> restart;MyName:=sfb;Today:="Sep 4, 2001";
> 
> #Syntax part one.
> #1. Expressions that begin with the comment character `#' are comments
> #2. Comments are not executed by Maple, but are a way of annotating the work
> #3. The difference between `:=' (assignment) and `=' (equals). 
> #The next line sets the variable `eqn' to be the equation `x^2-x-6=0'
> eqn := x^2-x-6=0;
> #We can use `eqn' just as if it were the equation, for example 
> solve(x^2-x-6=0);solve(eqn);
> Today;MyName;
> #Although Maple has functions, we will almost always work with expressions like
> f:=x^2;
> #Ways to get f(2) which should be 4
> subs({x=2},f);eval(f,{x=2});
> #Ways that might work, but DON'T
> f(2);subst({x=2},f);
> #function notation does NOT define functions
> h(x):=x^2;h(2);h;
> #Ways that sort of work, but cause problems so do NOT use them
> #(x:='x' clears the value of x. restart clears all variables).
> x;f;x:=2;f;x;g:=x^2;x:='x';x;f;g;
> #Syntax Part two, Parenthesize, starize, capitalize
> wrong:= x y;
> wrong:=x^-3;
> surprise:=a/b*c;surprise:=a/b/c;nosurprise:=a/(b*c);
> surprize:=pi;evalf(surprize);evalf(Pi);evalf(E);evalf(e);evalf(exp(1));
> surprize:=(x)(y);a:=subs({x=2,y=3},surprize);evalf(a);
> correct:=(x)*(y);b:=subs({x=2,y=3},correct);evalf(b);
> abc;
> plot(exp(x),x=-1..1,color=plum,thickness=2);
> with(student);with(plots);#Load some useful libraries
> completesquare(x^2+2*x+2,x);
> int(x^2,x);int(x^2,x=1..3);
> middlebox(x^2,x=1..3,4);
> leftbox(x^2,x=1..3,4);
> rightbox(x^2,x=1..3,4);
> #make our own trapbox -- done by a professional -- don't try this at home
> n:=4;a:=1;b:=3;f:=x^2;delta:=a+i*(b-a)/n;deltaPlus1:=delta+(b-a)/n;
> curve:=[seq(eval([delta,eval(f,x=delta)]),i=0..n)];
> boxes:=seq(POLYGONS(eval([[delta,0],[delta,eval(f,x=delta)],[deltaPlus1,eval(f,x=deltaPlus1)],[deltaPlus1,0]]),COLOR(RGB,.7,.9,.7)),i=0..n-1);
> plotA:=plot(curve,filled=true,color=COLOR(RGB,.7,.9,.7)):plotA;
> plotB:=PLOT(boxes):display(plotB);
> plotC:=plot(f,x=a..b,color=red):plotC;
> display(plotA,plotC);
> display(plotB,plotC);
> #Lets do some numerical work
> leftsum(x^2,x=1..3,100);value(leftsum(x^2,x=1..3,100));
> for i from 1 to 10 do evalf([2^i,leftsum(x^2,x=1..3,2^i)]); od;
> rightsum(x^2,x=1..3,100);value(rightsum(x^2,x=1..3,100));
> for i from 1 to 10 do evalf([2^i,rightsum(x^2,x=1..3,2^i)]); od;
> middlesum(x^2,x=1..3,100);value(middlesum(x^2,x=1..3,100));
> for i from 1 to 10 do evalf([2^i,middlesum(x^2,x=1..3,2^i)]); od;
> trapezoid(x^2,x=1..3,100);value(trapezoid(x^2,x=1..3,100));
> for i from 1 to 10 do evalf([2^i,trapezoid(x^2,x=1..3,2^i)]); od;
> simpson(x^2,x=1..3,100);value(simpson(x^2,x=1..3,100));
> Digits:=10;for i from 1 to 10 do evalf([2^i,simpson(x^2,x=1..3,2^i)]); od;
> #All at once
> for i from 1 to 10 do evalf([2^i,leftsum(x^2,x=1..3,2^i),rightsum(x^2,x=1..3,2^i),middlesum(x^2,x=1..3,2^i),trapezoid(x^2,x=1..3,2^i),simpson(x^2,x=1..3,2^i)]); od;
> #7.6
> f:=x^3*exp(x);a:=3;b:=6;answer:=int(f,x=a..b);error1:=array[1..10];error2:=array[1..10];
> d:=2;Digits:=20;
> for i from 1 to 10 do error1[i]:=value(leftsum(f,x=a..b,d^i)-answer); error2[i]:=value(rightsum(f,x=a..b,d^i)-answer); od:
> for i from 1 to 10 do evalf([i,error1[i],error2[i],error1[i]/error2[i]]); od;
> for i from 1 to 9 do evalf([i,error1[i]/error1[i+1],error2[i]/error2[i+1]]);od;
> for i from 1 to 10 do error1[i]:=value(trapezoid(f,x=a..b,d^i)-answer); error2[i]:=value(middlesum(f,x=a..b,d^i)-answer); od:
> for i from 1 to 10 do evalf([i,error1[i],error2[i],error1[i]/error2[i]]); od;
> for i from 1 to 9 do evalf([i,error1[i]/error1[i+1],error2[i]/error2[i+1]]);od;
> for i from 1 to 10 do error1[i]:=value(simpson(f,x=a..b,d^i)-answer); od:
> for i from 1 to 10 do evalf([i,error1[i]]); od;
> for i from 1 to 9 do evalf([i,error1[i]/error1[i+1]]);od;
>