MAT1505 19F 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.]
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of the old online HW hints that are now superceded by the e-book addons.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.
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 must be done
outside of WebAssign. Check this page for hints and some linked Maple worksheet
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 26.
By Wednesday August 28, e-mail me [firstname.lastname@example.org]
from your OFFICIAL Villanova e-mail account (which identifies you with your full name)
[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 at
(use your standard VU email username and
password) and check out our class photo roster (search for
Class Schedule with Photos), 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, or directly:
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 to illustrate document versus
worksheet mode in Maple:
here is a sample worksheet
report, with exported animated GIF.
we will return here later for volumes of revolution).
(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 .
Fill out the paper schedule form bob handed out in class. [see
handouts]; use the
dorm abbreviations to return in class the next class day.
Read 5.3. Do 5.3: 7,
using WebAssign, and the "Getting Started with WebAssign" assignment.
[Hint: this is what your WebAssignment 5.3
should look like.]
Freshmen read what Villanova students say about the most important
things you can do to succeed here.
- T: hand in filled-in schedule sheets;
check carefully your telephone number and dorm abbreviation on the
signup sheet, nickname?;
Think about paper handout on
algebra and differentiation rules (online only:
expanded diff rules);
Velocity example of net change and the
fundamental thm of calculus:
5.4: 1, 5,
31, 33, 45,
50, 52, 59, 65 (units! hrs, secs);
if you have a moment for reflection
differentiation versus integration: notation and
- W: bring your laptops today, with Maple installed; bob will help you
adjust your palettes and show you the interface.
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* 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);
The archived Quiz 0
(takehome over a weekend and then not for a grade!) involves a special function! [Lambert Big Pharma application]
- F: quiz on 5.3-4 (see 17F Quiz 0 from
archive, but we are 2 crucial days
out of sync with last time, see also 15F Quiz 1, or problem 1 from 17F quiz
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[-1]: Labor Day!
- T: syllabus handout
with office hours delayed by printer glitch;
handout: "u-substitution" and bell
curve example of change of integration variable [pdf,
optional but useful
5.5: , ,
81, 83, 85, 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
- W: syllabus handout
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, 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].
Maple5.mw assignment is due anytime next week through the weekend, the
earlier the better. You can use this template:
to get started, with one section for each of the two Maple problems.
- F: Quiz 2 on u-substitution, no previous quiz on this;
6.1: 1. 3.
9, 11, 15, 27, 31, 33, 49;
[see this approach];
numerical root necessary?;
is a serious problem today.
Read Applied Project "The Gini Index", the applied project following section 6.1 (inserted as a result
lobbying of our very own Math&Stat Dept prof. Klaus Volpert);
[If curious checkout
this Gini index calculus application only using calculus you already
- M: handout on regions of the plane: relationships between
variables [areas, volumes of revolution];
7, 9, 11,
41, 47, 49.
- T: 6.2: 53 [this
called a trirectangular tetrahedron; challenge: can you repeat this for side lengths
a, b, c?] ,
Maple solution and plots],
57, 61, 64.
optional fun: derive a volume formula for the
of Egypt and see if it works for the data you find online.
- W: 6.4 work: 3,
7, 13, 23,
34 [keep maximum significant figures in part a) to obtain correct integer
for part b).
- F: Quiz 3 volumes of revolution: 15F quiz 3, 04S quiz 3;
6.4: 21 , 24, ,
30 [this problem is all about units!);
If you are curious about how bob used Maple on the pyramid
work problem, click here.
- M: 6.5: [average value]: 1, 7,
17, 18, [first do by hand 23];
6.5.23* [Do rest of
problem with Maple]. See worksheet maple6.mw link on
Where to Sit at the Movies* (after 6.5): part 1 done in class together.
- T: 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]
Companion app to upload handwritten math to Maple.
- W: review problems 6.R: 11, 18,26, 29
flow as an example of dimensionless variables (6.5.18);
7.1 (integration by parts is useful in physics/math variational
problems, not so much as an integration technique that we need to worry
3, 5, 9, 17,
of using Tutor], 45; just for fun: [iteration
example]; [change of variable
- F: Quiz 4 (liquid work with volume of revolution tank: see Quiz 17F 3);
what is this good for?
7.1: 57, [59, 65], 66, , 68 [dimensional
discussion][integral by hand], , 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]
[Climate Day. Sep 20;
Today 12 noon. Your future
is at stake.]
- M: 7.6 Integration using Tables of Integrals (no!:
and Computer Algebra Systems (yes!):
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 3 WebAssign
problems: WebAssign: 1, 3,
11, [4, 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
7.7.11 solution. other
problems: Problems Plus Maple.
- T: 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];
[Maple approach to
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.
Quiz 4 answer key online.
- W: 7.7: (numerical error?): 21, [23* use
template problem 24 here],
approach to these problems]
Note that Newton Cotes formulas
(see the Aproximate Integration Tutor window menu) generalize
the trapezoidal and Simpson rules to higher order polynomials. [wiki]
Thursday Evening: 5:30 voluntary MLRC
problem session for test.
- F: Test 1 through chapter 6 plus 7.1: areas between curves, average
value, volumes of revolution, pumping tank work, variable substitution,
integration by parts. Come early ready to go. Fully charged laptop.
- M: 7.8 [improper
integrals]: 1, 3, 5, 13, 21,
29, 39, 57,
62 [in WebAssign but nothing 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; soln:
- T: 7.8: 7.8: 66, 68,70; handout on improper
integrals with parameters;
66*: Use Maple to evaluate the integral, simplify by combining terms for
WebAssign, then 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!]; This is an improper integral but the antiderivative is
continuous so one can just plug in the limits. This is what Maple does.
(comparison thm: limit comparison theorem translates directly
into this thm for improper integrals): [47*], 49, , , [79,use
Maple for antiderivative, neither integral alone converges so they have to
cancel for large x, this determines C], 515XP,
7.R: 67 (consistent time units!), 70 (answer in liters, look up
conversion factor), 72, 74 (let u = sqrt(x) and transform
the integral, compare with Maple result), 78,
No office hours today: bob is sick.
- F: Quiz 5 on improper integrals; Test 1 back. Work on Maple7 over
No office hours today: bob is still sick.
- M: 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).
- T: 8.1: 35, [36*], 37 [we have to simplify the integrand and then
simplify Maple's result for the integral by hand], 39, 43,
44 (you need to numerically solve for a
in the interval a = 40..100, we start this in class together: then
Solve, Numerically Solve From Point, choose a = 40);
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
Office hour today 11:00-12:00.
- (notice we skipped 2 sections)
W: 8.4 (read on-line blood flow and
new andout: cardiac output. then dye
dilution method example to
measure flow rate out of heart): [optional: 15, 16 (basic financial
literacy!), 17], 18,19, [20 power law manipulations], 21, [22 cardiac dye].
Office Hour 2pm-3pm today
- F: Quiz 6 on arclengths (15F Q7,17F Q5):
Mendel Award talk in Villanova Room. Usually a terrific speaker.
- M: 8.5: grade averaging
example to motivate weighted averages; handout on
gas tank filling example and changing variable: pdf,
(probability): 1, 2, 5, 6, 10 (median value of x: probability half below x, half
above x), 11.
OFFICE HOUR Delayed till 1:30 today [library
book talk on Italian immigration 12:30pm]
- T: 8.5: normal distribution
[template]: 15, 16, 17, 19
Maple to answer each part of the problem, keeping a0
symbolic except for the graph in part c)].
- W: 8.R:
- F: Quiz 7
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.
log from last time
1505-003 MWF 10:30: Sat, Dec 14 10:45 - 1:15
1505-004 MWF 11:30: Thurs, Dec 19 2:30 - 5:00 [switching times allowed with
MAPLE CHECKING ALLOWED FOR Quizzes, EXAMS