Login to the Villanova home page 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/ma2500/mat2500w.htm ],
and read the on-line links describing aspects of the course (no need yet to look at the
MAPLE command worksheet or examples or tutorial). Fill out your paper schedule form (get a copy in class) to return in class Wednesday or (if you forget) drop it by my office St Aug 370 (third floor, Mendel side, by side stairwell) and see where you can find me in the future when you need to.
In class: explore technology support... netscape class stuff [login to VU homepage, go to our classroom], open maple 7.
[Note the textbook appendices A,B,C,D for review of precalculus foundations if you find yourself a bit rusty. Also recall some rules of algebra.]
Homework: 12.1: 1, 2, 3, 5, 11, 13, 15, 19a, 21a, 23, 31, 35;
[problem 12.1.42 in class is just to tie the course back to calc2 and illustrate problem solving approach and documentation];
12.2: 1, 2, 5, 7, 11, 13, 15, 19.
12.3: 1, 3, 5, 9, 11, 15, 21, 23, 27, 33;
12.3: 39, 46 [ans: b_perp = orth_a b = 1/10*<11,33>], 49;
optional fun problem: 57.
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 D);
10.1: 1, [optional: 3], 5, 9, 11, 17, 19;
in class review of MAPLE worksheets, creating sections for each problem (put "restart" a beginning of each section), dotprod and crossprod commands loaded by "with(linalg)";
10.1.23*; read MAPLE commands for vector geometry so far, then do with MAPLE: 12.3.41* (also find orthog component "b_perp"; see projection section of previous worksheet link), 12.4.33*;
handout on lines and planes;
12.5: 1 (draw a quick sketch to understand each statement), 3, 5, 9 (parametric only), 11, 14 [ans: a: x=5+2t, y=1-t, z=t, b: (5,1,0), (0,7/2,-5/2),(7,0,1)], 17;
19, 21, 25, 27, 35, 43, 45.
12.5: 49 (also find angle between planes: 78º), 53, 61 (find pt on plane, project the 2 point difference vector along the normal), 63 (find pt on each plane, project their difference vector along the normal) [do not use formulas: this is practice in vector projection geometry];
optional problem if extra time and bored: 68 [ans: D = 2].
Maple12.mws due Feb 4-6 [see below];
13.1: 1, 3, 5, 7-12, 13, 15, 17, 21, 27* [refer back to 21: what is z-sqrt(x^2+y^2)? plot the spacecurve (or one complete period 0..2*Pi) and the surface together as in the template], 31 [eliminate z first by setting: z^2 = z^2 and solve for y, use x to express y and then in turn z, let x be t], read 35;
13.2: 1, 2, 3, 7 [recall: exp(-2t) = (exp(t))^(-2)], 9, 13, 15, 19, 21, 29.
TEST 1: Thursday Feb 7, Problem session: Wed Feb 6, 5:00pm MLRC;
13.2: 22, 27a (by hand), 27b*, 31 [angle between tangent vectors], 35, 39, 45, 47;
13.3: 3 (note the input of the sqrt in the integrand is a perfect square in this problem).
13.3: 7, 11, 19, 21 [do not use formula 11: instead use parametrized curve form r = [t,t^3,0] ], 33, 35.
maple12.mws due M-W;
13.4: 29 [note that v^2 = 3^2(1+t^2)^2 is a perfect square].
(for monday:)
Problems Plus (p.870): 2. [Note b) has answer 52 ft/sec = 36 mph];
13.R (p.868): 9 [angle between tangent vectors], 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*;
14.1: 1, 3, 7, 9, 11, 13, 19, 25, 29, 31, 37, 43, 49*, 67a (read only b,c ).
14.3: 1, 3, 7, 11, 13, 23, 27, 33, 43.
14.3: 39, 41; 45, 47, 51, 55, 57;
Quiz 3 thru 14.3 first HW set;
65, 67, 75 [use implicit differentiation of the equation], 76, 81; 9*.
maple13.mws due M-W;
14.4: 1, 5, 7, 7*[calc by hand then: > plot3d({f(x,y),L(x,y)},x=-5...5,y=-5..5); (choose appropriate ranges, then zoom in as instructed, check that they agree)],
[optional 9*], 11, 15, 21;
19, 23, 25, 27 [simpler to first use: ln(A^(1/2))=(1/2)ln A], 29, 33, 37 [remember 14.3.75].
14.5: 1, 7, 11, 13, 15, 19, 29, 33, 37a, 45, optional: 49 [maple, pdf].
14.6 (thru top p.932): 1, 3, 5, 7, 9, 11, 13, 15, 19.
14.6: 21, 25, 27b, 31, 36, 43 (first part by hand), 43*, 45, 51;
14.R: 31, 32a (now units DO matter);
look over Wed problems and try those you think you will have trouble with for discussion on Wed.
14.7: 7 (due M after Spring Break)
Spring Break
boundaries, word problems: 14.7: 27, 37 (minimize square of distance),
Test 2 rescheduled today G30 5:15pm If you cannot make this time, ask bob for an earlier time to do it;
14.R: 62 (assume the package has length plus girth equal to 84 for the largest box, intuititively obvious; answer: V=5488 in^3);
You must build a rectangular shipping crate with a volume of 60 ft^3. Its sides cost $1/ft^2, its top costs $2/ft, and its bottom costs $3/ft. What dimensions would minimize the total cost of the box?
15.1: 1, 3, 3b* [do this before next class: repeat this problem using MAPLE for (m,n)=(2,3), then (20,30), then (200,300), evaluating the average value (= average height of solid) as in the template worksheet as well: copy and paste 3 times then edit, deleting sequence listing after the first time; guess what the exact integral value is on the basis of this, respond with comment answer],
5, 6 [midpoint sampling: (m,n)=(2,3), x along 20 ft side, y along 30 ft side: answer = 3600], 7, 9, optional: 10.
15.3: 1, 5, 9, 15, 17, 19, 25; maple14.mws due next M-W.
15.7: 1, 3, 5, 9, 11 (like example 2), 19, 23, 27, 29, 31;
[we'll return to this section after a detour];
15.7: 17, 30; make sure you go over the previous 15.3,15,7 HW.
review polar coordinates (handout on polar coordinate integration):
10.4 pp.660-665 (stop midpage): 1, 3, 5, 7, 9, 11, 15, 17, 21, 23, 29, 31, 35, 71* [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;
15.4: 1, 3, 5, 7, 9.
Easter break.
3 handouts on cylindrical and spherical coordinates, using them to describe regions of space or surfaces and then doing triple integrals;15.8: 1, 3, 5, 6, 7, 17.
15.8: 9, 21, 24 [ans: 8 sqrt(2) Pi/3], 31 [set up integral by hand], 31*, 33, 35.
centroids etc:15.5: 5, 7, 11 [see example 3]; 15.7: 15 [see example 3]; 15.8: 25.
handout summary on 2D 3D integration regions;
in class problems:
15.R: 7, 9, 13, 25 (use polar coords), 27, 31, 37a, 41, 42 [ans: Pi/14], 47.
maple15.mws due next M-W;
16.2 (f ds integrals only: pp.1047-1050, 1051 midpage, 1153): 1, 3, 4, 9;
<F1,F2,F3> · <dx,dy,dz> integrals: 7, 17, 31, 37, 43;
handout on line integrals.
16.3: 3, 5, 11, 15 (same procedure as example 4), 19, 21, 33.
16.5: 1, 5, 9, 12, 15.
Catch up HW; Go over Test 3: Answers [MAPLE discussion].
Q8 thru 16.4: verifying Green's Thm (you may use MAPLE for integral evaluation).
handout on surface integrals;
Review problems 16.R: 1-23 (except 20), 37 (zero curl, find potential).
Final exam 2nd Friday after (see below).