@RAfossey You have invstrans, not invztrans. And why have you separated the two parts of the z expression with a comma? And why did you put y in the command? Where are you getting these wrong ideas from? The command that you need is

invztrans(z/(z-2)*5*z/(5-z)^2, z, n);

That's all that there is to it (for part a)!

For part b) use sum command. Look up ?sum. There's no need for the ztrans command.

Take the answers from parts a and b and form their quotient (as your professor suggests) and apply simplify to it. You should get 1, which shows that the expressions are equal. A more normal way to prove equality is to take the difference of expressions and try to simplify it to 0.

What you want to do can be done simply with piecewise, with no need for events. If the first derivative is 10 or greater, then the second derivative is 0. What did you try with piecewise?

Download piecewise_dsolve.mw

The second parameter of My is y. Inside My you have multiple subexpressions such as diff(a(y), y). This means the derivative of a(y) with respect to (wrt) y. For this to make sense, y has to be a name. But in your call to My, you pass -1/2*b as the second argument. This becomes the value of y. Perhaps what you intended was not the derivative of a(y) wrt y but rather the derivative of a wrt its parameter, then evaluated at y. This would be denoted D(a)(y) rather than diff(a(y),y).

Another problem that I noticed is your use of Pi. You use it both as a constant (as in sin(m*Pi*x/a)) and as a function (as in Pi(y)). It can't be both. Preferably, you should only use it as the constant (its default meaning) and choose another symbol for the Pi in Pi(y).

A similar problem is your usage of m: It is used both as a bound variable (as in m= 1..infinity) and as a function (as in m(y))

Lastly, How can you understand or manage such a long and sloppy function? You should break it up into smaller, more-understandable chunks.

You said that "at best" you'd like to access the points by name. The following lets you do that.

Download Points.mw

The commands matrix, vector, transpose, linsolve, and `&*` are all very old deprecated commands, which means that they shouldn't be used anymore. They only exist in current Maple so that legacy code still works. The `&*` was used for matrix multiplication, and linsolve was used to solve a linear system. In modern Maple the above code is

a:= < a1,a2; b1,b2 >;
b:= < c1,c2 >;
c:= a^%T; #transpose
LinearAlgebra:-LinearSolve(c.a, c.b)

For example:

A_vals:= [1,2,3]:
m:= min(A_vals):  R:= max(A_vals) - m:
Sol:= dsolve(
     {diff(y(x),x$3)=y(x), y(0)=0, D(y)(0)=-0.5, (D@@2)(y)(0)=A},
     parameters= [A], numeric, range= -2..2
):
for v in A_vals do
     Sol(parameters= [v]);
     P[v]:= plots:-odeplot(
          Sol,
          [x,diff(y(x),x)],
          color= COLOR(HUE, evalf(.85*(v-m)/R)),
          legend= [A=v]
     )
end do:
plots:-display(convert(P,set));

I will assume that you have read the variable names into Maple from Excel (perhaps by using Tom Leslie's method) and that they are stored as an Array/(Vector/Matrix) of strings named LABELS, and that you have the numbers from Excel stored in an Array VALUES. Convert LABELS into an Array VARIABLES via

VARIABLES:= parse~(map2(cat, " ' ", LABELS, " ' "));

Then assign the values of the variables with

assign(convert(VARIABLES=~ VALUES, list));

If you want to reassign the values in the same session, then you need to execute only the second command again.

Note that in the first command each of the two groups of quotes is a single quote (an aposthrope) surrounded by a pair of double quotes.

Hello Raquel,

Construct your Matrix (or Vector) like this: Immediately after the command omega[1]:= solve(...), do

eval(<u[1,1], u[2,1], u[3,1]>, omega[1]);

Let me know if that takes care of your problem.

Most of what DEplot3d does can be done by sol:= dsolve(..., numeric) followed by plots:-odeplot(sol, ...). In this case, "most" is "all". The odeplot is more flexible in that it allows for functions of the dependent variables, which is what DEplot3d gave you an error about. So, replace your DEplot3d with

Sol:= dsolve(
     {eqn||(1..3), u(0)=1, v(0)=Pi, theta(0)=Pi/4},
     {theta(s), u(s), v(s)},
     numeric, range= 0..5
);
GrGline:= plots:-odeplot(Sol, [X,Y,Z], linestyle= solid, thickness= 3);

My personal aestethic opinion is that the final plot will look better if you include the option transparency= 0.1 in the display command.

(1) Your Reply has appeared, numerous times, and I am about to delete all but one copy.

(2) When you attach a worksheet to a post, you have the option of displaying the worksheet in the post as well. This is the best way. To attach a worksheet to a post, use the green uparrow tool that is the last item on the second row of the toolbar in the MaplePrimes editor.

Some hints: Part (a) and both parts of (b) can each be done with a single one-line rsolve command. For part (c), treat x as a continuous variable. Use several plot3d commands, each at a fixed value of n, with a and b as the independent variables. I haven't done this part of the problem yet, but I suggest that you first try logarithmic scaling for n: n=2, 4, 8, 16, .... Because of the sign-alternating terms, do a companion series of plots for odd n: 3, 5, 9, 17, .... The even and odd will not necessarily be much different. An animation or Explore (Markiyan's suggestion) may be appropriate. You don't have to explicitly use a z-transform or any other algorithm for any part of this problem; the rsolve does it all.

This is usually the easiest computational monotonicity check in Maple: If the function is differentiable and its derivative has no zeros (no roots), then the function is monotonic. (If its derivative does have a zero, the function may still be monotonic; it requires slightly more investigation: Check whether the sign of the derivative changes as it passes through the zero. If it doesn't change, then the function is monotonic.)

All your troubles are because frem only takes numeric arguments. Using unevaluation quotes to prevent frem from receiving a nonnumeric argument will only get you so far. What's needed is a symbolic equivalent to frem. Here it is:

Frem:= (x,y)-> x - y*floor(x/y+1/2);

And here is a worksheet using this that solves all your problems: plot, symbolic integration, numeric integration, and dsolve of a single ODE and of a pair of ODEs.

Download frem.mw

There are so many problems in your code. We'll need to work through them a few at a time. Let's start with the first line. It's clear from the code that you intend for f to be a procedure and x0 a numeric constant. We'll reduce future mistakes by declaring those types:

kokoko:= proc(f::procedure, x0::complexcons)

The local line is okay for now.

What's the purpose of p:= problemm? Is problemm supposed to be a symbolic constant? or a global variable? If it's a symbolic constant, you can make that clearer by using unevaluation quotes:

p:= 'problemm';

I notice that p is effectively never used in the rest of the program. So what's its purpose?

Next, I suppose that you want to evaluate the derivative of f at x0, and decide what to do next based on whether it's greater than 1. There's no need for variables d and e. Simply do

if evalf(D(f)(x0)) > 1 then ...

See how far you get with that advice, and then Reply here if you need more.

Extracting a numeric parameter from an error message is easy. In the worksheet below, I present a short and simple procedure to do it. I use Preben's parentheses-corrected version of your ODEs and his nontrivial initial conditions.

Download find_sing.mw