2705 20F maple "homework"

In progress with a new approach for the online course delivery mode.

2705 18F maple homework

• submission instructions
• tips to remember
• home work list
  
  [10 minute introduction to clickable calculus interface][printed explanation]
  for the truly curious: [demos, clickable math video!][training videos]

submission instructions

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 E&P chapter 3 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: maplex.mws, where x is the chapter number the problems are coming from in the E&P DELinAlg 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:
[mat2705] lastname-lastname<-lastname>-maplex.mw
where the last names of all partners are listed (separated by hyphens, no spaces) and x stands for the chapter number of the maple assignment: 1,2,3,5.
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<-lastname>-maplex.mw
so I can extract them and tell where your worksheet is in my local folder (x is 1,2,3 etc!). When 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" choosing type "ALL FILES") and open it up in MAPLE: maple1.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 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: cmdlist4.mw.

"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.]

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. Since this is 10 percent of your grade, and I am very flexible about deadlines and helping you, it is absurd not to make sure you get full credit on all assignments.

Tips to remember:

• Maple is case-sensitive like mathematics, distinguish uppercase and lowercase letters and be consistent.
• Pi is the number π, exp(x) is e^x, exp(1) is e
  but in typing Maple,  e or e  is never the Euler number and e^x is never the exponential function
  (Maple now asks you if you meant Euler's number!)
  [use the Common Symbol palette entry to be sure (Pi)!]
• 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.]
• % 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.
• Shift Enter. Holding the Shift key and pressing the Enter key at the end of a Maple input allows you to go to the next line. If you wish to put two Maple inputs together in 2d math notation, they must be separated by a semicolon (or a colon to suppress the output of the preceding command).
• In 2d math mode input, spaces between variables imply multiplication (an * is required in 1d mode and between hard numbers like 2 and 3^1/2 in 2d input) and the right arrow key is needed to climb down from a superscript and continue or climb up from a denominator (use / for division and fractions) and continue entering input. Always use parentheses ( ) when needed for grouping!
• Control F2 gives you the quick summary of Maple interface help.
• Control Space invokes auto-complete when entering Maple commands to choose from a popup menu of all commands which begin with the typed letters.
• If the output of a worksheet on the web has been removed (Edit Menu, bottom, Remove Output, from entire worksheet), it can be restored by Edit Menu, Execute Worksheet or by clicking on the !!! icon on the upper tool bar.
• After deleting a range of Maple stuff, you must use the Edit Menu, Delete Element to get rid of the last input/output/text region of the selected stuff.
• If you enter an expression for a real function that you want to plot, choose plot builder from the right click menu, not 2d plots (where you have to further rightclick on the smartplot and choose axes, range to reset the window). If you click on an equation say y = f(x) you must right click and first choose right hand side to get the expression to then plot with plot builder.
• MORE TIPS...

home work list

maple1.mw (due the week following completion of chapter 1):

• to get started as explained above, open and save this file: maple1.mw.
   
• 1.3: 8* : our first Maple HW problem: read the Maple HW instruction page, then try the Maple direction field command in this linked template to reproduce the two given curves by using two appropriate initial data points [Hint: notice that the y-axis crossing points are integers!] Then include all the initial data points of the red dots (some half-integer values); this is also described on p.29  for both Maple and Matlab, but the above template already has the appropriate section copied into it for you; if you can find a partner to work with in time fine, otherwise try this yourself and find a partner for future problems, then merge your work. DE: y' = x² - y .
• 1.5: 21* check both the general solution and the initial value problem solution by using the dsolve template or right click menu to solve them.
• * 1.5: 41* [This assumes you have done the problem by hand first. See note on HW page entry.] Use the dsolve template to solve this DE with its initial condition; evaluate answer to question of word problem to a floating point number and give the result in dollars and cents in a comment, then think about significant figures and give a response with fewer significant digits].
  When you are satisfied, compare with the hand written solution retirement.pdf (don't submit a Maple worksheet without consulting this to be sure your text comments are correct).
  
  Useful Maple commands:
  > deq:= y'=2 y
  > dsolve(deq, y(x))
  > dsolve( {deq, y(1)=2}, y(x))
  > with(DEtools):
  > DEplot(deq, y(x), {[0,0],[,[1,0],[1,1]}, x=-2..2, y=-2..2)
  [or enter DE plus IC separated by a comma, right click on output]
  > y ' = x y , y(0)=1
  > odecheck(sol,deq)   [this returns 0 if LHS-RHS of DE is 0]

maple2.mw (due the week following completion of chapter 2):

• quick Maple assignment for exposure to numerical solutions of DEs.
  Edwards and Penny 2.4 Application exercise, pp. 123-124 in textbook:
  Famous numbers investigation, Exercises 1 and 2.
  The problems below describe the numbers e (Euler's number) and ln 2 as specific values of certain initial value problem solutions. In each case, apply Euler's method with n = 50, 100, 200,... subintervals (doubling n each time). How many intervals are needed to obtain—twice in succession—the correct value of the target number when it is rounded off to 3 decimal places?
  How much does the percentage error seem to decrease by roughly each time you halve the stepsize? Respond to this question with a Maple text mode comment.
  
  1. The number e = y(1)  ≈ 2.718 where y(x) is the solution of the initial value problem y ' = y , y(0) = 1
     [since the exact solution is y(x) = exp(x)]. [note: here the interval and starting y value are the same as in the example in the worksheet, only the RHS of the DE needs editing.]
  2. The number ln 2 = y(2) ≈ 0.693 where y(x) is the solution of the initial value problem y ' = 1/x , y(1) = 0
     [since the exact solution is y(x) = ln(x)].  [note: here the interval shifts one unit to the right and the starting y value is different from the example in the worksheet.]

  Execute and read the euler.mw template worksheet which illustrates Euler's method, then open maple2.mw, and put your names and date at the top first and save it by renaming it with your partner's last names (hyphenated) before maple2 in the filename as you did for maple1.  It has two sections (one for each of these two problems) for you to edit the differential equation, the starting and stopping values of x, and the initial value of y, and then follow the instructions to improve the accuracy of Euler's method by increasing the number of divisions of the interval repeatedly. Be sure to make a comment answering the questions at the end of each.

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

• 3.2* (read this linked worksheet in class with a partner; nothing to insert in maple3.mws)
• 3.3: 19* [[use the tutor and record your final result, compare with the right pane solution]
  [no longer possible: Maple no longer allows copying from the tutor window; so this documentation cannot be done efficiently any longer to record your step by step reduction, annotating each step as in the rowredex0.mw worksheet];
  29* [= 3.2.19, after inputting the Student Linear Algebra package with the Tools Menu, check the solution to this problem by solving with Red...(control space will autocomplete to RREF) and Back... (BackwardsSubstituting) of the augmented matrix, compare your solution for the variables x1,...,x4 with the book answer; do they agree?];
•  chemical reaction problem* [pdf] (what can you find out on the web about interpreting this chemical reaction? chem site reaction balancer gives balanced reactions but no description, this one of our exercise turns out to be interesting);
• 3.6: 17* [record your Gaussian elimination steps (no RowMultiplications!, ie, no dividing row by entry to make 1) in reducing this to triangular form and check det value against your result]
• *3.5. Application:  7* from textbook on p.201, using the inverse matrix as described on p.200,
  be sure to answer the word problem question with a text comment;
  are these sandwiches cheap or not?
  [if you know how to use MathCad, try it and compare with MAPLE]
  
  useful Maple commands:
  To solve a linear system, input augmented matrix with the palette or Matrix command:
  > with(Student[LinearAlgebra]):
     A:=Matrix([[3,8,7,20],[1,2,1,4],[2,7,9,23]]);
     ReducedRowEchelonForm(A);
     BackwardSubstitute(%);
  To step by step reduce a matrix and solve the system do (pick Gauss-Jordan):
  > LinearSolveTutor(A)
  Matrix multiplication, matrix inverse, determinant
  > A B
  > A^-1
  > |A|

maple5.mw (due the week following completion of chapter 5):

• 5.1:  9* [use the 2nd order dsolve template to solve the 2nd order IVP as a check].
• 5.1: 49*[check your IVP solution for the highest curve in Figure 5.1.6 using the dsolve template and plot it together with the horizontal line y=16/7 claimed by the book as the highest value of that function; recall how to plot multiple functions in the same plot:
  > plot([<expression_for_y(x)>,16/7],x=a..b,y=c..d,color=[red,blue]);
  the color option is useful in distinguishing two functions when it is not already clear which is which as in this case; is 16/7 the peak value of your solution?].
• 5.3: 49* [check you solution with the higher order dsolve template, and also check the IC linear system solution as in the template].
• handout on driven (nonhomogeneous) constant coeff linear DEs
  [complete final exercise on this handout sheet, Maple: *check this with dsolve, (pdf solution; the algebra works if you are careful!)];
• 5.4: 21* [solve the two DEs with the same initial conditions using Maple and plot the two solution curves together, but also plot the corresponding third solution with pure damping but no oscillator as in the template]
• [first by hand: 5.6: 1 [rewrite as a product of sines using the cosine difference formula:
  cos(A) - cos(B) = {-2 sin((A-B)/2)} sin((A+B)/2), the expression in {} is the sinusoidal amplitude envelope function [and its period is T = 2(2 π)/(A-B)], look at the plot of x and +/- this amplitude function (the envelope) together in this beating example worksheet] then do:
  5.6.1*: as explained here, repeat for the HW problem at the end of this beating example worksheet (be sure to plot one full period of the envelope function to see 2 beats) and include only that HW problem section in your maple5 worksheet],,
  
  useful Maple commands:
  > deq:= y'' + 3 y' + 2 y = 6 e^x
  > inits:= y(0) = 4, y'(0) = 5
  > solgen:=dsolve(deq,y(x))
  > solivp:=dsolve({deq,inits},y(x))
   
•  for EE students only [not this semester?]

maple6-7.mw due or not due (that is the question), NOT! (i.e., there is no assignment after Maple5)
but you should know how to use the Eigenvectors command

• Useful Maple:
  > x1''(t)=x2(t), x2''(t)=x1(t), x1(0)=1, x1'(0)=0, x2(0)=0, x2'(0)=0   [enter, right click and use Solve DE Interactive]
  
  Right-click on the output of a square matrix and select Eigenvectors from the menu to get both eigenvalues and eigenvectors.
   
• 6.1.13* [check with Eigenvectors command, choose eigenvector basis matrix B, evaluate A_B = B^-1AB].
• For the DE system x ' = A x with the matrix A = Matrix([[5,-4],[2,-1]]) input by rows (the matrix of 6.2.1) and initial conditions x(0) = [0,1]: check your general solution for this DE system and the solution satisfying the ICs using the dsolve system template.
•   x" = Ax, x(0)=[0,1], x'(0)=[0,0] for A = Matrix([[-5,2],[2,-2]]) : *check your solution with the second order dsolve system template.
  
  useful Maple commands:
  > with(Student[LinearAlgebra]):
  > A:=<<1,-3>|<2,-4>>
  > λ , B := Eigenvectors(A)