> myname := 1.5;Once you hit return after this Maple line, any time the string of characters myname is used, it will have the value of 1.5. Note the use of the colon in front of the equal sign. This is necessary and if you forget the colon, Maple will not give an error message. It will appear as if you correctly assigned the value 1.5 to the label myname, however when you try to use myname again in the worksheet, it will not have the value 1.5.
> p := 5; > p; > p := 'p'; > p;Once you have cleared the variable, you are free to use it again. Another thing to keep in mind is that if you close your Maple worksheet for any reason and reopen it, none of the commands will be stored in memory until you re-execute each command by hitting return after each of the Maple lines. This can also be done by clicking on the Edit menu and choosing Execute worksheet, however, this could be time consuming if there are a lot of plots in the worksheet.
> expr := x^3+3*x^2-x+1;Note that in the expression above, there is an asterisk between 3 and . A common mistake is to write two functions next to each other without the "*" symbol. This would give incorrect results when using this expression since Maple doesn't understand implied multiplication. Another thing to keep in mind is when entering expressions in Maple that require the use of parentheses for grouping, the symbols ``(`` and ``)'' should be used since square brackets and curley brackets have special purposes in Maple.
> f := x-> x^3+3*x^2-x+1;Below is how ``NOT'' to enter a function:
> f(x) := x^3+3*x^2-x+1;The difference between expressions and functions are first the obvious, that expressions do not have to satisfy the definition of a function in the sense that for each input , there is a unique value . A function may be defined as an expression, but not all expressions can be defined as functions. The differences in Maple are numerous as you will see below when we evaluate the expression or function for a given value as well as when using the plot command.
> subs(x=2,expr); > eval(expr,x=2); > subs(x=2.,expr); > subs(x=1/2,expr); > subs(x=0.5,expr);In the subs command, the first argument tells Maple what you would like to substitute in for . The second argument tells Maple what expression you are substituting into. Note the difference in outputs when a whole number or fraction is entered compared to a decimal. In many cases, the subs command inserts values into the exptession but does not perform the evaluation in which case the eval command may be better for evaluating an expression. This can be seen in the example below.
> subs(theta=Pi,sin(theta)*cos(theta)); > eval(sin(theta)*cos(theta),theta=Pi);In Maple, functions are much easier to evaluate than expressions. In order to evaluate the function at , then simply type
> f(2);Here are a few more examples of evaluating functions.
> f(a+h); > f(Pi); > evalf(f(Pi));Note the use of the evalf command in the last example above. This command is used when we want Maple to output the answer in decimal form. If this command is not used, the output to your Maple commands will be calculated analytically, where as the evalf command forces Maple to calculate the answers numerically. The evalf command has one essential argument, however a second argument can be added in order to tell how many digits we want to be in the answer. The example below evaluates using 10 digits, not 10 decimal places.
> evalf(Pi,10);
> f := x-> x^2; > plot(f(x),x=-2..2);The plot command above has two essential arguments. The first argument is the function(s) or expression(s) that you want to plot. The function or expression can be typed in before the plot command or you can simply type it in as the first argument. The second argument is the range of numbers for the -axis. The plot command allows you to add additional optional arguments as well. For instance, you may want to also restrict the y-axis range or add a title to your plot.
> plot(x^2,x=-2..2,y=-5..5,title=`My First Plot`);This particular command allows you to add arguments, but if you were to leave off one of the essential arguments, you will get an error message. You can also plot more than one function or expression on the same graph by enclosing them in curly braces ``{}'' and separating them by commas. For example, we can plot and on the same graph.
> f := x-> x^2-2; > g := x-> -x+2; > plot({f(x),g(x)},x=-4..4);