[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.]
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.
WEEK 2:
optional fun problems if you like math: 51 (geometry), 53 (chemical geometry).
12.3: 35, 42 [ans: b_perp = orth_a b = <-3.6,1.8>], 45;
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:
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>
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.
> 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:
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.
oops: most of you have cell phones, why didn't somebody call bob? read email.
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:
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
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];
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)
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.
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:
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*].
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];
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].
14.5: 43.
Fall break :-) Enjoy.
WEEK 8:
midterm grades due in Wed 12 noon: for Maple upgrades, quiz5 grades;
14.6: 1, 3, 5, 7, 9, 11, 15, 19, 23, 29;
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
> 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]
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] .
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...
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.
Test 2 Problem Session today 5:30pm MLRC.
Optional: Read 36 [this enables one to sum the probability under a normal curve in statistics]
WEEK 10:
2 handouts on cylindrical and spherical coordinates and using them to describe regions of space or surfaces.
15.8: 1, 3, 5, 6, 7, 11, 17, 23.
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*.
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:
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].
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.
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].
34 [ans: <4.60,0.14,-0.44>]
WEEK 12: Maple15 due next week [get it done early for fast feedback]
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
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
16.2: 40, 41, 45; optional 44.
19, 23, 33; optional 15 (same procedure as example 4).
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:
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
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)
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
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)