall sides of isosceles right triangle are hypotenuse divided by sqrt(2), Maple plots],
    68, 85 (wine barrel: lots of parameters).

    optional fun: apply the pyramid volume formula to the Great Pyramid of Egypt using the data you find online to verify its stated volume

  10. F: Quiz 3 (posted online after class, paper copy handed out in class);
    Bring laptops for Maple workshop. bob will help you adjust your palettes and show you the interface.
    Then open up this file: and read it with a partner, then do the final section exercise with the data from Stewart 5.4.84* on a shuttle liftoff height calculation (convert to mile units at the end). Ask bob when you are confused about anything.

    We are skipping 6.3 on cylindrical shell volumes! [example]

    WEEK 4[-2]:  please use the Extension and Ask Your Teacher tools correctly to help me help you
  11. M: Lecture Notes 6.4 on Work in 1-d motion;
    6.4:   3, 7, 13,
    15 [READ THIS WORKSHEET FIRST: tricky, the extra single weight is moved a constant distance, so the associated constant product work value can be incorporated into the integral for the cable as a constant force term in the integrand, see this Maple worksheet explanation],
    30 [this problem is all about units! you need to convert inches to feet to get ft-lbs in the final answer],
    36 [Evaluate the work needed to build the Great Pyramid of Egypt: setup keep maximum significant figures in part a) to obtain correct integer for part b).]  [solution]

  12. W:  Lecture Notes 6.5 on Average Value of a Function; [temperature example][lung inhale example 23]
    6.5:  1, 7, 9, 7, 9, 11, 17,
    20 [blood flow as an example of dimensionless variables (we return to this in section 8.4)].

  13. Th: we haven't done very much to review so far!
    6.R: 11 (in class), 17, 20, 28, 31,
    optional: 6.Plus.2Hint: solve for the point x = a of intersection in terms of the slope m of the line ym x (easy!) , and express m as a function of a.  Then use this value to set the area over x = 0..a equal to half the area over the entire interval. This condition is easily solved by hand if you are careful! Plot the resulting line with the curve. 

    Maple group exercise in class:
    6.AppliedProject: Where to Sit at the Movies (after 6.5)  Assume the result of part 1 (just trigonometry), then do parts 2-4 to get a real life example of an average viewing angle. Here is a worksheet to accomplish this. Work on this together with one or a few partners, and finish after class, if you wish submit worksheet by email with subject header:
    [mat1505]    and same filename attached so I can give feedback.

  14. F: Quiz 4 (work, avg value but no Int by Parts yet!)  [remark: words and math]
    Chapter 7:1-4 "Methods of Integration" is obsolete in the age of computer algebra systems; there is no general approach to finding antiderivatives.
    Lecture Notes 7.1a on Integration by Parts;
    7.1:  (integration by parts is useful in physics/math variational problems, not so much as an integration technique that we need to worry about, but we need to be aware of the process):
    3, 5, 9, 13, 23, 45 [example of using Tutor]; 
    just for fun: [Explore iteration example].

    WEEK 5[-2]:  Test 1 Thursday
  15. M: Lecture Notes 7.1b on Integration by Parts etc;
    7.1: 71,
    74  [dimensional discussion and HW template; first transform with a u-sub or just do definite integral with Maple],
    75, 77.

    Optional. transforming an integral with an unknown function.

  16. W: Lecture Notes 7.7a on Approximate Integration;
    7.7 (Simpson formula calculation):  2,
    3, 10 [for both these use the ApproxInTutor and the "Compare" button which gives all the approximations simultaneously],
    30 [template for Simpson], 35 [graphical], 37 [template for tabular data with Simpson], 42 [use this template];

    [Optional: Maple approach to the unlinked problems, with explanations.] [compare Midpoint versus Simpson]

    Is there a desire for a 5pm problem session today in Mendel G90 to ask any questions for me to solve? The room is booked.

  17. Th: Test 1 thru 7.1 (see archive). Come early if you can to get started.

  18. F:  No quiz during Test week;
    Lecture Notes on Approximate Integration;
    7.7: (numerical error?): together: 21 [saving you tedious input in WebAssign], catch up on past HW since no WebAssign tonight!

    Aside. If you use Maple's Approximate Integration Tutor, note other methods listed. Simpson 3/8 rule uses a 3rd degree polynomial, while Newton Cotes formulas (see the Approximate Integration Tutor window menu) generalize the trapezoidal and these Simpson rules to even higher order polynomials. [wiki]
    Amusingly enough the proof of the error estimate for the trapezoidal rule involves two clever integration by parts and once verified, the whole proof becomes relatively straightforward. So as I mentioned, integration by parts is essential for advanced mathematics and applications. The Simpson's rule error estimate proof  is more of the same.

    Parents Weekend. potato head family

    WEEK 6[-2]: check answer key for test 1 and study the additional pages please
  19. M: Lecture Notes 7.8a on  Improper Integrals (infinite limits);  [normal curve example]
    7.8 [Maple examples]: use Maple for needed antiderivatives if you have trouble with the change of variable:
    1, 3, 5, 19, 29, 31, 33 [Hint: u-sub!].

  20. W:   Test 1 back;
    5.5: 52, 53,
    66 [note u = exp(x) is the only way to proceed! in other words the exponential is inside the composed function],
    70 [transform definite integral to new variable for practice],
    73, 74,
    78 [note dx/sqrt(x) 2 d (sqrt(x)), what does that suggest? the sqrt(x) is inside the composed function, let it be u];
    [in each case, 1) re-express integrand in terms of u AND  re-express differential in terms of u and du, and 2) change to new u-limits of integration. Then evaluate this completely new integral expressed entirely in terms of the new variable.]

  21. Th: W: Lecture Notes 7.8b on Improper Integrals (infinite integrands);
    7.8: use Maple for needed antiderivatives: 37, 39, 40, 41 [odd roots in Maple require care: ab-surd!],
     [int by parts]: 43, 47, 48.

  22. F: Weekend Take home Test 1b due Monday (see archive for copy); please read the test rules;
    to solve an equation numerically see this worksheet;
    Lecture Notes 7.8c on Improper Integral (comparison and applications);  [examples]
    [74: mw, wiki classical gas velocity distribution];
    7.8: use Maple for needed antiderivatives
    57, 61, 64, 67;
    80, 82.

    Optional: What? A Nobel prize for an improper integral?

    WEEK 7[-2]:
  23. M: take home test due in class;
    7.8: 78 [in class quickie exercise together];
    7.R: see Maple worksheet collection of problems
    71; what must be true of n for convergence at infinity? what must then be true of n for convergence also at the origin?
    80 [liters!], 82 [hyperbolic function!],
    88 [games with limits];
    89 [this is just a change of variable problem, we don't have to actually do the integral).

  24. W: Lecture Notes 8.1a on arclength;  [fun: all powers lead to special functions]
    8.1(arclength Tutor):  1, 7,
    9 (simple u-sub), 14 (perfect square!),  16,
    27 (use Maple evalf of inert form of integral or wait 25 seconds to be amazed),
    39 (how to plot; solve for y, perfect square is a power function!, do one quadrant, multiply by 4).

  25. Th: Test 1B back:  see answer key;
    Lecture Notes 8.1b on arclength functions;
    8.1 (HW problems in Maple):
    41, 42 [there are three equivalent different looking forms for the arclength function due to the ln and trig identities; only one is accepted by WebAssign:  s(x) = ln(csc(x) - cot(x))],
    45, 47 (numerical solve needed);
    in class exercise:
    49 (remember definitions of cosh and sinh; you need to numerically solve for a in the interval a = 40..100,  Solve, Numerically Solve From Point, choose a = 40);

    We skip 8.2 on surface area since this is not even required in the syllabus of multivariable calculus MAT2500.
    We skip 8.3 since moments will be  dealt with in MAT2500, while hydrostatic pressure seems to far afield for most of us.

  26. F: Provisional Midterm grades in BlackBoard; check that uploaded grades are correct;
    Quiz 5 due Wednesday after break;
    Lecture Notes 8.4a on business calc [a little business literacy never hurt anyone!];
    8.4: 3, 5, 9, 12, 17 [most of these are just areas between a curve and a horizontal line, set them up, evaluate with Maple]

    Fall Break.  

    WEEK 8[-2]:
  27. M: Lecture Notes 8.4b on blood flow, cardiac output;
    8.4 (dye dilution method example worksheet to measure flow rate out of heart, ignorable cardiac output summary): 
    21 (plug in numbers, blood flow),
    23 [dye problem with functional expression for c(t)],
    AE2 like 24 [cardiac dye, use the above template for tabular data].

  28. W: Lecture Notes 8.5a on probability;
    8.5: 1, 2, 5, 6, 9,
    Poisson (decaying exponential) distribution applications (pre-tech days: tables!):
    10 (median value of x: probability half below x, half above x),
    11 [part c) solve for the time T such that P(t>T) = 0.05 or P(0<t<T) = 0.95 ,
    12 [use maple for integral].

  29. Th:  Lecture Notes 8.5b on probability: normal distributions etc;
     8.5: normal distribution [short version]:
    14, 15,
    16 [template: adjusting the mean to achieve a goal],

    [ignorable: optional gas tank filling example and changing variable: pdf, mw]; [circular target]

  30. F: Quiz 6 on probability [use short template for normal distribution];
    open and execute together: [8.5.21 electron cloud!];
    8.R: 9 [also find s(x)], 21, 22, 23.

    WEEK 9[-2]: Test 2 thru chapter 8 in class Thursday this week (improper integrals, arclength, probability)

    Sequences and series: we don't need to be experts on the preliminaries,
    the emphasis is on Taylor series at the end of chapter 11.
  31. M: Lecture Notes 11.1 on infinite sequences; (long section but we only need an intuitive idea, not so much detail);
    Watch 11.1 first page introduction 8 minute video; (see also motivating sequences and series worksheet):
    11.1: 1, 7, 8, 21, 27, 35,  47 (l'Hopital's rule: ∞/∞), 55 (combine ln's first), 57.

    > f(n):=1/2n
    > seq(f(n), n = 1..10)    this is how you generate sequences in Maple; use evalf(f(n)) if you want the decimal values instead.

  32. W: Test 2 prep: ask bob to work whatever problems still confuse you. Quiz 6 answer key is online.

  33. Th: Test 2 in class.

  34. F: Lecture Notes 11.2 on infinite series; [Maple notation]
     (short problems, I avoided tedious entry of numerical values of first n terms):
    11.2 (series application): 1, 3, 15, 23, 25, 29, 33, 39, 49, 59,
    71 [wording misleading, limiting amount after each injestion, not the minimal level always remaining in body],
    77 [assume (1+c) is a proper fraction, sum the series, solve condition on c, pick the solution making the ratio a proper fraction].

    WEEK 10[-2]:
  35. M:  Lecture Notes 11.3 on the integral test [mw];
    11.3: 7, 8, 11, 13, 17, 18, 19, 29, 33, 39 (use Maple integral test template).

  36. W: see archive for Test 2 answer key please;
    Lecture Notes 11.4 on comparison tests (limit comparison test best! useful for Taylor series);
    11.4: 1, 2, 7, 9, 11, 17, 26,  33, 41 [note the missing differential in the WebAssign comparison integral!].
    Note: rn = en ln(r) is an exponential function of n, while n p is a power function of n, explaining why geometric series and p-series are the two important kinds of limit comparison series for series whose formulas are constructed from the term number n.

    The factorial n! is even faster in growing than powers or exponentials [Sterling's approximation]: exponentials on steroids!

  37. Th: Lecture Notes 11.5 on Alternating Series;
    (alternating series);
    11.5: 1, 2 [what is the formula for the nth term?],
    5, 7, 17, 19, 37, 47.

  38. F: Quiz 7;
     Lecture Notes 11.5b on Absolute Convergence;
    [irregular signed series, divergent alternating series]
    11.5: 21, 23, 25, 27, 29.

    WEEK 11[-2]:
  39. M:  Lecture Notes 11.6 on Ratio [& Root] Tests;
    11.6: 1, 3, 5, 9, 14, 15,
    19 [notice that this a_n factors so that the factorial in the denominator cancels the factorial in the numerator, leaving behind the nth power of that common factor, so it is a geometric series!],
    21, 39.

    [Optional FUN! if you want to be amazed, read this short worksheet of problem 50 which mentions William Gosper calculating 17 million digits of Pi (!) and shows dramatically how using an efficient series representation pays off.]

    We are skipping 11.7 since general series convergence tests are not as important for Taylor series, where the "absolute convergence ratio test rules" and the ratio test plus p-series comparison is all that matters, apart from the alternating series error estimate; now we start the important stuff of functions represented by Taylor series.

  40. W: Lecture Notes 11.8 on power series (almost Taylor, finally!);
    11.8: 2, 4, 6, 11, 13, 15, 21, 24,
    35 [Hint: just consider the additional factors in the numerator and denominator as n goes from n to n+1 to get the ratio of successive terms, then take its limit].

  41. Th: Lecture Notes 11.9 on power series tricks;
    11.9 (tricks with power series):
    1, 3, 5, 7, 9,
    21 (reorder the indexing!), 27, 
    34 [like example 8: explained by this Maple worksheet and this PDF but a calculator is sufficient].

    optional: Bessel approximations compared

  42. F: Quiz 8;
    Lecture Notes 11.10a on Taylor series;
    11.10 (Taylor series!):
    3, 4, 5, 6, 24, 27 [recall cos(n Pi) = (-1)^n , why? think],
    55 [convert degrees to radians, use alternating series estimate!].

    "Maclaurin series" = Taylor series centered at origin, term not used outside Calc books!
    > taylor(exp(x),x = 1, 6) ; convert(%,polynom)       # up to 5th power, centered at 1

    WEEK 12[-2]:
  43. M: see Quiz 7 answer key;
    Lecture Notes 11.10b on  binomial series;
    [wiki:; binomial thm];
    11.10: 35, 45, 65  (alternating series estimate)

  44. W: Lecture Notes 11.10c: Taylor series loose ends;
    [Taylor remainder formula: theory, practice but not for testing, just to be aware);
     (products and quotients of series? not for us, leads to tan(x): video of long division, wiki; tantaylor; ditto for other quotient trig functions];
    [exp,ln,trig,binom series (all we can handle, missing are arcsin,arccos, use binomial series integration to get those];
    11.10: useful limits with Taylor:  68, 69 [similar to 68], 70.

     [optional: for fun look at an unusual function 96 which does not have a Taylor series at x = 0 even though it and all of its derivatives exist there].

  45. Th:11.11: Lecture Notes 11.11 on Taylor series apps  [kinetic energy, black body radiation]
    11.11: we only need the alternating series estimates for the cosine and sine for example, so take this first section as a read only section; the second section Applications to Physics shows some examples of how often one or two terms in the Taylor series are enough to give a good approximation;
    No WebAssign for this section; we look at the following two problems in class together: 35  [details worked out here],
    and: 37 (solution given).

  46. F:  Quiz 9 online;
    11.R: in 11-21 recognize how to quickly identify the large n behavior for many of these;
    19 just use ratio test; ratio is quotient of new factors in numerator and denominator;
    22 [binomial series: expand this in terms of  x = 1/n after factoring out an n from the square roots to get sqrt(1+-1/n) to see large n behavior from leading term in this expansion, the linear approximation],
    look at some of the following problems that seem reasonable: 40-44 you should be able to answer all of these (for example 43 or 41);
    47-54 use tricks by manipulating simple series;
    56a [like 11.10.59 it becomes alternating after the first term, use Alt Series estimate], 59;
    is a great application we will do together in class. [solution].
    Taylor series summary: the big picture.

    2pm Mendel Medal Award talk in the Villanova Room, speakers usually exceptional!

    WEEK 12[-1]:
  47. M: chapter 11 problem catchup day: bring problems you want to see solved from the HW or quizzes, past tests.
    practice exercise 11.11.23
    22F Test 3: PDF [answer key:  PDF].

    T-Day break   

    WEEK 13[-1]:
  48. M: Lecture Notes 10.1 on parametrized curves;
    parametrized curves can be fun (tease)!;
    10.1 (ignorable: execute worksheet and look at many other examples):
    (use Maple to visualize curves):
    3 [see this worksheet for how to plot parametric curves,
    but can choose WebAssign plot by finding starting and ending points]
    8 [do b) first or where is t = 0? what is the slope of the straight line?],
    9 [where is t = 0? where is start, stop?],
    17 [does x increase or decrease?],
    21, 26,
    58 a only, 3 inputs [ignore rest of problem; optional see how you can Explore the trajectories for all forward angles].

  49. W: Take home Test 3 starts in class (emphasis on power series)
    [Read test rules please.]

  50. Th:  Lecture Notes 10.2 on calculus of parametrized curves: tangents;
    10.2: 1, 9, 13 [pick the best tangent line by eye], 15, 24.

    remember the template for plotting parametrized curves:
    > plot([x(t),y(t),t=0..2]) 
    and for animations:
    > with(plots):
    > animatecurve([x(t),y(t),t=0..2])

  51. F: Lecture Notes 10.2b on calculus of parametrized curves: areas and arclengths
    10.2:  positive areas, only the sign is troublesome:
    36 [y dx/dt>=0 so integrate this t = 0 ..Pi/2],
    39 [-y dx/dt>=0 so integrate this t = 0 ..2 Pi],
    these arclength problems can be done by hand:
    47 [obvious u-sub, factor common power outside of sqrt];
    48 [perfect square].

    WEEK 14[-1]:
  52. M:  Lecture Notes 10.3 polar coordinates; [fun: Earth centric venus orbit!];
    (trig refresher online: trigpolar coords); Maple polar curve plots;
    10.3:  3, 5, 9, 11, 17 [mulitply both sides by r]
    19, 22, 25 [replace x^2+y^2 by r^2, then replace y, divide through by r],
    35 [where does it start with theta = 0?],
    43 [where does it start with theta = 0?].

  53. W: Test 3 due in class;
    Lecture Notes 10.4 on polar curve areas; [video example; circle and cardioid]
    10.4: 3 [this traces out the loop exactly once, with a small interval of negative r between 3Pi/4 and Pi that sweeps out the part below the x axis],
    7, 21 [plot and find exact two angles where r = 0, integrate between them for inner loop],
    23 [draw these by hand, both circles], 35 [like in class example].

  54. Th: Lecture Notes 10.4 on polar curve arclength;
    10.4: 49 [this is a semicircle of arclength Pi times radius: integrand is constant];
    51 [obvious u-sub after factoring out largest power from sqrt],
    59 [Maple evaluation of integral! what is the angular range for r>=0?].

  55. @  F: Test 3 answer key online ;
    Lecture Notes 10.4 on polar curve tangents  [example 5]
    10.4: 63, 69 [obvious points on circle, derive polar coords].
    (not on final exam)

    WEEK 14 last day:
  56. M: CATS on BlackBoard; review for final:
    10.R.44 polar coord arclength and area
    [limited to parametrized curve tangent lines and slopes like 10.2:7-12, 21-24, polar curve areas and arclengths].


Weeks 3 and 4 or 5 or earlier: come by and find me in my office SAC370, spend 5 minutes, tell me how things are going. This is a required visit.  If you are having troubles, don't wait to see me.

Tests: week 5, 9, 12 -13? [week long take home] (tentatively)

FINAL EXAM:             review Wed Dec 13, 5-6pm Mendel G92
MAT1505 [MWF 09:35 PM] Fri, Dec 15 08:30 am - 11:00 am
MAT1505 [MWF 10:40 AM] Mon, Dec 18 08:30 am - 11:00 am

[exchanging exam slots is possible; ask bob]

                          MAPLE CHECKING ALLOWED FOR all Quizzes, EXAMS

log from last time 9-aug-2023 [course homepage]

does anyone ever scroll down to the end?