MAT2500 05F 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.] Usually it will be summarized on the white board in class, but if
not, 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. Homework is understood to be done by the
next class meeting (unless that class is a test).
Textbook technology: Red numbered homework problems have hints on
your red TEC CD that comes inside your textbook [open the index.html file with
internet explorer, go to homework hints in the Main Menu; if you like to play
games, try the appropriate math modules when relevant to a section]. The
green Video Skillbuilder CD has detailed video discussed examples from each
section of the book as well as a video introduction by the author [click on the
Start.html file to get the Main Menu]. There are also tutorials and on-line
quizzes and web extras at the
textbook website.
- W: GETTING STARTED STUFF. By Friday, 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 "[MAT2500-XX]", where XX is your section number
01 or 04, telling about your last math courses, your comfort level with graphing
calculators and computers and math itself, [for sophomores only] how much experience you have with MAPLE (and Mathcad if appropriate) so far, why you chose your major, etc. Tell me
what your previous math course was named (Mat1500 = Calc 1 or Mat1505 = Calc
2).
[In ALL email to me, include the string "mat2500" somewhere in the
subject heading if you want me to read it. I filter my email.]
In class: log on to your machine [G90] and open
Internet Explorer.
(IE allows you to open MAPLE
files linked to web pages automatically if MAPLE is already open, in
Netscape you must save the file locally and then open in it MAPLE.)
G87 does not require a log on first.
bob will
quickly show you the computer environment. [We will edit your internal VU
homepage right hand side links (bottom of column) to add a link to
http://citrixweb.villanova.edu
for access to Maple anywhere on the internet.]
In class: within Internet explorer
log on to the Villanova home page (click
on the upper right "login" icon and use your standard VU email username and
password) and check out our My Classrooms classroom site, and visit the link to
my course homepage from it
[
http://www.homepage.villanova.edu/robert.jantzen/courses/mat2500/ ],
After class: check out the on-line links describing aspects of the course (no need yet to look at the
MAPLE stuff). Fill out your
paper
schedule form (get a copy in class to fill out or print it out
back-to-back earlier
to fill out in advance and bring to your first class already done)
to return in class Thursday.
[You can
drop by my office St Aug 370 (third floor, Mendel side, by
side stairwell) to talk with me about the course if you
wish and to see where you can find me in the future when you need to.]
Read computer classroom etiquette.
Handouts: algebra/calc background
sheet;
student schedule sheet sections
01 ,
04
(10:30, 11:30) [you can print these double-sided to fill out in advance]
Homework Problems:
12.1: 1, 2, 3, 5 (short list so you can check out our class website and read about the
course rules, advice, bob FAQ, etc, respond with your email). It is
important that you read the section in the book from which homework problems
have been selected before attempting them. Here is an example of a PDF
problem solution: Stewart 12.1.42 [Okay, I
cheated and looked at the answer manual to see how to get started.]
- Th: Return your schedule forms at the beginning of
class;
REMEMBER DIFFERENT ROOM ON THURSDAYS!
12.1: 11, 13, 15, 19a
[hint: show the distance from P1 to M is the same as from P2 to M
and equal to half the total distance.],
21a, 23, 31, 33, 35;
12.2: 1, 2, 5, 7, 11, 13, 15, 19,
25.
- F: 12.2: 29, 31, 33 (tension result
given in units of force; vertical component balances downward gravitational
force F = mg, g = 9.8 N/kg, where m = 0.8kg), 37.
WEEK 2:
- M:
12.3: 1, 3, 5, 9, 11, 15, 21 (it is enough to
find just one angle), 23, 29;
optional fun problems if you like math: 51
(geometry), 53 (chemical geometry).
- W: handout on course rules, syllabus; handout on resolving a vector;
12.3: 35, 42 [ans: b_perp = orth_a b = <-3.6,1.8>], 45;
- Th:
12.4: 1, 5, 8, 9, 11 (move u right so initial points coincide),
15, 17,
23 (find 2 edge vectors from mutual corner first), 27, 29, 31, 33 (zero triple scalar
product => zero volume => coplanar), 35 (first redo diagram with same initial points
for F and r).
- F: Quiz 1 thru 12.3; it is not very useful to try to draw parametrized curves based on what
the graphs of x and y look like: technology is meant for
visualizing math!;
10.1: 1,
9,
13, 17, 19, 21, 28
[it does not hurt to use technology if you cannot guess them all]
[textbook
example curves][curve tutorial]
> plot([t^3-2*t,t^2-t,t=-2..2]);
WEEK 3:
- W: handout on lines and planes;
never use the symmetric equations of a line: they are useless for all
practical purposes!;
quiz 1 answer key published (see also
the maple worksheet);
12.5: 1 (draw a quick sketch to understand each statement), 3,
5, 9 (parametric only), 13,
16 [ans: a: x=5+2t, y=1-t, z=t, b: (5,1,0), (0,7/2,-5/2),(7,0,1)], 17,
19; 23, 25, 31,
39, 45, 49.
> with(Student[LinearAlgebra]):
> <2,1,1>.(<1,-1,2> ×
<0,-2,3>) [times sign from operators palette]
> <2,1,1>.<2,1,1>
- Th: St Thomas Day class times: 9:00 -> 8:30-9:20; 11:30->10:30-11:20;
Maple lab, read the Maple FAQ on our homepage before coming to class;
HOMEWORK: play a little bit with the standard maple, do the "10 minute tour"
and then "symbolic and numerical calculations" from the HELP menu, look at
the mathematical dictionary link there if you wish. Download the quiz answer
key, execute it and look at how the work was documented and setup; freshmen
expecially can learn more about maple commands by using classic maple and
doing the first 6 sections of the New User's Tour available from the Help
Menu. Or you can download and execute the command list files for calc1 and
calc2 that are linked inside the calc3 command list file linked to our
homepage.
- F: Quiz 2 on cross-products;
> with(Student[VectorCalculus]):
> <1,2,-3> &x <1,1,1>;
5 ex -4 ey -ez
[new notation for unit vectors i, j, k; >
BasisFormat(false): returns to column
notation]
handout on geometry of lines and planes (distances between).
12.5: 53 (also find angle between planes: 78º), 57,
65 (find pt on plane, project the 2 point difference vector along the
normal), 67 (find pt on each plane, project their difference vector along
the normal---do not just plug into a formula: this is practice in vector
projection geometry];
optional problem if extra time and bored: 72 [ans: D = 2].
WEEK 4:
- classlist handout; Test 1 on chapter 12? sep 21(W), problem
session sep 20 (T:5:30pm MLRC);
13.1: 1, 3, 5, 7,
11, 13, 19-24
(quickly), 25,
31*[.mws, .mw] [refer back to similar problem 25: what is z^2-(x^2+y^2)? plot the spacecurve
and the surface together as in the template],
35
[eliminate z first by setting: z^2 (cone) = z^2 (plane) and solve for
y in terms of x, then use x to express y and then in
turn z, let x be t], read 41;
12.5.53*: using the answer in the back of the book and the example in the
command list cmdlist3.mw file at our website in the section "visualizing
lines and planes", plot the two planes and the line of intersection and
confirm that visually it looks right. Adjust your plot to be pleasing.
- W:
13.2: 1, 2, 3, 7 [recall: exp(-2t) = (exp(t))^(-2)], 9, 13,
15, 19, 21,
29, 27a
(by hand), 27b*[.mws,
.mw].
- Th:
13.2: 22, 31 [angle between tangent vectors], 35 [use technology to do the integrals:
(.mws,
.mw)],
39, 45, 47;
oops: most of you have cell phones, why didn't somebody call bob? read
email.
- F: W HW discussion first, then Quiz 3 thru 13.2 W HW;
13.3: 3 (note the input of the sqrt in the integrand is a perfect square in
this problem); do 7 instead by numerical integration either with your
graphing calculator or Maple (you only need single integral of a scalar, but
this is an occasion to see how to do vectors.mws,
.mw).
WEEK 5:
- M:
(for Thursday) 13.3: 11, 13, 21,
23 [do not use formula 11: instead use parametrized curve form r
= [t,t^3,0] ], 39 [perfect square!], 41;
MLRC problem session T 5:30pm; quiz 3 answer key out with Test 1/02S on back
for exam prep; handout on dot and cross products and length, area,
volume;
> (Student[VectorCalculus][SpaceCurveTutor])();
from the Tools Menu, Tutors, Vector Calculus,
Space Curves
- W: Test 1 through 13.2.
- Th: handouts on geometry of spacecurves
and space curve curvature and acceleration;
13.4: 1, 2 [avg velocity = vector displacement / time interval], 5,
11 [recall v = exp(t)+exp(-t) since
v^2 is a perfect square], 17, 17b*[pick an appropriate time interval
starting at 0], 31 [note that v^2 = 3^2(1+t^2)^2 is a perfect square], 35
[also perfect square, see 11];
- F: handout on projections revisited
just for those who like vector geometry;
13.4: 19;
13.R (p.882):
14a [use parametrized curve r
= [t,t^4-t^2,0], evaluate T '(0) before simplifying derivative to find
N(0)
easily, find osc circle: x^2 + (y+1/2)^2 = 1/4], 14b*[.mw,
.mws; edit the template with your hand
results including comments and also do the zoom plot];
This is the most interesting one:
Problems Plus (p.884): 2. [Note b) has answer 52 ft/sec = 37 mph].
WEEK 6: Maple13.mw or .mws due this week (earlier means better chance
of immediate feedback)
- M: 14.1: 1, 3, 7, 9, 11,
13, 19, 25,
29, 31, 35, 43,
51* [.mw,
.mws, just do a single appropriate
plot3d and contourplot after loading plots and defining the maple
function f(x,y)],
71a (read only b,c, if you are interested to see how the data is fit
see example 3 [.mw,
.mws]);
after finishing the preceding, for fun look at
53-58 and try to first match
contour plots with the 3d plots (not all are so easy!) and then think about
which formulas might go with which pairs [.mw].
Test 2 back with answer key and banked highway problem solution.
- W: 14.2: 1, 2, 5,
7, 11, 15, 17,
21*[toolbar
plot option: contour, or "style=patchcontour" or right-click
style patch+contour, explain in comment], 23,
27, 35.
- Th: 14.3:
1, 3, 5, 13, 15, 17, 25, 29, 35,
45
[in class if time: 18, 20, 37, 38].
- F: Quiz 4 thru 14.2;
14.3: 41, 43, 47, 49, 53, 57, 59;
65 [just average the adjacent secant line
slopes on either side of the point where the partial derivative is to be
evaluated, as in the opening example: pdf], 77, 78.
WEEK 7:
- M: 14.4
(tangent planes, linear approximation): 1, 3, 7,
11, 15, 21.
7*[calculate by hand, then do two plots: first > plot3d({[f(x,y),L(x,y)],x=a...b,y=c..d);
(choose appropriate ranges to show a good part of the surface behavior with
the plane), then zoom in as instructed by the textbook, check that they agree)],
[optional 9*].
- W:
differentiability illustrated;
14.4 (differentials): 17, 19;
23, 25, 27 [simpler to first use: ln(A^(1/2))=(1/2)ln
A (yes!), compare with 14.3.64 where ln diff is essential], 29, 33, 37 [remember 14.3.77];
- Th: W: 14.5: 1, 7, 11, 15,
17, 21, 31, 35,
39a, 47,
optional: 51 [use answer only to check work
after an honest try: maple,
pdf; note this "coordinate transformation"
of this second order derivative expression is extremely important for
gravitational, electromagnetic, quantum mechanical and heat transfer
problems, among many others].
- F: Quiz 5 thru 14.4;
14.5: 43.
Fall break :-) Enjoy.
![](../../images/bmrisottotravelingcat_small.jpg)
WEEK 8:
- M: if you did not take your Quiz 5, today is the day;
midterm grades due in Wed 12 noon: for Maple upgrades, quiz5 grades;
14.6: 1, 3, 5, 7, 9,
11, 15, 19,
23, 29;
- W:
handout on multivariable derivative and
differential notation;
14.6: 27b, 31, 38, 45 (derive
equations of plane and line by hand), 47, 53;
45*
[plot your results in an appropriate window, ie, adjust windows of function,
plane, line to be compatible, after doing problem by hand];
head start in class with any partner? f(x,y,z) = xy+yz+zx = 3 at (1,1,1) ->
tan plane, normal line
- Th: 14.7: 1, 3, 5,
7, 13, 15, 17, 19 (do by hand,
including second derivative test and evaluation of f at critical points);
19* [template
shows how to narrow down your search to find extrema by trial and error, record your
tweaked image or images confirming your hand results, include commentary].
- F: Quiz 6 thru 14.6;
>
plot3d(x^2+2*x*y+3*y^2,x=-1..2,y=x-1..1,axes=boxed);
>
plot3d(x*y*(12-x*y)/2/(x+y),x=0..10,y=0..12/x,axes=boxed);
14.7: boundaries, word problems: 27, 37
(minimize square of distance);
41, 45, 47, 52
[use constraint to eliminate r, max resulting function of 2 variables],
read
53 [this explains least squares fitting of lines to data].
WEEK 8: [maple14 due this
week] [Test 2: next week F, MLRC 5:30 session W]
- M: handout on 2D max-min;
15.1:
1, 3 [do by hand first], 3a [.mw,
.mws] [do this before next class: repeat this problem using
MAPLE for (m,n)=(2,2), then (20,20), then (200,200)],
5, 6 [midpoint sampling:
(m,n)=(2,3), x along 20 ft side, y along 30 ft side: answer = 3600],
7, 9;
15* [.mw,
.mws; stop at 2^8=256 since after this,
Maple takes too long to wait patiently] .
- W: 15.2: 1, 3, 7, 11
[factor the exponential first:
exp(2x) exp(-y)], 19, 21, 27, 31* [.mw,
.mws].
- Th: 15.3: 1, 5, 9, 15,
17, 21, 23;
33* [.mw,
.mws], 41, 43, 47, 51.
- F: Quiz 7 thru 15.2;
15.7 [.mw,
.mws]: 1, 3, 5, 9, 11
[like example 2, but first write eqn of plane (result: x/a +y/b +z/c=1,
where a,b,c are intercepts), then solve for z], 19, 25, 29
(this is the handout exercise tomorrow, try reiterating 26 if you need more
of this practice), 31,
33; use standard maple expression palette icon
for definite integral to check at least one problem of your choice, include
in maple15 hw.*
[we'll return to this section after a detour].
step by step checking of multiple integration:
> x + y
> ∫ % dx
> eval(%,x=b) - eval(%,x=a)
> ∫ %
dy
> eval(%,y=d) - eval(%,y=c)
> etc... if triple integral
WEEK 9: maple14 past due...
- M: handout
exercise on cartesian multiple integrals;
review polar
coordinate trig; handout on
polar coordinates and polar coordinate integration
(read page 2 for W);
10.3 pp.669-674 (stop midpage: tangents unnecessary in polar coords), last
subsection midpage 676-677:
1, 3, 5, 7, 9, 11, 15,
17, 21,
25, 29, 31, 35,
69*
[.mw, .mws; starting at 0 how far does theta have to go for the sine to undergo one full cycle? this
is the plotting interval];
keep in mind that our most important curves for later use are circles centered
at the origin or passing through the origin with a center on one of the
coordinate axes, and vertical and horizontal lines, and lines passing through
the origin.
![](../../images/xxxhalloweenbunny1_small.jpg)
- W: 15.4 (areas but no lengths): 1,
3, 5,
7, 9, 21, 23 [double volume under hemisphere z=sqrt(a^2-x^2-y^2) above circle
x^2+y^2<=a^2], 25.
Test 2 Problem Session today 5:30pm MLRC.
- Th: 15.4: 29, 31, 33 [what is
the average depth? (integral of depth divided by area of region)], 34 [ans:
a): 2*Pi*(1-(1+R)*exp(-R))], 35;
Optional: Read 36 [this enables one to sum the probability under a
normal curve in statistics]
- F: Test 2: 13.3 through 15.2.
WEEK 10:
- M:
12.7: 1, 2, 3, 5, 9, 15, 19, 21, 23, 27, 31,
33, 37, 39;
2 handouts on cylindrical and spherical
coordinates and using them to describe regions
of space or surfaces.
- W: 12.7: 55, 61;
15.8: 1, 3, 5, 6,
7, 11, 17,
23.
- Th: handout on
triple integrals in cyl/sph coords;
15.8:
24
[ans: 8 sqrt(2) Pi/3], 31 [set up integral by hand], 31* (do this for class
to check your answer), 33, 35; optional
37*.
- F: Quiz 8 thru W:15.8HW;
15.5 (center of mass, centroids p.1014): 5, 7, 11 [see example
3]; 15.7: 15 [see example 3]; 15.8: 25.
WEEK 11:
- M: handout on distributions/density/center of stuff;
handout on polar coordinate curves for
2d/3d integration;
15.5 (probability, recall 8.5 of calc2 probability):
23, 25,
26a [P(x<=1000,y<=1000) = .3996], 26b
[P(x+y<=1000) = .2642].
- W: in class problems:
15.R(eview): 7, 9, 13, 25 (use
cylindrical coords with polar coords in yz plane), 27,
31; 37a , 37b [see page 1028: Int (x^2+y^2) dV]; 41, 42 [ans:
64 Pi/9];
47.
- Th: handout on calc3: where we've been, where we will end;
16.1: 1, 5, 9;
11-14: <y,x>, <2x-3y,2x+3y>, <sin x,
sin y>, <ln(1+x^2+y^2),.x> ;
15-18, <1,2,3>, <1,2,z>, <x,y,3>, <x,y,z>
;
19* [.mw,
.mws]; just try it, no need to submit;
21, 25;
Quiz 8 back [rule change: lowest 2 quiz grades dropped].
- F: 16.2 (f ds integrals: pp.1062-1065 midpage): 1,
3, 9, 11; 31;
34 [ans: <4.60,0.14,-0.44>]
WEEK 12: Maple15 due next week [get it done early for fast feedback]
- M: Quiz 9 thru probability/centroid integrals?? NOT!;
handout on line integrals;
(F • dr = F
• (dr/dt) dt integrals):
7 [ ∫C <xy,x-y>•<dx,dy>],
17, 19, 21, 23, 25a.
T-day Break
![](../../images/ucbfryers0_small.jpg)
WEEK 13: Take home Test 3 thru chapter 15 out Monday November 28 7pm
in manila envelope on my office door, Back Monday Dec 5
- M: MLRC 5:30pm; Test 3 out 7pm;
16.2: 40, 41, 45; optional 44.
- W: 16.3: 1, 3, 5, 11 (b: find potential
function and take difference),
19, 23, 33;
optional 15 (same procedure as example 4).
- Th: in class work on Test 3.
- F: handout on potential functions;
16.4: 1, 2.
> with(plots):
> fieldplot([y^2,x^2],x=0..1,y=0..1,
scaling=constrained, grid=[8,8],thickness=2);
WEEK 14:
- M: Test 3 due today in my office (any time before next morning);
16.4: 17, 19;
read handout on Green, Gauss and Stokes for next class.
step by step checking of multiple integration:
> x + y
> ∫ % dx
> eval(%,x=b) - eval(%,x=a)
> ∫ %
dy
> eval(%,y=d) - eval(%,y=c)
> etc... if triple integral
- W: 16.5: 1, 5, 9, 11, 12,
15, 17,
31 [but read 35,36 and look at identities 23-29].
- Th: handout on Green Stokes Gauss div and curl;
16.6: read the section, play with the mix and match 11-16;
31;
to visualize a parametrized surface or piece of one:
> plot3d(<x(u,v),y(u,v),z(u,v)>,u=a..b,v=c..d,axes=boxed)
- F: Test 3 answer key out: hand work and maple worksheet;
go over this weekend;
optional handout on surface integrals, Gauss and Stokes in 3D;
upgrade any maple worksheets you wish full credit on by end of exam period.
Final Class Day: there is no Maple 16 assignment
- M: CATS evaluation forms; discussion of final exam;
paper copy of previous final exam (too ambitious, ours will be shorter!);
problems selected from/requiring knowledge of:
line integrals, div and curl, double and triple integrals, polar and
cylindrical coords,
tangent plane (linear approx, gradient), scalar and vector normal and
tangential
components of a vector in relation to a tangent plane.
Final exam MLRC problem session: Monday 5:30pm
W: final exam
(you may switch between sections if convenient as long as there are enough
seats: seek permission from bob)
Weeks 3, 4 and 5 (NOT TOO LATE!): come by and find me in my office, tell me how things are
going. This is a required visit. Only takes 5 minutes or less.
Current MAPLE file :
maple.mws due: week .
maple.mws due: week .
maple.mws due: week .
maple.mws due: .
maple.mws due: by end of final exam period
*MAPLE homework log and instructions [asterisk
"*" marked homework problems]
Test 1: Sept 21; MLRC problem session Sep 20
.
Test 2:
Nov 4 ; MLRC problem session Nov
2.
Test 3: Take home out
Monday Nov 28, in Monday Dec 5; MLRC problem session
Monday Nov 28.
FINAL EXAM:
10:30MWF/9:00R
Mendel G90 class: 2500-01 Wednesday Dec 14 1:30-4:00
11:30MWF/11:30R
Mendel G87 class: 2500-04
Wednesday Dec
14 4:15-6:45
MAPLE CHECKING ALLOWED FOR QUIZZES/EXAMS
12-dec-2005 [course
homepage]