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of the old online HW hints that are now superceded by the e-book addons.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.

**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. **
Textbook problems
** are labeled by chapter and section and problem number, and identify
each WebAssign problem

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 [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**l**og in**to MyNova at http://mynova.villanova.edu/ (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:

[ 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 to illustrate document versus worksheet mode in Maple:

document mode, worksheet mode;

here is a sample worksheet report, with exported animated GIF. we will return here later for volumes of revolution).**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.]

Watch this short video about**New Users of Maple.**

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.]

**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: s5-4-60.mw;

5.4: 1, 5, 31, 33, 45, 50, 52, 59, 65 (units! hrs, secs);

if you have a moment for reflection read:

differentiation versus integration: notation and associated pictures

- W: 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^{*}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
1);

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*];

**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, mw];

optional but useful alternative example;

5.5: [74], [79], 81, 83, 85, 86, 87, 91;**square bracketed problems on this HW page are not on WebAssign;**

[WebAssign HW problem numerical parameters online change so you can't just enter the answer from the back of the book for odd numbered problems!] - 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].

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.

- F: Quiz 2 on u-substitution, no previous quiz on this;

6.1: 1. 3. 9, 11, 15, 27, 31, 33, 49; 53 [see this approach]; numerical root necessary?;

Income inequality is a serious problem today.

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);

[If curious checkout this Gini index calculus application only using calculus you already know.]**WEEK 3[-1]:** - M: handout on regions of the plane: relationships between
variables [areas, volumes of revolution];

6.2: 1, 7, 9, 11, 33, 41, 47, 49. - T: 6.2: 53 [this
called a trirectangular tetrahedron; challenge: can you repeat this for side lengths
*a*,*b*,*c*?] ,

55 [see Maple solution and plots], 57, 61, 64.

optional fun: derive a volume formula for the Great Pyramid 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, [29], 30 [this problem is all about units!);

If you are curious about how bob used Maple on the pyramid work problem, click here. Conical tank?**WEEK 4[-1]:** - M: 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. - 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]

cute Maple Companion app to upload handwritten math to Maple.

- W: review problems 6.R: 11, 18,26, 29
solution worksheet;

handout: blood 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 about):

3, 5, 9, 17, 39 [example of using Tutor], 45; just for fun: [iteration example]; [change of variable example]. - 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, [**67**], 68 [dimensional discussion][integral by hand], [**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]

[Climate Day. Sep 20; Why? When? Where: Oreo Today 12 noon. Your future is at stake.]**WEEK 5[-1]:** - M: 7.6 Integration using Tables of Integrals (no!:
6,7,8,9,10)
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 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 wish.

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 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.

Quiz 4 answer key online. - W: 7.7: (numerical error?): 21, [23* use
template problem 24 here],
37;

[Maple 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.
**WEEK 6[-1]:** - 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:*,*pdf].

- 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, [51], [55], [79,use Maple for antiderivative, neither integral alone converges so they have to cancel for large*x,*this determines*C*], 515XP, 529XP.

- W:
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, 79, 80].**No office hours today: bob is sick.** - F: Quiz 5 on improper integrals; Test 1 back. Work on Maple7 over
weekend.
**No office hours today: bob is still sick.****WEEK 7[-1]:** - M: 8.1(arclength
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), 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 numerical solution].

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):

2pm today Mendel Award talk in Villanova Room. Usually a terrific speaker.

**Spring Break**.**WEEK 8[-1]:** - M: 8.5: grade averaging
example to motivate weighted averages; handout on
probability [circular
target example];

gas tank filling example and changing variable: pdf, mw;

8.5 (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

[21* Use Maple to answer each part of the problem, keeping*a*_{0}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.**

**
FINAL EXAM:**

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
instructor permission]

MAPLE CHECKING ALLOWED FOR Quizzes, EXAMS