2500 maple homework (still tentative!)

Homework problems marked by an asterisk * on the homework log page are to be done using Maple with one to three partners in groups of 2 to 4 students. 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 13.1.2 for Stewart chapter 13 section 1 problem 2)  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. Filename: maplexx.mw, where xx is the chapter number the problems are coming from in the textbook as designated on the due date list below. 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. Begin to learn how to document your work.

SUBMISSION INSTRUCTIONS [Why they are important!]:
1) Worksheet submission will be done as an email attachment where the subject header is:
[mat2500] lastname-lastname-maplexx.mw
(if there are only 2 partners, add the third if 3)
where the last names of all partners are listed (separated by hyphens) and xx stands for the chapter number of the maple assignment: 13 for the first one.
2) Include the partners as email recipients using the CC option so that I can REPLYALL with the graded commented worksheet.
3) The filename must be the same as in the email subject heading:
  lastname-lastname-maplexx.mw
so I can extract them and tell where your worksheet is in my local folder (xx is 13,14,15). Before you attach your worksheet, first change its name to agree with this longer format so I can save it that way onto my hard drive.

Here is a Maple template file to get started. Save it (right-click on link and "SAVE AS") and open it up in MAPLE: maple13.mw .
Add a new section for the next problem etc.
[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 INDENT after the Maple prompt icon to enclose the region in a section.]

Everyone must have 1 to 3  partners unless agreed upon in advance with bob. [You may change partners on different assignments.]

"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. [If you do not get a reply to the email submitted in your name for a given assignment, it probably means I did not receive it. Check with me after a reasonable amount of time.] COVID conditions: worksheets will be marked Pass/Fail and will not enter into the grade cum, but performance on these will be considered in terms of letter grade assignments.

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. If any glitch occurs, email bob immediately.

I will return all worksheets that are not perfect either with comments for you to learn from, or to fix and resubmit for upgrading.

Tips to remember:

• Maple is case-sensitive like mathematics, distinguish uppercase and lowercase letters and be consistent;
  D is reserved for differentiation, I for sqrt(-1) usually written i in mathematical notation.
• Pi is the number π, exp(x) is e^x, exp(1) is e [never do exp^(x) or e^x! e is not the Euler number in Maple input]
  [use the symbol palette for these!]
• All Maple commands obey function notation with rounded parentheses (,) enclosing their inputs separated by commas. All groupings overriding the usual rules for order of performing the basic operations are done using matching rounded parentheses only (no brackets or braces of any kind).
• Square brackets [,] enclose a list of objects (numbers, functions, color names) whose order is to be maintained, like vector components, or a list of functions to coordinate with a list of colors in a plot command. Curly braces {,} are used to enclose sets of objects whose order is unimportant, as in a set of equations to be solved.
  [Square brackets are also used for subscripts on vectors or matrices: v[1] becomes v₁, A[1,2] becomes A_1,2.]
• Triangle brackets < , > are used for listing vector components.
• % stands for the last output in time (not necessarily the previous output in position in the worksheet). When a series of inputs using % goes bad and has to be re-edited and executed, you must re-execute from the first statement to which they refer to reset the sequence [Select them and use Edit Menu: Join to put them in the same "execution group" so they automatically execute as a group.].
• Maple  opens either in document mode ( in which calculations are just listed horizontally in text mode from left to right) or in the more organized worksheet mode (input/output required for maple homework). Please choose worksheet mode.
  
  An important tip for Math input is that you must use the right arrow key to continue inputting an expression after raising to an exponent or dividing by a denominator (using the forward slash for division, asterisk for multiplication), in fact you can use all 4 arrows to move around an expression to edit its various pieces, while when entering from the palette, the tab key moves you through the characters to be replaced. With the cursor in a math output region, the context sensitive menu  allows you  to select operations you wish to perform on that expression/equation/object.
   
• MORE TIPS...

maple13.mw (due the week following completion of chapter 13):

• Start by saving this worksheet: maple13.mw. Then create a section for each successive problem and copy and paste templates into each section as needed, if there is a template. There should be 5 completed problems in the first worksheet when you are done. Be sure to add your names to the filename as explained above before submitting.
   
• 12.5.57*: 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)
• 13.1:  39* [refer back to similar problem 27: note that  z² = (x²+y²)! so the surface is a cone, plot the spacecurve (period 2 π) and the cone together as in the template, adjust the ranges for the surface so it is just contains the curve and it not a lot bigger: ask yourself what are the largest and smallest values x and y can take for the spacecurve, and use these for the range to plot the surface],
• 13.2: 29b* (graph your results using this template; make a comment about how it looks). 
• 13.4: 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 Appendix I, page A122, 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].
• 13.Review: 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 before they both straighten out to the tangent line, including the separate original plot showing the large scale behavior; what value of the horizontal window makes this happen?.
  ***
  To plot functions [solve plane equation for z = f(x,y)] or parametrized planes:
  > plot3d(f(x,y),x = -1..1, y = -1..1)
  > plot3d(<1,2,3>+t1*<2,0,-1>+t2*<1,-1,1>,t1=0..1,t2=0..1)
  To plot curves:
  > with(plots):
  > spacecurve(<t, t²,t³>,t=0..1)
  To display plots together:
  > plot3d(...): p1:=%:
  > spacecurve(...): p2:=%:
  > display(p1,p2)
  To do vector stuff:
  > with(Student[VectorCalculus]): BasisFormat(false):
   

maple14.mw (due week after finishing chapter 14):

• 14.1: 55*, just do a single appropriate plot3d and contourplot after loading plots and defining the maple function f(x,y) or use PlotBuilder]
• 14.2: 23*; toolbar plot option: contour, or "style=patchcontour" or  right-click style patch+contour, explain in comment].
• 14.2: 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]
• 14.4: 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].
• 14.6: 47*; plot your results in an appropriate window (using the 1-1 toggle or the option "scaling=constrained" to see the right angle correctly), ie, adjust windows of function, plane, line to be compatible, after doing problem by hand, comment on relation of plot to exact results].
• 14.7: 23*; template shows how to narrow down your search to find approximate values for the obvious critical points  (x,y) by trial and error in a  contourplot, record your tweaked image or images, then compare your estimated values of  (x,y) with those in the back of the book, include commentary comparing what you estimate to the actual critical points (x,y) found by hand or using Maple or taken from the back of the book. In this problem it is enough to add the option "contours=100" and click on the contourplot in some white space to make it live, and then put the mouse cursor (first right click, choose: Probe Info, Cursor position) over your estimate of each critical point and read off the coordinates. The plot3d tells you what kind of extrema the critical point is (local max or  min), which the contourplot also reveals if you remember that dark blue is higher, light blue is lower for higher and lower values of the function. Try to solve the differential conditions for the critical points (hint: first subtract the two equations, find the obvious solution for x and y, then back substitute into either equation alone to solve for one variable using the double angle formula for the cosine).
  Remember: give your numerical estimates of the critical points (x,y) in the correct region of the plane and compare them with the numerical values of the exact values given in the back of the book.
• COMMENTS ARE IMPORTANT. Make sure every problem has some brief text mode comments putting the problem into context or indicating what was done.

maple15.mw (due week after finishing chapter 15):

• 15.1: 15* [after the first few plots, just use output = value to see how the numerical approximation converges as you keep doubling the number of divisions per side; compare to the exact value maple finds for this integral; 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] .
• 15.2: 33*.
• 15.3: 70* [Follow the instructions in the template.]
• 15.4: 31* [do a 3d plot as in the example with boxed axes to estimate the volume to compare with the numerical value of the integral to see if it makes sense, roughly]
• 15.6 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.
• 10.3: 67* [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].

There is no maple16.mw assignment. By now you should have gotten the point, or not.
   :-)