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  • Vladimir Popov and Ekaterina Leleka

    Solitary waves, or solitons were first described by Scott Russell, who noted the phenomenon while riding alongside a canal in 1834. He described a peculiar wave in the canal wave a single well-organized heap that propagated, seemingly without dissipation, for several miles. As a naval designer, Scott recognized that there were important things to be learned from these unusual waves.

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    Here is an example to illustrate the problem.
     > y := SQRT(4);
                                       y := SQRT(4)
    To get the square root function, you must use the name "sqrt", because Maple is case sensitive. Other examples of this are:
    • use "Pi" rather than "pi" to get 3.141etc
    • use "exp(1)" rather than "e" to get 2.718etc
    • use "I" rather than "i" to get the square root of minus 1
    Also note that, for example, "Int" and "int" are both Maple commands, but work differently.

    Here are some examples to illustrate syntax errors.
     > fsolve((1-x)/x^2),x);
     `)` unexpected
    In this case, I made a typing error; there is an extra right parenthesis after the "2". Removing it fixes the problem.
     > fsolve((1-x)/x^2,x);
     > y : = sqrt(4);
     `=` unexpected
    In this case, the problem is that the ":=" has a blank separating the ":" and the "=".
     > y := sqrt(4);
                                          y := 2
     > by:=3;
     `:=` unexpected
    In this case, the problem is that the variable name "by" is a word

    Here are some examples illustrating this problem
     > x:=3;
       ...various other calculations, during which you forget that you
          gave x a value
     > solve(2*x=1,x);
     Error, (in solve) invalid arguments
     > plot(2*x,x=-1..1);  No complaint is written out, but the plot is
                           just the line y=6.
    Here x already equals 3, so it doesn't make sense to use it in an assertion like "2*x=1", and plotting "2*x" is just plotting "6". Just as the above section shows an example of having too many indeterminates, this example shows what happens when there are too

    Here are two correct ways to define functions.
     > f:=2-x;           One way is by assigning a formula to a name.
     > plot(f,x=-1..1);  If you use this method you can refer to f,
     > solve(f=0,x);     BUT referring to "f(x)" yields nonsense.
     > f(x);      WRONG      
                                         2 - x(x)
     > f:=x->x^2;          Another way is by using an arrow. 
     > f(x);               If you use this method you can refer to f(x),
     > f(1);               BUT referring to just "f" only yields "f",
     > plot(f(x),x=-1..1); not the function.
     > solve(f(x)=0,x);
    Some commands change the internal state of the calculation, so the results have to be different each time. For example, if x is 1, entering x:=x+1; repeatedly obviously yields values of x that count up. A less obvious way that a command can do different things different times it is used is if it includes the % reference to the previous result. Then, the result from the command will depend on what the previous result was. It is less confusing to assign a name to a result you want to use again, rather than referring to it with %.
    To undefine x, enter x:='x'; To restart Maple with its memory cleared, enter restart.
    Help with using the simple Maple Commands
    Any questions that apply to plotting in Maple will appear here.

    A1: You forgot to specify a range on the independent variable.

     > f:=2-x;
     > plot(f);              WRONG
     Plotting error, empty plot
     > plot(f,x=-1..1);      RIGHT

    A2: You might be plotting a quantity that isn't defined. For example, you might have defined Y but then asked Maple to plot y. Maple is case-sensitive, and many strange behaviors are the result of typing a variable name in the wrong case.

    Another way a plotted quantity can be undefined is if you didn't use the assignment operator := to define it.

     > y=sin(x);              WRONG
    When you open a Maple worksheet you must execute it to get the variables defined. You can do this by stepping through the commands from the beginning, or by clicking on the execute all button on the toolbar which looks like this, !!!
    Click on "File" and select "Print" from the menu.
    Instead of trying to follow the numerous Help menus, try entering ?topic to go directly to the help page you want. For example, to get help with the int (integration command), enter ?int at the Maple prompt. You will working examples for each command at the bottom of the help page for the command.
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