21F homework and daily class log
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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. (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). 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.] Red numbered problems are a relic
of the old online HW hints that are now superceded by the e-book addons.
*" asterisk marked problems are to be done with MAPLE as explained in the separate
but still tentative
MAPLE homework log,
which will be edited as we go.
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.
are labeled by chapter and section and problem number, and identify
each WebAssign problem. Those problems which are not available in WebAssign will be square bracketed and
should be done
outside of WebAssign. Check this 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.
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.
- GETTING STARTED STUFF Monday August 23.
In class open your favorite browser and
log in to MyNova at
(use your standard VU email username and
password) and check out our class photo roster (search for
Class Schedule with Photos), and visit my course homepage
and bob will give you and overview of the class materials.
need yet to look at the MAPLE examples and tips yet: we will get around to
5.3 on reviewing diff/int notation; [Exploreplot.mw]
(light first day assignment):
Make sure you read my welcoming email
sent on the weekend, and register with WebAssign.
[If not already done:
Maple here. Then install it.]
Watch this short video about
New Users of Maple.
Explore the on-line resources. Browse the pages linked to our class home
online handout on functions and differentiation
to see what background is assumed.
Read 5.3. Do 5.3: 7,
using WebAssign, and the "Getting Started with WebAssign" assignment. Notice
the "Ask Your Instructor" button!
Read what Villanova students say about the most important
things you can do to succeed here.
By Wednesday August 25,
reply to my welcoming email
heading "[MAT1505-00?] <cell#> <nickname> <dormabbreviation>
where <cell#> is your cell phone number (I will give you mine in
<nickname> is the first name other than your legal first name by which you wish
to be addressed (leave blank if legal name ok),
is from the list 3
letter dorm abbreviations (OFF for offcampus).
include the string [MAT1505] 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,
and anything about yourself for me to get to know you better, etc.
attach your class schedule from MyNova saved to PDF, or as an image file, or
perhaps a screen shot saved to JPG, and name the file
LastName-FirstName.extension so I can easily
extract them to a folder on my laptop.
W: Lecture Notes
5.4 indefinite integration;
Think about this online
algebra and differentiation/integration rules (and:
expanded diff rules);
does not add the constant of integration when evaluating an indefinite
integral, leaving you to choose its symbol.]
Velocity example of net change and the
fundamental theorem of calculus:
5.4: 1, 5,
31, 33, 45[hint: separate into two integrals],
50, 52, 59,
tabular data: 65 (units! hrs, secs);
if you have a moment for reflection
differentiation versus integration: notation and
associated pictures [just a summary of day 1 lecture]
Th: bring your laptops today, with Maple installed; bob will help you
adjust your palettes and show you the interface.
Here is the worksheet
bob used in class to illustrate document versus worksheet mode in Maple:
open up this file: datafitint.mw and
read it with a partner, then do the final section exercise with
the date from Stewart
5.4.74* on a shuttle liftoff
height calculation (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 (class
contact info will be available after drop and add);
F: Quiz 1 on 5.3-4 (see
use Adobe scan to upload your work;
5.5a change variable in integral;
chain rule for scaled integration
variable in a function;
5.5 ("u-substitution"): 1, 3, 7,
13, 19, 21,
[hint: separate into two integrals], 59
[express as a definite integral in u];
WEEK 2: Read
WebAssign Access choices!
M: Lecture Notes
5.5b symmetry and transforming definite integrals;
5.5: 81, 83,
dimensionless variable discussion: 85
(read!), 86, 87,
square bracketed problems on this HW
page are not on
[WebAssign HW problem numerical parameters online
change so you can't just enter the answer from the back of the book for odd
with office hours;
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, 47, 53, 58, 59, 61, 63,
66 [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];
problem, use template; forget parts a,b,
just 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,The
Maple5.mw assignment is due anytime next week through the weekend. You can use this template:
to get started ]; 18* [Use Maple to evaluate this definite integral in a
second section in your worksheet, just to prove you can enter a definite
integral and evaluate it.]
Th: Lecture Notes
Areas between Curves;
6.1: 1. 3.
9, 11, 15, 27, 31, 33, 49;
[see this approach];
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
[If curious checkout
this Gini index calculus application only using calculus you already
F: Lecture Notes 6.2 on
Volumes (of Revolution, etc); [elliptical version of example 7:
Quiz 2 on u-substitution;
7, 9, 11,
41, 47, 49.
WEEK 3[-1]: Monday is Labor Day!
W: in class group work:
48 [with bob hint], we then work on these WebAssign setups:
called a trirectangular tetrahedron; use horizontal plane cross-sections] ,
sides of isosceles right triangle are hypotenuse divided by sqrt(2),
Maple solution and plots],
online handout on regions of the plane: relationships between
variables [areas, volumes of revolution];
optional fun: apply the
volume formula to the
of Egypt using the data you find online.
Th: Lecture Notes 6.3 on
Work in 1-d motion;
6.4 [skip 6.3]: 3,
13 [hint: this is tricky and only works for lifting halfway, no
other fraction, see the Maple worksheet
15 [hint: also tricky,the extra single weight is moved a
constant distance, so the product work value can be incorporated into the
integral for the cable, see the Maple
30 [this problem is all about units!
you need to convert inches to feet to get ft-lbs in the final answer],
34 [keep maximum significant figures in part a) to obtain correct integer
for part b).]
- F: Please read remarks on Quiz 2
answer key (page 2);
Quiz 3 on volumes;
Average Value of a Function; [temperature
6.5: 1, 7,
9, in class: 11,,
17, 18 [blood
flow as an example of dimensionless variables].
M: 6.R: 11 (in class), 15, 25, 26 [part b gives you the answer!],
Hint: solve for the point x = a of intersection in terms of
the slope m of the line y = m 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. [soln].
Maple6.mw assignment: 6.AppliedProject: Where to Sit at the Movies* (after 6.5) (p 465).
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 maple6.mw to accomplish this.
- W: Chapter 7:1-4 "Methods of Integration" is obsolete in the age of computer
algebra systems; there is no general approach to finding antiderivatives.
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, 17,
of using Tutor], 45 [this can also be done by change of variable, but
just for fun: [iteration
example]; [change of variable
- Th: Lecture Notes 7.1b on
Integration by Parts etc;
7.1: 57, [59, 65], 66, , 68 [dimensional
discussion and HW template], , 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]
- F: Quiz 4 on integration by parts due Tuesday;
7.7 (approximate integration;
2, 3, 7 [ApproxInTutor!], 30, 35, 42;
[You can use the ApproximateIntTutor, and the "Compare"
button which gives all the approximations simultaneously];
[Hint: Maple approach to
these problems, with explanations.]
WEEK 5[-1]: Test 1 Thursday in class through
- M: Lecture Notes on
7.7: (numerical error?): 22,
37 (tabular data with Simpson);
[in class: 23* use
template problem 24 here]
Simpson 3/8 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.
- W: Lecture Notes 7.8a on Improper Integrals
7.8 [Maple examples]: 1, 3, 5, 13, 21,
23, 25 [Hint: u-sub!].
- Th: Test 1 through chapter 6 in class [no work problems.] [no lined
paper needed, bob will bring it]
- F: Lecture Notes
Improper Integrals (infinite integrands);
29, 31, 32, 33 [ab-surd!], 35, 40 [Hint: u-sub
WEEK 6[-1]: Quiz 4 answer
- M: Lecture Notes
Improper Integral (comparison and applications); [62: mw,
49, 51, 53, 54, 55
applications: 68, 70 [in class, first do rescaling u-sub to
dimensionless variable, then handle the improper integral in the
- W: Lecture Notes 5.5c on change of
variable in Definite Integrals; [5.5: 64 example, 65 by students]
A Nobel prize for an improper integral?
66 workshop with Maple (voluntary
completion with partner(s), submit if you wish feedback).
Please study Test 1 Answer
5.5: 62, 63, 67, 69,71 [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
- Th: This evening special Zoom panel
on feeling off as a student: how to get help;
Maple worksheet collection of problems: 70
[liters!], 72 [hyperbolic
74 (area: let u = sqrt(x) and
the integral to a simpler form, then compare with Maple result:
78 [games with
79 [this is just a
change of variable problem, we don't have
to actually do the integral), 80.
[boldface done together in class]
- F: Quiz 5 on improper integrals;
8.1a on arclength; [fun: powers]
Tutor): 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 or wait 25 seconds to be amazed:
to plot; solve for y, perfect square is a power function!,
do one quadrant, multiply by 4).
- M: Lecture Notes
8.1b on arclength functions; [revisit
8.1: 35, [try this for fun: 36*],
37 [we have to
simplify the integrand by combining fractions],
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);
curious, 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
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
- W: Lecture Notes 8.4a on
business calc [demand curve,
8.4: 5, 6, 8, 12 [9: total surplus: maximized?? bob finds
- Th: Lecture Notes 8.4b on blood
flow, cardiac output;
dilution method example
measure flow rate out of heart, cardiac output
not enough problems on WebAssign!
basic financial literacy! 15 (future value), 16 (present value) , 17 (incnme
18 (net change integral),
19 (plug in numbers, blood
21 [dye problem with expression for c(t)],
AE2 [cardiac dye, like 22 cardiac dye].
- F: Quiz 6 on arclength, due Tuesday after break.
- M: Lecture Notes 8.5a on probability;
8.5: 1, 2, 5, 6,
Poisson (decaying exponential) distribution
10 (median value of x: probability half below x, half
above x), 11.
- W: Lecture Notes 8.5b on probability:
normal distributions etc;
[gas tank filling example and changing variable: pdf,
mw]; [circular target];
8.5: normal distribution: 15, 16
[template: adjusting the mean to achieve a
Maple to answer each part of the problem, keeping a0
symbolic except for the graph in part c)].
WebAssign has a smart
Cengage Mobile app!
And today a
post with 3 sigma, 5 sigma mentioned!
- Th: 8.R: [9 also find s(x), 21, 22, 23 recall Poisson mean
is 0.69 mu!];
Quicky in class exercise Maple
- F: Short Quiz 7 on probability distributions
11.1 on infinite sequences;
Read 11.0 ultraviolet catastrophe;
Watch 11.1 video on Fibonacci sequence; (read this
motivating example: planck, sequence worksheet):
11.1: 1, 5, 11,
, 23, 25, 29, 33, 41 (l'Hopital's rule: ∞/∞), 49, [59* (use the
template in this worksheet)], 65.
n = 1..N) this is how you generate
sequences in Maple; use evalf(f(n)) if you want the decimal values.
WEEK 9[-1]: Facinated by math?
Check this out [YouTube]
- M: Lecture Notes
11.2 on infinite series;
(short problems, I avoided tedious
entry of numerical values of first n terms):
11.2 (series): 1, 3, 15, 17, 18, 22,
27, 31, 41, 43 [Hint: convert(1/(n^2 - 1), parfrac)],
49 [d: all rational numbers that have a terminating decimal representation except for 0],
51, 57, 69 [wording misleading, limiting amount
after each injestion, not the minimal level always remaining in body],
- W: Lecture Notes
11.3 on the integral test [mw,
, 7, 8, 11, 14, 15, 27, 29, 35, 37 (use
Maple integral test template), 39 [template].
- Th: Test 2 through chapter 8. arclength, improper integrals,
- F: Lecture Notes
11.4 on comparison tests;
11.4: 1, 2, 5, 7, 23, 27, 28, 29, 31, [35*];
2pm Mendel Award
Public Talk in the Villanova Room. Don't miss it!
- M: Lecture Notes
11.5 on alternating series; [limit comparison easier than direct
(alternating series mw);
2, 3, 5, 7, 11, 17, 23, 32.
Check blackboard grades against test grades.
Test 2 answer key online. Test 2
back Thursday (oops, forgot them at home)
- W: Lecture Notes
11.6 on Absolute Convergence, Ratio [& Root] Tests;
11.6: 1, 2, 5, 7, 13, 17, 23, 25,
31, 37, 43;
[optional fun reading 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, read this
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; now we start the important stuff.
- Th: Lecture Notes
11.8 on power series (almost Taylor, finally!); [Bessel]
11.8: 5, 7, 9, 15, 17, 19, 21, 27,
- F: Quiz 8 on series so far;
11.9 on power series tricks;
(tricks with power series): 3, 5,
[9, to make this less painful, use the fact
that (x-1)/(x+2) = 1 -3/(x+2)],
this worked example pdf,
25, 32 [use Maple worksheet].
- M: Lecture Notes 11.10a
on Taylor series;
11.10 (Taylor series!): , 3, 4, [5, 7], 11, 12,
[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
- W: Lecture Notes 11.10b
on binomial expansion series;
11.10: 31, 33, 37, 51,
integrated series is alternating after the first term, so next term in
series is error estimate],
- Th:Lecture Notes 11.10c
on Taylor series maybe not: grabbag day?;
practice not for testing);
(products and quotients of series?
not for us):
limits with power series;
series (all we can handle)];
62, 78 [for fun look at
- F: Quiz 9 on Taylor series;
Lecture Notes 11.11
on Taylor series apps
11.11 (applications): [kinetic
energy, black body radiation]
[use Maple > taylor(f(x),x=0,6) to get
Taylor series you need in these problems].
35, 37 [Hint: the angle from the center in radians
is so small that it can be approximated by its tangent L/R;
lowest terms of secant series from Maple! For part c) you need
Digits:=20; forget about parts a), b) they are worth 0 pts and no one will
ever see what you enter.]
optional: [33, 36 Hint: factor out d
from the radical to use binomial series in small ratio R/d, as in
33 for d/D].
- M: 11.R: in 11-22 recognize how to quickly identify the large n
behavior [22 taylor expand in x = 1/n after dividing through)], some diverge, consider absolute value when not
a positive series etc;
37 [remainder series less than geo series without
2, use its sum to place constraint on error];
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;
57 (just read s11-R-57.mw);
60 is a great application we will do
together in class;
summary: the big picture.
Lecture Notes 10.1
on parametrized curves;
parametrized curves can
be fun (tease)!; [hearts!];
(execute worksheet and look at many other examples):
(use Maple to
visualize curves [set parameters =1 to plot]! Google named curves if
[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:
[43: use identity cot^2+1=csc^2 to eliminate parameter, what
continuous range of angle makes it a continuous curve?],
both animatecurves!], 46 [see how you can
Explore the trajectories for all forward
fun: Venus in
- Th: Lecture Notes 10.2
on calculus of parametrized curves; (semicircle
7, 13, 17, 31, 48, [53, 55];
Maple worked HW problems];
[optional viewing: Project 10.1/2 running
circles around circles: fun with
- F: no quiz! [fun: Earth centric venus
Lecture Notes 10.3
(trig refresher online: trig,
inverse trig; handout:
10.3: 3, 5, 11, 17, 19, 21, 25, 27, 30, 32,
37, [49, 62]. [cardioidfamily.gif]
- M: Lecture Notes 9.0 on
series soln of DEs and Maple sol (for fun);
[Zoom recording in
ODE 101 with Maple, a preview,
plus how power series solution of DEs defines special functions like Bessel.
F: Take home Test 3 out on BlackBoard. First read the
test rules carefully please.
- M: Hard copy of Test 3 distributed in class; continue working on this
- W: Lecture Notes 10.4a
on polar curve angular ranges; [mw]
after this preliminary issue with polar curves, work on Test 3 will continue
- Th: Lecture Notes 10.4b
on polar curve areas; [video example]
[circle and cardioid]
10.4: 7, 21,
plot([cos(2*t), sin(2*t)], t = 0 .. 2*Pi, coords = polar) 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?),
numerical solution for angle of intersection).
- F: Lecture
Notes 10.4c on polar curve arclength; [circle]
in class arclength of r = sin(theta/4), what is period over which you have
47 (easy u-sub!), 50 (perfect square!), 51 (exact via Maple),
517.XP [convert(L,ln) to force arcsinh to ln expression for
- M: Test 3 due in class today stapled;
Notes 10.5 on ellipses;
group exercise: area and
circumference of a specific ellipse (as part of review for both parametrized
curves and polar coordinate integration).
ellipses in action [even
- T [F]: 10.R (plots): 1,
11, 19 (what happens at theta = 0?),
23 (m =
[areas of loops, not discussed in the text! A=4.05];
(hor/vert tangents: plot with a
30 (6 Pi a^2); 31 (18), 40
(perfect square! 0.9).
- W: checking a solution of a differential equation;
Spaghetti curves? How an innocent math problem can lead to crazy
Th: Last Class; CATS at beginning of class (instructions:
discussion of final exam
on Chapter 10:
areas enclosed by parametrized curves or polar curves,
arclengths in both contexts, vertical and horizontal tangents, tangent lines
of parametric curves or polar curves.
We made it!
end of list! scroll up for current day assignment.
Weeks 3 and 4 or 5 or earlier: come by and find me in my office, 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.
switching times allowed with instructor permission
log from last time
1505-001 MWF 10:30: Fri, Dec 17 08:30 AM - 11:00 AM
1505-002 MWF 11:30: Sat, Dec 11 10:45 AM - 01:15 PM
MAPLE CHECKING ALLOWED FOR all Quizzes, EXAMS
here is a sample worksheet
report, with exported animated GIF.
we will return here later for volumes of revolution).
curve example of change of integration variable [pdf,