This is a boundary-layer BVP. It can only be solved numerically, and that requires supplying numeric values for all the parameters. You also need to treat infinity as a parameter and give it a numeric value, such as 10.

I've seen this phenomenon also, but I didn't care enough about it to investigate what was causing the difference.

@nm Your Answer (both the plot and the integral) treats y=0 as one of the boundaries of the region. It is not.

Are you capable of even reading what you have posted? And do you care? The questions are obvioiusly incomplete. The right sides are cut off, and the essential information from "figure Q4a" is completely missing.

Do not check off all the product boxes. This is extremely rude, and I'm inclined to have your account flagged for deletion.

@JAMET You wrote:

• Sorry your suggestion doen't work.

Tom's Answer (vote up) doesn't contain any "suggestion", and thus it could neither be said to "work" nor not to work. The Answer explains the cause of the warning message, not how to correct it. Since the cause is fundamentally mathematical rather than being due to your coding, a bug, an anomaly (such as complex floats with infintesimal imaginary parts), or a Maple idiosyncracy (such as its rightful refusal to store nonreal numbers as real plot coordinates), this Answer is acceptable to me as an official Answer.

@tomleslie I don't see any connection between the Question and the Kronecker delta function. The integer first argument to Dirac is the derivative order.

@robertocooper If you take the worksheet as posted in your Question and only make my changes 1 and 3 and then hit the !!! button to "execute entire worksheet", I guarantee you that it will not work. Please try again. It can't possibly work because t will not be assigned any value. After a long wait, plot3d will return a warning about that and an empty plot.

If you assign t=1 in the eval, then it will "work" in a sense, but it's a very bad thing to do because it's very prone to error. If you do U:= (x,y,t)-> test where test is some variable which has been assigned an expression containing x, y, and t, then those variables are not parameters of the function U, they're just global variables. Indeed U couldn't even be considered to be a function of x, y, and t. Notice that your line U(1, 8, 1) doesn't substitute 1 for x or 8 for y!

In order for the arrow -> to work, all references to the parameters on its left side must explicitly appear on its right side; in other words, the references to the parameters can't be hidden in some other variable such as test. If the variables are hidden, then you need to use unapply. If they're explicit, the arrow is much more efficient. (The inefficiency is only in the function-definition step, not in the uses of the function.)

While I was typing the above, you added a question about a "multi-function" b[0]. There are a vast number of ways that that can be handled, but every general solution that I can think of is too arcane to descibe to you at this point in your Maple learning. I suggest that at this point you simply define them as two separate functions.

Your Question doesn't make sense. Are those two separate questions? If so, are they related somehow? I don't understand "convert this value in single"; it doesn't mean anything in English. Do you mean that you want to separate the real and imaginary parts of that number?

Your equation has four variables. There is no way to find their values. Generally that requires that there be the same number of equations as variables.

@Kitonum My statement "There are no real roots" was not based on fsolve's inability to find a real root. I would never assume that fsolve not returning a result meant that the result didn't exist. Indeed, it very often means that it found an approximate root but was unable to refine it to Digits precision.

My statement was based on several plots of N:= numer(P1) and its derivative. The denominator of P1 is obviously strictly positive, and hence irrelevant to the root-finding. N is essentially a degree-18 polynomial: There are some arctan factors in some terms, but they are essentially constant considering the huge range of the polynomial, so safe to assume arctan= -1 (just for the purpose of deciding whether there's a real root). The plots and derivative indicate that N has a unique local minimum that's positive.

@Christian Wolinski Even after defining the aliases your way, the following will not work:

for k to 4 do op(a[k]), op(u[k]) od;

Yet this is exactly what the OP wants to do: Use a variable to index the aliased functions. It's not a bug; by design it will not work.

@BennyMopps

 $ is the repetition operator. `$`~ applies it elementwise to each member of a list.

@Preben Alsholm My interpretation of the OP's intended meaning is identical to Kitonum's. Of course, I also immediately realize that this is ambiguous.

@robertocooper 

The symbol-forming operator `...`​​​​​​​: A symbol (in its specific sense as a Maple type) is what might be commonly called a "variable" in programming languages. (They are a subset of Maple names, the only difference being that a name can have indices.) You probably already understand, at some level, the basic rules for making symbols: just about any combination of letters, numerals, and underscores that doesn't begin with a numeral. But actually any sequence of characters whatsoever, no matter how weird, can be a symbol if you enclose it in `...`. If the symbol would otherwise be a reserved word, then the quotes are required to use it in any other context. Such is the case with Kitonum's `if`---if without quotes is a reserved word---and the "other context" is that it's being used as a function name. That `if` and ifelse mean the same thing is irrelevant (to the meaning of `...`, not to the meaning of `if`).

Symbol forming is the only way that the back quotes are used in Maple. They are always used in pairs. Symbols have many similarities with strings, which are formed with double quotes "...". Single forward quotes '...' are also used in pairs in Maple; however, their meaning is completely unrelated to symbols or strings, so be careful not to confuse them with back quotes.

The elementwise operator ~: This operator has an action similar to the commands map and zip. It duplicates the action of some other operator (to which it has been appended) over the contents of a container or containers. This is called elementwise operation (see ?elementwise). In the case at hand, the matrices are the containers. The result of M = Id is exactly what it looks like: an equation whose both sides are matrices. But the result of M =~ Id is a single matrix whose every entry is an equation formed from corresponding entries of M and Id.

Unlike the back quotes, the tilde (~) has several uses in Maple, both in input and output. The majority of its uses in input are elementwise operations.

For further help: In my opinion, this website, MaplePrimes, is by far the best place to get help about these things. There's also the Maple Programming Guide, which is available directly within Maple's help system.

@Yo Since Maple 17 (I think), one seq with no index is sufficient:

Sys:= {seq}(M =~ Id);

@student_1 There is a sigularity for any rho <= -1, so you need to assume rho > -1.

Each ​​​​​​psi[i] is piecewise linear in t. Your integral is thus essentially the same as

J:= simplify(int((A^(rho+1) - t^(rho+1))^(alpha-1)*t^rho*(B*t+C), t= 0..A)
    assuming alpha > 0,  rho > -1, A > 0;

My Maple can easily do that integral, although the result before simplification is a bit scary looking. You then just need to change A to j*h and change B and C to their appropriate values over the piecewise branches.