{"id":836,"date":"2016-09-16T19:19:43","date_gmt":"2016-09-16T19:19:43","guid":{"rendered":"http:\/\/wordpress.rose-hulman.edu\/rickert\/?page_id=836"},"modified":"2016-09-16T19:21:38","modified_gmt":"2016-09-16T19:21:38","slug":"maple-command-summary","status":"publish","type":"page","link":"https:\/\/wordpress.rose-hulman.edu\/rickert\/maple-command-summary\/","title":{"rendered":"Maple Command Summary"},"content":{"rendered":"

Please e-mail me<\/span><\/u><\/a> if you have any useful suggestions about this page.<\/strong><\/h3>\n

All Maple<\/i> commands must end with a semi-colon ;<\/tt>
\n<\/span> To define a variable, use :=<\/span><\/tt>. The lone =<\/span><\/tt> sets up an equation, it does not define the variable.
\nMaple<\/i> may be used to do arithmetic computations. For example, 2+3; 17-8; 2*5; 1001\/13; 2^20;<\/tt>
\n<\/span> The evalf<\/span><\/tt> command will numerically evaluate an expression (it gives a f<\/span>loating point eval<\/span>uation)
\nevalf(Pi);
\n3.141592654<\/span>
\nevalf(sqrt(2));
\n1.414213562<\/span>
\nevalf(exp(1));
\n2.718281828<\/span><\/span><\/tt><\/p>\n

Manipulating algebraic expressions<\/i>
\nThe expand<\/tt> command may be used to expand an algebraic expression. For example,
\nexpand((x+2)^3);
\nx3<\/span><\/sup>+6x2<\/span><\/sup>+12x+8<\/span><\/tt>
\nThe simplify<\/tt> command may be used to simplify complicated expressions.
\nThe subs<\/tt> commands may be used to make a substitution,
\n<\/span>f=x^3+2*x + 7; subs( x=x^2, f);
\nx6<\/span><\/sup> + 2x2<\/span><\/sup> + 7<\/span>
\nsubs( x=1, f);
\n10<\/span><\/span><\/tt><\/p>\n

Graphs<\/i>
\nThe plot<\/tt> command may be used to plot simple graphs,
\nplot( x^3, x=-3..3);
\nplot( 1\/x, x=-2..3, y=-5..5);
\nf:=x-x^3; g=sin(x); plot({f,g},x=-1..1);<\/tt>
\nf:=x-x^3; g=sin(x); plot([f,g],x=-1..1,color=[red,blue]);<\/span> (you won’t generally have to worry about making graphs different colors)
\nTo plot parametric equations, place the parametrizations and the limits on the parameter inside []<\/tt>:
\nplot( [cos(t),sin(t),t=0..2*Pi]);<\/tt><\/span><\/p>\n

Equations<\/i>
\nThe solve<\/i> command may be used to solve equations,
\nsolve( 3*x+y=9, y);
\n3x+9<\/span>
\nsolve( x^2 + x -6 =0, x);
\n-3, 2 <\/span>
\nsolve( { x+y=2, 2*x+y=3},{x,y});
\n{x=1,y=1}<\/span>
\n<\/tt>
\nThe results of these Maple<\/i> evaluations may be used in later calculations
\n<\/span>sol:=solve( x^2 + x -6 =0, x);
\nsol<\/i>:=-3, 2 <\/span>
\nsubs( x=sol[1], 2*x+1);
\n-5<\/span>
\nplugs the first solution (x<\/i>=-3) into the expression 2x<\/i>+1 and returns the value produced. (2(-3)+1=-5)<\/span><\/tt><\/p>\n

The fsolve<\/tt> command may be used to numerically determine real solutions to equations,
\nfsolve( cos(x)=x,x);
\n.7390851332<\/span>
\nfsolve( x^3-3*x+1=0,x);
\n-1.879385242, .3472963553, 1.532088886<\/span><\/span><\/tt><\/p>\n

functions<\/i> The trigonometric funcstions are defined in Maple<\/i> by
\n sin(x), cos(x), tan(x), cot(x), sec(x),csc(x)<\/tt>
\nThe exponential function ex<\/span><\/sup><\/i> is given by exp(x)<\/tt>
\nThe natural logarithm is given by log(x)<\/tt>
\nThe absolute value function is given by abs(x)<\/tt><\/p>\n

vectors<\/i>: We may define a vector by
\nv:=[3,4];<\/tt>
\nIf we wish to find the magnitude of the vector, we must load the Maple<\/i> linalg<\/span> package.
\nwith(linalg):<\/tt>
\nand use the command
\n<\/span>mag:=norm(v,2);
\nmag:=5<\/span>
\n<\/tt> The direction vector is given by a parallel unit vector v<\/b>\/||v<\/b>||;
\n<\/span> dir:= v\/mag;
\ndir:=[3\/5,4\/5]<\/span><\/tt>
\nTo bypass the linalg<\/tt> package, you may simply compute the magnitude by finding the square root of the sum of the squares of the components;
\n<\/span>mag1:= sqrt( v[1]^2+v[2]^2);
\nmag1:= 5<\/span><\/tt>
\nThose of you who enjoy digging more deeply into Maple<\/i> could also try creating your own Maple<\/i> function to compute the size of a vector;
\n<\/span> siz:= v -> sqrt(v[1]^2+v[2]^2);
\nsiz(v);
\n5<\/span>
\n<\/tt>
\nHelp<\/i>: Maple<\/i> help for functions may be called by type a ?<\/tt> followed by the command. For example,
\n<\/span> ?plot;
\n?log;
\n?solve;
\n?subs;<\/span><\/tt><\/tt><\/tt><\/p>\n

parentheses, braces and brackets<\/i> Braces (curly braces), {}<\/tt>, are used to make lists (or sets) of elements in Maple<\/i>. The order of the terms is irrelevant, Maple<\/i> will reorder according to its own “whims” and remove redundant elements. For example,
\n {1,5,3,3,2};
\n{1,2,3,5}<\/span>
\n{x^2,sin(x),x,cos(x)};
\n{x,sin(x),cos(x),x^2}<\/span>
\nBrackets (square brackets), []<\/tt>, are used to make Ordered lists. Maple<\/i> will keep elements in the same order that you listed them. This is very useful for describing points (ordered pairs) and vectors and subscripts in a list.
\n<\/span> [1,5,3,3,2];
\n[1,5,3,3,2]<\/span>
\n[x^2,sin(x),x,cos(x)];
\n[x^2,sin(x),x,cos(x)]<\/span>
\nfn:=[x^2,sin(x),x,cos(x)];
\nfn:=[x^2,sin(x),x,cos(x)]<\/span>
\nfn[1];
\nx2<\/span><\/sup><\/span>
\nfn[4];
\ncos(x)<\/span>
\nparentheses, ()<\/tt>,are used by Maple<\/i> to enclose a sequence of expressions to be evaluated in a function.
\n<\/span>f:=(x,y)->x^2+y^2;
\nf(3,4);
\n25<\/span>
\nf(1,10);
\n101<\/span><\/tt><\/span><\/tt><\/tt><\/p>\n

<!– diff(sin(x),x);<\/tt> differentiates the sine function with respect to x<\/i>.
\n–><\/p>\n

\n

Go to<\/p>\n