1500 04F maple homework [still provisional until assigned in daily homework log]

Homework problems marked by an asterisk * on the homework log page are to be done using MAPLE with a partner (or two partners). Save each chapters' problems in a single worksheet (with all partners' names inside the worksheet at the top with date) as  "MAPLE sections" with a section title labeling the problem (as in 3.1.2 for Stewart chapter 3 section 1 problem 2 or CLM 2.4.1 for the CalcLabs with Maple problems)  on your personal hard drive or network space (each partner keeps a copy for safety) until requested to submit the chapter worksheet the week following chapter completion. You may work individually on any given problem if successful, but must meet, discuss and merge your work with a fixed partner(s) for a given maple worksheet collection of assignments. Try to put in comments that explain what you are doing in your worksheet, rather than just listing a series of maple inputs and outputs.

Here is a template file to get started. Save it (right-click on link and "SAVE AS" choosing type "ALL FILES") and open it up in MAPLE: maple1.mws
Add a new section for the second problem.

If you are able to use MATHCAD to achieve the same goals in a given homework set, you may submit a mathcad worksheet mathcad<...>x.mcd with the same naming conventions. However, there are certain operations MATHCAD is simply not set up to do.

SUBMISSION INSTRUCTIONS:
Worksheet submission will be done as an email attachment where the filename is:
lastname-lastname-lastname-maplex.mws
and the subject header is:
[mat1500] lastname-lastname-lastname-maplex.mws
where the last names of all partners are listed (separated by hyphens) and x stands for the number of the maple assignment as given below.
Include the partners as email recipients using the CC option so that I can REPLYALL with the graded commented worksheet.

Everyone must have a partner (or two) unless agreed upon in advance with bob. [You may change partners on different assignments.]

Consult the command list worksheet for examples when necessary: cmdlist1.mws.

"Upgradable" after the grade [0/2, 0.5/2, 1/2, 1.5/2, 2/2] means you can correct your worksheet based on my comments and resubmit it for a better grade. I will help you in person if you do not understand how to correct any problem. It is easy to do well on this grade input, if not initially, then by getting help from me.

Remember, you may come to my office for consultation on any problem, or request preliminary help via email (attach worksheet) if you are stuck on something.

[MAPLE sections can be inserted empty and later filled, using the INSERT menu, Section selection, then insert a MAPLE prompt |> icon on the top  toolbar, or one can select a region of a worked problem with the mouse and hit the second icon after the maple prompt icon to enclose the region in a section.]

maple1.mws (due the week following completion of chapter 1: M-F 13-17 September):

• NOTE: unless you are going to do several activities with an expression, there is no point to introducing a name for a Maple expression: > f:=log[1.5](x); or a Maple function > f:=x->log[1.5](x); so that one can then put respectively "f" or "f(x)" into another command like a plot instead of the expression itself.
  [f(x) : = x^2 is not a good idea in Maple since you cannot change the input x in this 4 character string name, although it is valid MathCad syntax.]
  Each of the 4 multiple function plots in this first assignment can be done with a single plot command line. To respond to "how are the graphs related" think why this sequence of functions was plotted together to answer (i.e., how does the graph change as the base changes, etc).
• 1.5: 3*, 5* [See instructions. Hint: Either use the symbol palette for entering "e^x" since "e^x" is not the exponential function in MAPLE or use MAPLE notation: "e" is "exp(1)" in MAPLE, "e^x" is "exp(x)"; use color option to distinguish graphs, say: red, green, blue, black; begin your maple1.mws worksheet with the template file; answer the textbook problem question in text mode after each graph]
• 1.6: 43* [ base a log: log[a](x), natural log: ln(x) in pallette; put answer to problem instruction question in MAPLE worksheet as a comment]
• 1.6: 73*
  [same instructions as before, use option "scaling=constrained" in plot command to make units same on both axes, use a square viewing window:
  > plot([...],x=-Pi/2,..Pi/2,scaling=constrained);
  Why are the horizontal and vertical ranges automatically the same here...?]

Helpful MAPLE hints from HW page:

> plot(f(x),x=-10..10);
> plot(f(x),x=-10..10,y=-10..10);
> plot([f(x),g(x)],x=-10..10, color=[red,blue]);
> fsolve(f(x)=g(x),x=0..1); [Always use plot before fsolve to know where to look for solutions.]

> f := x -> x^2-c*x;
> seq(f(x),c=[-2,-1,0,1,2]);
> plot([%], x = -2..2);
 

maple2.mws (due the week following completion of chapter 2: Oct 18-22):

• 2.2: 11* [exp(x) in MAPLE, answer question with text comment, check with limit command]
• 2.5: 51* [follow this MAPLE example after subtracting the righthand side from the left hand side of the equation you want to solve]
• 2.3: 34* [comment on your choice of functions f, g, h and what your graph suggests is the correct limit; check with limit command (day 12)]
• 2.6: 35* [do an appropriate plot for part a) and plot your guess as a constant function together with the function to compare in an appropriately wide enough window to see the squeezing together, then use the seq command (day 11) to get your floating point values for part b), then use the limit command to evaluate the limit exactly for part c)],
  55b* [graph appropriately (plot the terminal velocity and the 99% terminal velocity value lines together with the function), then use fsolve to find the desired time, make sure this time is in your graphing window, adjust if necessary]
• 2.7: 5c* [plot two expressions together, then zoom in, make comment about whether it looks right or not]
• 2.8: 11* [a) use seq command to numerically evaluate derivative limit, b) zoom in on graph using boxed axes (click on the plot and then on the boxed axes icon on toolbar) to read off rise and run within box to estimate slope, evaluate quotient in worksheet not with a calculator]
• CalcLabs 4.7: 1a* [simplify also], 2*.

Helpful MAPLE hints from HW page:

> seq(g(x), x=[1.5,1.1,1.01,1.001]);
to evaluate an expression g(x) for a sequence of multiple inputs (always use decimal point values like 1.0 to force floating point evaluation but if the expression g(x) involves ? you must use evalf to force it to approximate that as well
> evalf(%);

> limit(f(x),x=0);
> limit(f(x),x=0,right);
 
> Limit(f(x),x=-infinity);
> value(%);

> f : = x-> x^2;
> f(x);
> D(f)(x);
 > plot([f(x),D(f)(x)],x=a..b,color=[red,blue]);
an evaluated MAPLE function is just a MAPLE expression, so you can also use the diff command:
> diff(f(x),x);
> simplify(%);

maple3.mws  (due the week following completion of chapter 3: ):

• 3.1: 37* [note: zooming in on x = 1 really means zooming in until the graph looks like a straight line, whose slope we can then calculate by estimating the values of the function at the leftmost and rightmost points in the window (use axes =boxed or click on the corresponding icon to better estimate the rightmost value), dividing by the width of the window using Maple to do the arithmetic; guessing the slope by looking at the window is not very productive]
• 3.4:
  32* [define s to be a Maple function s of t, then plot [s(t),D(s)(t)] for t = 0..2*Pi, answer questions c,d,e in maple comments, remember equilibrium position means  s = 0, speed is absolute value of velocity],
  34c*[define a MAPLE function F using 3/5 as the coefficient instead of 0.6 to keep exact arithmetic, then after clicking on the graph with theta = 0..Pi/2 to determine the value of theta, use fsolve to find it to high precision, and then use solve to find it exactly, and give its numerical approximation with evalf, be sure to comment a response to the question asked]
• 3.5: 69*[make some comments about features of the graph of s reflected in the graph of s'],
  74* [first define f as a  MAPLE function; for part a), use the simplify command, after which one can solve part b) exactly (in terms of fourth roots), even by hand; answer the questions of the book with MAPLE comments]
•  3.6: 27* [display plot with hand-derived tan line]
• 3.7: 21b*[make comments comparing 3 graphs, remember this is periodic, so show just one period: comments should indicate why it is plausible from looking at the graphs that one is the derivative of the other and the third is the derivative of one of the first two], 49b*,c* [also answer c in a comment referring to the plot]
• 3.11: 13b* [for the accuracy, follow example 3]

Helpful MAPLE hints from HW page:

> with (Student[Calculus1]);
> DiffTutor(exp(x)/x);

> with(plots):
> implicitplot(x^2-x*y+y^2=3,x=-10..10,y=-10..10);
> implicitdiff(x^2-x*y+y^2=3,y,x);

> plot([f(x),D(f)(x),(D@@2)(f)(x)],x=a..b,color=[red,blue,green]);
> with(Student[Calculus1]);
> CurveAnalysisTutor(f(x));

maple4.mws due by the end of exam period

• 4.1: 69* [see example 10 in worksheet]
• 4.1: optional for rocket scientists: 72* [data fitting plus max/min template given]
• 4.2: 9*[read carefully: combination of hand work and MAPLE]
• 4.3: 55*[do what the textbook asks you to do, guestimate intervals of concavity and state your guesses before checking the graph of the second derivative, then compare with a comment],  
  skip this one: 61*[now do what the textbook problem requests and compare your guestimate with the numerical value of t obtained by setting the second derivative to zero];
  ***** ASSIGNMENTS SO FAR Fall 04; those below are preliminary, not final *****
  The last one was a substitute quiz:
• 4.6: 15* [produce several graphs that show all the details that one graph cannot supply, use MAPLE to find the (x,y) for the critical points and points of inflection, finally make an exaggerated hand sketch "road map" labeling all points with 3 significant digit accuracy that summarizes your results]
• only one optional(?) problem left in 4.9

Notes for bob:

• when multiple curve plots are requested, add instruction that they should be on the same axes.
• when slope estimation is requested, add instruction that slope should be evaluated by dividing increments over zoom window.
• speeding up/slowing down must be pre-explained.
• implicitplot must be explained in terms of grid and window.