MAT2500 09S [jantzen] 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]. Alternatively there are also tutorials and on-line quizzes and web extras at the textbook website, where homework hints can also be found on the TEC link (you may have to do a JAVA install first).

M (January 12, 2009): GETTING STARTED STUFF. By Wednesday, January 14, 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]", 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, anything you want to let me know about yourself. Tell me what your previous math course was named (Mat1500 = Calc 1, Mat1505 = Calc 2, Mat2705 = DEwLA).
HINT: Just reply to the welcome email I sent you before classes started.
[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 our computer classroom, on your laptop or the computer at your desk:
1) Log on to your computer and open Internet Explorer. (IE allows you to open MAPLE files linked to web pages automatically if MAPLE is already open or if it is available through the Start Menu Program listing under Math Applications, in Netscape you must save the file locally and then open in it MAPLE using the File Open task.)
2) Log on to the Villanova home page in Internet Explorer (click on the upper right "login" icon and use your standard VU email username and password) and check out our My Courses classroom site, and visit the link to my course homepage from it
[ http://www.homepage.villanova.edu/robert.jantzen/courses/mat2705/ ],
3) Open Maple 12 Standard (red not yellow icon) from the Windows Start Menu Program listing under Math Applications
[or click on this maple file link: cmdlist3.mw]
4) bob will quickly show you the computer environment supporting our class.
5) afterclass: log on to MyWebCT and look at the Grade book: you will find all your Quiz, Test and Maple grades here during the semester.
[This is the only part of WebCT we will use this semester.]

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. Then read the first paper handout: algebra/calc background sheet.

Handouts:
student schedule sheet sections 03, 04 [you can print these double-sided to fill out in advance]
[use the 3 letter dorm abbreviations]

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; freshmen who do not yet have the book: handouts/stewart6e_12-1.pdf). 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 12.1.40 [Okay, I cheated and looked at the answer manual to see how to get started. Then I made a nice Maple worksheet of the problem.]
W: Return your schedule forms at the beginning of class;
REMEMBER DIFFERENT TIME (one hour later) 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; this is the hard way with points and not vectors], 21a, 23, 31, 35;
12.2: 1, 2, 3, 5, 7, 11, 13, 15, 19, 23.
Th: 12.2: [example 7];
30 (draw a picture, express the components of each vector, add them exactly (symbolically), evaluate to decimal numbers, think significant digits),
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),
39.
F: 12.3: [example 3];
1, 3, 5, 9, 11, 15, 21 (it is enough practice to find just one angle), 23, 29;
optional fun problems if you like math: 51 (geometry [pdf,.mw]), 53 (chemical geometry [.mw]).

WEEK 2[-1]: (Monday off: MLK Day, Tuesday Inauguration!)
W: handout on course rules, syllabus;
handout on resolving a vector [using Maple (for dot and cross products and projection)];
12.3: 35, 41, 42 [ans: b_perp = orth_a b = <-3.6,1.8>], 45.
Th: 12.4: [crossprodetails.pdf];
1, 5, 8, 11, 15, 15 (move u right so initial points coincide),
19, 21, 27 (find 2 edge vectors from a mutual corner first),
31 (Maple example: trianglearea.mw),
33, 35, 37 (zero triple scalar product => zero volume => coplanar),
39 (first redo diagram with same initial points for F and r).

> <2,1,1> · (<1,-1,2> × <0,-2,3>)
[boldface "times" sign and boldface centered "dot" from Common Symbols palette]
> <2,1,1> · <2,1,1> then take sqrt (Expressions palette) to get length [example worksheet: babyvectorops.mw]
F: Quiz 1 thru 12.3;
[textbook example curves: s10-1.mw (wow!)][parametrized curve tutorial];
open these worksheets and execute them by hitting the !!! icon on the toolbar;
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 [eqns; it does not hurt to use technology if you cannot guess them all];
33, 37.

> plot([t³-2 t, t²-t, t = -2..2])
plots the first two expressions for x and y as a parametrized curve in the xy plane but
> plot([t³-2 t, t²-t], t = -2..2, color = [red, blue])
plots the first two expressions versus t as two graphs, the color option helps distinguish them (notice the difference in location of the closing square bracket in each case).

WEEK 3[-1]:
Weeks 3, 4 and 5 (better early than late but NEVER 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.
M: Happy Chinese new Year!
handout on lines and planes [.mw];
never use the symmetric equations of a line: they are useless for all practical purposes!;
12.5: 1 (draw a quick sketch to understand each statement),
3, 5, 9 (parametric only),
13, 16 [ans: a) x = 2+ t, y = 4 - t, z = 6 + 3 t ; b) (0,6,0), (6,0,18)],
17, 19; 23, 25, 31, 39, 43, 49, 53.
W: SNOW DAY. Enjoy the day off, BUT...

"HOME" WORK: play a little bit with Standard Maple on your laptop, go to the Help Menu, click on "Take a tour of Maple" and do the "10 minute tour" and then "symbolic and numerical calculations" , look at the mathematical dictionary link there if you wish. Look at the various menus.The Maple tips page is very helpful. From the quiz archive page, download the 09s quiz 1 answer key worksheet, execute it and look at how the work was documented and set up. Do the same for 08s archived quiz 2, after reading the paper solution. There will be a quiz on Friday.
Th: on-line handout on geometry of lines and planes (distances between);
12.5: 55,
69 (find pt on plane, project the 2 point difference vector along the normal),
71 (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, we really don't care about the distance!);
optional problem if extra time and bored with routine problems: 76 [ans: D = 2].
F: Quiz 2;
Maple assignments start: note asterisks;
13.1: 1, 3, 5, 7, 11, 13, 19-24 (quickly, note technology is not necessary here to distinguish the different formulas: .mw, .pdf),
25, 33* [refer back to similar problem 25: note that z² = (x²+y²)! plot the spacecurve and the surface together as in the template, adjust the ranges for the surface so it is just contains the curve and it not a lot bigger],
37 [eliminate z first by setting: z² (for cone) = z² (for plane) and solve for y in terms of x, then use x to express y and then in turn z, finally let x be t],
read 41;
12.5.55*: 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: subsection unparametrized planes" (you need > with(plots): for the spacecurve and display commands), plot the two planes and the line of intersection and confirm that visually it looks right. Adjust your plot to be pleasing, i.e., so the line segment is roughly a bit bigger than the intersecting planes. [I will make a template for this.]

WEEK 4[-1]:
M: Test 1 date next week? which day?;
let's try to find one or two partners for Maple assignments;
13.2: 1, 2, 5, 7 [recall: exp(3t) = (exp(t))³], 9, 13, 15, 19, 21, 29, 27a (by hand), 27b* [graph your results using this template; make a comment about how it looks].

> with(Student[VectorCalculus]):
> <1,2,-3> × <1,1,1>
5 e_x - 4 e_y - e_z
[this is just new notation for the unit vectors i, j, k; > BasisFormat(false): returns to column notation]
> F := t → <t, t² , t³> : F(t)
> F '(t)
> ∫ F(t) dt
> with(plots):
> spacecurve(F (t), t=0..1, axes=boxed)
W: 13.2: 22, 31 [angle between tangent vectors],
35 [use technology to do the integrals, then repeat using u-substitution on each simple integral and compare results],
39, 45, 47 [use cross product differentiation rule 5 on page 826].
Th: 13.3: 3 [note the input of the sqrt in the integrand is a perfect square in this problem];
7 [use numerical integration either with your graphing calculator or Maple: right-click on output of integral, choose "Approximate"; oops! what a mess!];
11 [hint: to parametrize the curve, let x = t and express y and z in terms of t],
13, 17, 25,
27 [do not use formula 11: instead use the parametrized curve form r = <t,2 t - t²,0> ];
[on-line reminder of dot and cross products and length, area, volume];
handouts on geometry of spacecurves (page 1 for 13,3) and space curve curvature and acceleration (pages 2-4 for 13.4)
F: Quiz 3;
13.3: 43 [perfect square!], 45;
> with(Student[VectorCalculus]):
SpaceCurveTutor(<t,t²,0>,t=-1..1) from the Tools Menu, Tutors, Vector Calculus, Space Curves [choose animate osculating circles]
parabola osculating circle zoom.

WEEK 5[-1]: Test 1 Thursday MLRC 5:30 voluntary problem session Wednesday
13.4 (no Kepler's laws): 1, 2 [avg velocity = vector displacement / time interval],
5, 11 [recall v = exp(t) + exp(-t) since v² is a perfect square],
17, 17b*[graph your spacecurve using the template; pick the time interval t = 0..4π, rotate the curve around and compare with the back of the book sketch; then animate the curve with the template provided.],
33 [note that v² = 3²(1 + t²)² is a perfect square],
37 [also perfect square, see 11] .
W: on-line handout only: projections revisited just for those who like vector geometry;
13.4: 19 (minimize function when its derivative is zero!);
13.R (p.850):
14a [use parametrized curve r = [t, t⁴- t²,0], evaluate T '(0) before simplifying derivative (i.e., set t = 0 before simplifying the expressions after differentiating) to find N(0) easily, find osc circle: x² + (y+1/2)² = 1/4],
14b*: edit the template with your hand results including comments and also do the zoom plot to see the close match of the circle to the curve];
This is the most interesting HW problem: Problems Plus (p.852): 2. [Note b) has answer 52 ft/sec = 36 mph] [solution].

5:30pm optional MLRC problem session today
Th: Test 1. Darwin Day
F: 14.1: 1, 3, 7, 9, 11, 13, 19, 25, 29, 31, 35, 43;
|maple14.mw problems begin:
53*, just do a single appropriate plot3d and contourplot after loading plots and defining the maple function f (x,y)],
75a (read only b,c; if you are interested to see how the data is fit see example 3);
after finishing the preceding, for fun look at 55-60 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 [see plots].

Happy Valentine's Day:

WEEK 6[-1]: maple13.mw is due this week M-F Feb 18-22 [earlier submission means better chance of immediate feedback]; maple14.mw begins
M: 14.2: 1, 2, 5, 7, 13, 15, 17, 23* [toolbar plot option: contour, or "style=patchcontour" or right-click style patch+contour, explain in comment],
25, 29, 37 [does a 3d plot of the expression support your conclusion? that is, your conclusion drawn before looking at the back of the book obviously].
W: 14.3: 1, 3, 5, 15, 17, 21, 29, 31, 39, 49 [in class if time: 22, 24, 28].
Th: 14.3: (higher derivatives, implicit differentiation!) 45, 47; 51, 53, 57, 61, 63;
69 [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],
81, 82.
F: Quiz 4 thru W HW;
14.4: (tangent planes, linear approximation: plain, fancy; differentiability illustrated): 1, 3, 7, 11, 15, 23.
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 by choosing a smaller window about the point of tangency as instructed by the textbook, check that they agree, make a comment)],

WEEK 7[-1]:
M: 14.4 (differentials): 19, 21; 25, 27, 29, 31, 35, 39 [remember partials from 14.3.81].
W: 14.5: 1, 7, 11, 15, 17, 21, 31, 35, 39a, 49;
optional: 53 [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].
Th: Quiz 5 thru 14.4 (partial diff, linear approx, implicit diff);
14.5: 45 [pdf]; optional 53 (2nd derivatives, for wave equation, heat equation on a disk).
F: Maple lab, bring your laptop, maple13.mw too if you wish to correct it.

Spring Break. enjoy and be safe.

WEEK 8[-1]:
M: 14.6 (thru p.915): 1, 3, 5, 7, 9, 11, 15, 19, 23, 29.
W: handout on derivatives of 2d and 2d functions;
14.6: 27b, 31, 36, 38, 45 (derive equations of plane and line by hand), 47, 53;
45* [plot your results in an appropriate window, i.e., 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) = x y + y z + z x = 3 at (1,1,1) -> tan plane, normal line.
Th: 14.7: 1, 3, 5, 7, 13, 15, 19, 21 (do by hand, including second derivative test and evaluation of f at critical points); 21* [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, see additional comments on Maple HW page summary];
optional: if you are interested in the more realistic case of example 4 where numerical root finding is required, read this worksheet.
F: Quiz 6;
on-line handout on 2D 2nd derivative test and multivariable derivative and differential notation; some on-line only notes if you are interested;
boundaries, word problems: 31, 39 [minimize square of distance], 43, 47, 54 [use constraint to eliminate r, max resulting function of 2 variables, consider triangular boundary];
read 55 [this explains least squares fitting of lines to data].

Tomorrow 3/14 is π-day! [and Einstein's birthday]

WEEK 9[-1]: Test 2 date Thursday Mar 26 through chap 14
M: 14.R (review problems; note some of the highest numbered problems refer to 14.8, which we did not do): some in class if time: 1, 7, 17, 18 , 21, 25, 29, 33, 34a, 39, 53,
14.7: 50 [ans: the height is 2.5 times the square base; obviously cost of materials is not the design factor in this case, no?].
W: Breather Day. Check out carefully quiz 6 answer key and the archived test 2.
Parametrizing lines and planes, preview of parametrizing regions of the plane and space.
Th: Maple Tools Menu, Select Calculus Multi-Variable, Approximate Integration Tutor (midpoint evaluation usually best)
15.1: 1, 3 [do by hand first], 3 [after doing this by hand, before next class: repeat this problem using the MAPLE Approximate Integration Tutor (with midpoint evaluation for (m,n) = (2,2), then (20,20), then (200,200), comparing it with the exact value given by the Tutor],
5, 6 [midpoint sampling: (m,n)=(2,3), x along 20 ft side, y along 30 ft side: answer = 3600], 7, 9;
15* [note: (m,n) = (1,1), (2,2), (4,4), (8,8), (16,16), (32,32) = (2^p,2^p) for p = 0..5 is what the problem is asking for; what can you conclude about the probable approximate value of the exact integral to 4 decimal places?] .
F: Maple14.mw due next week [happy persian new year, vernal equinox];
15.2: 1, 3, 7, 11, 21, 23, 31, 33*;

step by step checking of multiple integration (work sheet):
> x + y
> ∫ % dx
> eval(%,x=b) - eval(%,x=a)
> ∫ % dy
> eval(%,y=d) - eval(%,y=c)
> etc... if triple integral

WEEK 10[-1]:
M: 15.3: handout on double integrals;
1, 5, 9, 15, 17, 21, 23; 35*, 43, 45, 49, 53.
W: MLRC voluntary problem session 5:30pm;
jump to 15.6: 1, 3, 5, 11, 15 [do x or y integration first, note that the tilted plane faces are described by the equations of lines in the xz or yz planes], 21, 27.
Th: Test 2 on chapter 14.
F: 15.6: exercise in setting up triple integrals in Cartesian coordinates;
29, 31 [two projections onto coordinate planes are faces of the solid, the third has a border obtained by eliminating y from the two equations given in the figure to describe the condition on x and z for that edge];
if you cannot get both 29 and 31, try 33 where the diagram is made for you.
31* use the standard maple expression palette icon for the definite triple integral of the constant function 1 to check the agreement of two different iterations with two different variables for the innermost integration step;
try to finish up maple 14 by this weekend.

WEEK 11[-1]:
M: review polar coordinate trig (no paper handout);
handout on polar coordinates and polar coordinate integration (the integration is next time);
10.3 pp.639-644 (stop midpage: tangents unnecessary in polar coords),
last subsection midpage 646-647:
10.3: 1, 3, 5, 7, 9, 11, 15, 17, 21, 25, 29, 31, 35,
71* [Nephroid of Freeth: starting at θ = 0 how far does theta have to go for the sine to undergo one full cycle? i.e., θ/2 = 2 π ; 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, as in the handout examples.
April Fools' Day!
Test 3 back (no april fools :-(), study answer key;
W:15.4: (areas but no lengths): use 1, 4, 5, 7, 21,
23 [twice the volume under the hemisphere z = sqrt(a²- x²- y²) above the circle x²+ y² ≤ a²],
25 [integrand is difference of z values from cone (below) to sphere (above) expressed as graphs of functions in polar coordinates].
Th: exercise in setting up triple integrals in Cartesian coordinates: solution;
Recall 15.6.ex3 and re-express the outer double integral, inner limits of integration and integrand in polar coordinates in the x-z plane (pretend z is y): ∫ ∫ _r<=2 [∫_{y= 0..x^{^2}+z^{^2}} x²+z² dy] dA;
15.4: 15 [at what acute angular negative or positive values of theta does cos(3θ) =0? these are the starting and stopping values of θ for one loop],
29, 31, 33 [what is the average depth? (integral of depth divided by area of region)], 34 [ans: a): 2π(1-(1+R) e^-R)], 35 (make a diagram, assembing the 3 integration regions into one simple region);
Optional: Read 36 [this enables one to sum the probability under a normal curve in statistics]
F: Quiz 7 iterated integrals in Cartesian coordinates [like previous quiz 8 (note upper and lower limits y and y³ in answer key problem 1 were misordered by human error!)];
handout on distributions/density/center of stuff;
15.5 (centroids p.1014): 5, 7, 11 [see example 3];
[5,7,11 integrals, visualize etc: .mw]
(probability):
27, 29, 30a [P(x<=1000,y<=1000) = .3996], 30b [P(x+y<=1000) = .2642]. [Maple is the right tool for evaluating probability integrals!].

WEEK 12:
M: 3(!) handouts on cylindrical and spherical coordinates and using them to describe regions of space and bounding surfaces;
15.7 (cylindrical): 1, 3, 5, 7, 9, 13, 15, 17, 21, 27.
W: another handout on cylindrical and spherical coordinates (lines and circles of revolution);
15.8 (spherical): 1, 3, 5, 7 (hint: multiply equation by rho first), 9, 11, 13 , 15, 17, 21, 25, 39.

Easter Break.
W: 15.7: 25;
15.8: 19, 20, 29a, 35;
15.R: 27, 37, 39, 40.
Th: MLRC 5:30pm problem session;
16.1: 1, 5, 9; 21, 25;
comparison shopping:
11-14: <y, x>, <1, sin y>, <x - 2, x + 1>, <y, 1/x> ;
15-18, <1, 2, 3>, <1, 2, z>, <x, y, 3>, <x, y, z> ;
29-32: xy, x²-y², x²+y², (x²+y²)^1/2;
19*; just try the template, no need to submit [check here for result, with bonus problem 25 done as well].
F: TEST 3 out. [no collaboration, see bob if stuck, print out Maple work if you do any Maple checking, read test rules].

WEEK 13:
M: [on-line only: progress report: where we've been and where we're going (to end)];
handout on line integrals;
new printout of test 3 with slight correction;
16.2 (f ds scalar line integrals: pp.1034-1039 midpage): 1, 3, 9, 11 [write vector eq of line, t = 0..1]; 33;
36 [ans: <4.60,0.14,-0.44>, worksheet compares with centroid]
W: Maple15 due within next week;
16.2 (F • dr = F • (dr/dt) dt = F • T ds vector line integrals):
7 [ ∫_C <xy, x-y> • <dx, dy>], 17, 19, 21, 27, 29a;
43, 47;
optional: 42 [ans: K(1/2-1/sqrt(30)], 46.
Th: TEST 3 back to bob;
handout on potential functions;
16.3: 1, 3, 5, 11 (b: find potential function and take difference, or do straight line segment line integral), 15 (potential function); 23, 33.
F: 16.4: 1, 3, 17 [do the line integral too],
18 [convert double integral to polar coordinates; ans: 12 π];
optional: the line integral technique for integrating areas of regions of the plane is cute but we just don't have time for it.

WEEK 14:
M: handout on divergence and curl, Gauss and Stokes versions of Green's Theorem.
16.5: 1, 5, 9, 11, 12 [easier to interpret vectorially if convert to "del, del dot, del cross" form], 15, 17, 31 [but read 37, 38 and look at identities 23-29].
T=F: handout on interpretation of circulation and flux densities for curl and div;
Teaching evaluation CATS forms
W=M: handout surface integral demo [.mw] [not required for final exam];
brief remarks about Gauss's law and Stokes' Theorem [not required for final exam]
Th: Quiz 8 NOT! [Final exam discussion].
Test 3 answer key finally on-line;
Make sure Maple15 is submitted this week.

Monday 4:00pm MLRC voluntary problem session for final exam.
Office hours Monday 1-4, Tuesday 1-4, Wednesday 11-1.
FINAL EXAM: you can switch section exam times with permission (email me)

MWF 12:30 Wed, May 6 1:30 - 4:00

MWF 1:30 Tue, May 5 8:00 - 10:30

Final exam answer key posted. Grades posted in WebCT Blackboard Friday

Current MAPLE file :
maple13.mws due: Week 6
maple14.mws due: Week 10
maple15.mws due: Week 14

*MAPLE homework log and instructions [asterisk "*" marked homework problems]

Test 1: Week 5: ; MLRC 5:30 problem session .
Test 2: Week 10: ; MLRC 5:30 problem session .
Test 3: WEEK 13: Take home out ; in ; MLRC problem session

FINAL EXAM: you can switch section exam times with permission

MWF 12:30	Wed, May 6	1:30 - 4:00
MWF 1:30	Tue, May 5	8:00 - 10:30

Graphing Calculator / Maple Checking ALLOWED FOR ALL QUIZZES/EXAMS

7-may-2009 [course homepage]
[log from last time taught with Stewart Calculus 5e, but some problem numbers slightly different for older edition 5e!]