MAT2500 10S [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 the textbook website TEC site, which also has tutorials and on-line quizzes and web extras. You just need to do a short JAVA install on your laptop first to use it.

M (January 11, 2010): GETTING STARTED STUFF. By Wednesday, January 13, 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 in to MyNova on 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 class photo roster, 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, directly:
[ http://www.homepage.villanova.edu/robert.jantzen/courses/mat2705/ ],
3) Open Maple 13 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, just to have an example of a Maple worksheet to show you. Don't worry, we will take it slow with Maple.]
W: Return your schedule forms at the beginning of class;
check phone number, dorm info on signup sheet;
check out the textbook website homework hints (Calculus, Early Trancendentals, in the TEC area) and extras;
REMEMBER DIFFERENT TIME (one hour later, and different classroom: JB202A) 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: handout on course rules, syllabus;
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) [pdf,.mw],
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.)
W: 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 (move u right so initial points coincide),
19, 21, 27 (find 2 edge vectors from a mutual corner first, use 3 vectors and cross product),
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 [look at quiz archive to get idea what I expect];
[textbook example curves: s10-1.mw (wow!)][parametrized curve tutorial];
open these worksheets and execute them by hitting the !!! icon on the toolbar (then read them!);
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 [hyperbolic functions, Stewart 6e section 3.11: cosh² x- sinh² x = 1, recognition is enough],
19, 21, 28 [eqns; it does not hurt to use technology if you cannot guess them all];
33, 37.

> plot([cos(t), sin(t)], t =0..2) square bracket after last function, plots functions versus t on same axis
> plot([cos(t), sin(t), t =0..2]) square bracket after parameter range, plots parametrized curve in plane

WEEK 3[-1]:
M: 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: on-line handout on geometry of lines and planes (distances between);
in these problems do not just plug into a formula: this is practice in vector projection geometry, we really don't care about the distance!:
12.5: 55, 69 (find point on plane, project their difference vector along the normal),
71 (find pt on each plane, project their difference vector along the normal;
76 (find pt on each line (set parameters to zero!), project the 2 point difference vector along the normal to the parallel planes that contain them; ans: D = 2).
Th: Quiz 2 [see archived quiz];
Maple assignments start: note asterisks;
13.1: 1, 3, 5, 7, 11, 13, 19-24 (do 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, and then express z in terms of x and finally let x be t],
read 41;
12.5.55*: using the answer in the back of the book and this template, 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 (choosing the range of values for t).

EVERYONE is requested to stop by my office for a 5 minute visit before our first test in week 5. Test 1 date? Thursday we have no one in our classroom before or after my two consecutive classes, so less time contraints. Is this an acceptable date for Test 1?
F: let's try to find one or two partners for Maple assignments;
13.2: 1[pdf], 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)
and recall:

> plot([cos(t), sin(t)], t =0..2)           square bracket after last function, plots functions versus t on same axis
> plot([cos(t), sin(t), t =0..2])           square bracket after parameter range, plots parametrized curve in plane

WEEK 4[-1]:
M: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 from this section].
W: 13.3: 3 [note the input of the sqrt in the integrand is a perfect square in this problem];
7 (or 9) [use numerical integration either with your graphing calculator or if you use Maple, try 9 instead: 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)
Th: 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.
F: 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 = -n π..n π, where n is a small integer, and by trial and error, reproduce the figure in the back of the book, rotating the curve around and comparing with the back of the book sketch (note the horizontal axis tickmarks); if you wish, 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] .

WEEK 5[-1]: did you do your 5 minute office walk thru yet? it is meant to help you. never too late. [well...]
M: 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].

5:30 MLRC problem session for Test 1?? handout: past two tests 08s, 09s (although both say 08s) [solutions online].
W: SNOW DAY. Enjoy the day off, BUT.. catch up on Maple. Prepare for test.
Th: Test 1 postponed 1 week. SNOW DAY 2.
F: SNOW DAY 3! enough; today is an on-line course day; read 14.1 and do the following problems:
14.1: 1, 3, 7, 9, 11, 13, 19, 25, 29, 31, 35, 43;
|maple14.mw problems begin:
53*, using this template 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].
Maple 13 is due any time next week

Darwin Day! Happy Almost Valentine's Day:

WEEK 6[-1]: maple13.mw is due this week;
M: 14.2: 1, 2, 5, 13, 15, 17,
23* [toolbar plot option: contour, or "style=patchcontour" or right-click style "surface with 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, plot and explain].
W: 14.3: 1, 3, 5, 11, 15, 17, 21, 29, 31, 39, 49 [in class if time: 22, 24, 28].
Th: Test 1.
F: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, this is not a testing problem! tedious],
81, 82.
Takehome Quiz 4 on material thru W HW, due Monday (sorry if you misinterpreted this).

WEEK 7[-1]:
M: Turn in Quiz 4;
14.4: (linear approximation and tangent planes: differentiability illustrated): 1, 3, 7, 11, 15, 19, 21, 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 centered about the point of tangency to show a good part of the surface behavior together with the tangent 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 that it looks right confirming differentiability, see template in last section of plots worksheet)].
W: 14.4 (differentials): 25, 27, 29, 31, 35, 39 [remember partials from 14.3.81].
Th: Test 1 back; corrected answer key on line;
Quiz 5;
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].
F: SNOW DAY 4. A record. Climate change?

Spring Break. enjoy and be safe.

WEEK 8[-1]:
M: check WebCT/Blackboard grades;
14.5: 41 [units?], 43 [in degrees per second?], 45 [pdf];
optional 53 (2nd derivatives, for wave equation, heat equation on a disk, only for the truly interested, see last Th HW).
catch up on maple.
W: Midterm grades due by noon;
14.6 (stop at tangent planes): 1, 3, 5, 7, 9, 11, 15, 19, 23, 29.
Th: handout on derivatives of 2d and 2d functions;
14.6: 27b, 31, 36, 38, 41, 45 (derive equations of plane and line by hand), 47, 53, this one is fun: 57;
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.
F: Quiz 6; handout on 2D 2nd derivative test;
14.7: 1, 3, 5, 7, 13, 23 (do by hand, including second derivative test and evaluation of f at critical points); 23* [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.

Sunday is Pi Day: π! [and Einstein's birthday]

WEEK 9[-1]: in class test 2 through 14.7: week 10 thursday? maple14.mw due next week
M: on-line handout on multivariable derivative and differential notation;
14.7: 19 (a warning that extrema are not always isolated points),
boundaries: 31;
word problems: 39 [minimize square of distance],
43, 47 (similar to 43 only with different coefficients in the constraint),
51, 54 [use constraint to eliminate r, maximize resulting function of 2 variables on triangular region, consider triangular boundary];
read 55 [this explains least squares fitting of lines to data, and perhaps the most important application of this technique to practical problems].
W: ST Pats Day!
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, 31, 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?].
Th: Read 15.1; catch up on Maple14 HW, fix Maple13 if not 2/2.
F: Quiz 7 on max-min problems (no such quiz last time);
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 (see 3 line Maple template); what can you conclude about the probable approximate value of the exact integral to 4 decimal places?] .

[happy persian new year, vernal equinox]

WEEK 10[-1]: Test 2 on Chapter 14 Thursday, MLRC volunteer problem session Wednesday 5:30pm
M: Maple14.mw due this week
15.2: 1, 3, 7, 11, 21, 23, 31, 33*;

step by step checking of multiple integration (worksheet):
> x + y
> ∫ % dx
> eval(%,x=b) - eval(%,x=a)
> ∫ % dy
> eval(%,y=d) - eval(%,y=c)
> etc... if triple integral
W: MLRC volunteer problem session today at 5:30; remember summary of 2d/3d derivatives;
15.3: handout on double integrals; HW for Friday:
1, 5, 9, 15, 17, 21, 23; 35* [just use Maple to evaluate the integral once you set it up],
43, 45, 49, 53.
Th: Test 2.
F: jump to 15.6: 1, 3, 5, 11,
15 [make a diagram, 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.

WEEK 11[-1]: maple14 past due (partners required to make it easier);
M: 15.6: handout: exercise in setting up triple integrals in Cartesian coordinates (please take this seriously);
29, 31 [see 3d Maple plot: two projections of the solid onto coordinate planes are actually faces of the solid, the third face 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 curve];
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.

CONTEXT: While a few of you may learn how to illustrate triple integrals (my hope), I will only test all of you on being able to iterate triple integrals given the 3d figure already drawn for you as in problems 33, 34, and the handout problem once you have the 3d figure given to you. AT LEAST master that part of the technique, if you simply cannot figure out how to make the figures themselves.
W: Test 2 back (please study answer key); check grades on webct, compare with those on your quiz/test/maple (I make mistakes);
don't wait till the end of the semester to upgrade your maple13 to 2/2, time will run out when you are most busy;
handout: review polar coordinate trig;
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), pp.646-647 (read graphing in polar coords);
10.3: 1, 3, 5, 7, 9, 11, 15, 17, 21, 25, 29, 31, 35 (all short review problems);
part of Maple15.mw:
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! and Easter Break.

paper handout: exercise in setting up triple integrals in Cartesian coordinates: solution

WEEK 11:
W: pick up paper handouts and your test from last Wednesday if you missed class;
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];
now look at polar coordinate integration examples handout;
Th: 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, or simply interchange them since they are dummy variables of integration):
∫ ∫ _r<=2 [∫_{y= x^{^2}+z^{^2..4}} (x²+z²)^1/2 dy] dA = ∫ ∫ _r<=2 [∫_{z= x^{^2}+y^{^2..4}} (x²+y²)^1/2 dz] dA (see book discussion on page 994);
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 8 on polar coordinate integration;
Read 15.5 carefully;
15.5 (center of mass, "centroids" when constant density; skip moment of inertia): 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: catch up on Maple 14, 15, correct maple13 if not a 2/2; you will run out of time at the end of the semester coming up quick!:
handout 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: handout on cylindrical and spherical regions of space and their bounding surfaces: examples;
handout on cylindrical and spherical triple integral: examples;
15.8 (spherical): 1, 3, 5, 7, 9, 11, 13 , 15, 17, 21, 25, 39.
Th: in class review problems, homework:
15.7: 25;
15.8: 23, 29, 35;
15.R (p.1022): 19, 20, 27, 37, 39, 45.
F: 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: x²+y², x(x+y), (x+y)², sin(x²+y²)^1/2;
19*; just try the template, no need to submit [check here for result, with bonus problem 25 done as well].
look over archived Test 3.

WEEK 13:
M: 5:30 voluntary MLRC problem session for Test 3:
Test 3 out at end of problem session and online at 7pm; no homework to get head start.
16.2 (f ds scalar line integrals: pp.1034-1039 midpage, for Thursday): 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: obvious midpoint, also bonus: 33 solution]
W: bring laptop to work on Test 3 Maple evaluations.
Th: handout on line integrals;
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.
F: 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.

WEEK 14:
M: Test 3 back in class or if need another day, just bring to class Tuesday (Friday schedule); if you need an extension because of all your other work, just ask me (email);
16.4: 1, 3, 17,
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 so you can ignore it.]
T[=F]: handout on divergence and curl, Gauss and Stokes versions of Green's Theorem.
Final section 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].
W[=M]: optional handout on interpretation of circulation and flux densities for curl and div.
Th: Teaching evaluation CATS forms. Final exam discussion. [archive]
check grades online in web/ct; 2 lowest quizzes dropped, maple total needed only 4/4.

Next week:
4:30 MLRC problem session Monday May 3; office hours Monday afternoon??, Tuesday afternoon??
FINAL EXAM: Tues May 4 (8am), Wed May 5 (1:30pm) (see below, you may switch days if you wish).

Current MAPLE file :
maple13.mw due: Week 6
maple14.mw due: Week 10
maple15.mw 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 5 1:30 - 4:00

MWF 1:30 Tue, May 4 8:00 - 10:30

Graphing Calculator / Maple Checking ALLOWED FOR ALL QUIZZES/EXAMS

28-apr-2010 [course homepage] [My Courses: 2500-003, 2500-004]
[log from last time taught with Stewart Calculus 6e]