This is short introduction to MAPLE. I will review some of the basics of the programming languagethat will help you get doing basic programming.TOPIC 1: NUMBERS and POLYNOMIALSMAPLE can do arithmetic but unlike you calculator it is exact and calculations are done using as many digits are necessary: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:=%;One can refer to the previous command by using %.Maple also knows special kinds of numbers such as binomial coefficients, Fibonacci numbers, etc.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 can also create ordered lists by including into brackets the sequence: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JSFHJSFHf:=x^9+3*x^7-x^5+5*x^3+1;JSFHdiff(f,x,x,x);diff(f,x$6);JSFHJSFHOne can easily define abstract summations:sum(i^5,i=0..n);JSFHJSFHTOPIC 2: BASIC DATA STRUCTURES, OPERATORSMAPLE is a programming language that supports lists, sets, tables, arrays, etc.One can also generate sequences very easily and from them generate a set of numbers:seq (i^3,i=1..20);S:={%};T:={seq(2*i,i=1..46)};S union T;S intersect T;member(1331,S);member(17,T);JSFHNow we illustrate more commands about lists and how to transfer from set to lists. We also showhow to apply functions (map) to lists.L:=convert(T,list);map(x->x/2, L);JSFHMAPLE has a standard array data structure. U:=array(1..4,1..4);for i to 3 do for j to 4 do U[i,j]:=i^2-j^2; od; od;print(U);A string can also be formed by enclosing any sequence of characters in back quotes, for example`This is a strange string`;St:=%;n:=5;`n-1`:=n-1;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One can also write sequences:seq(i^2, i=2/3..8/3);The map function replaces each operand of an expression or a list or a set with the result ofapplying a function to it. Here are some examples:map(x->x^2,{7,9,10,11,2,3,7});L:=[seq(x^(3*i), i=0..7)];map(z->diff(z,x),L);map(z->int(z,x),L);The operators SUBS and SUBSOP are used for replacing a subexpression in a expression with a new value:a:=x^3+3*x+1;subs(x=y,a);subs(x=2,a);subs(x=weight,a);f:=x*y^2;subs(x=y,subs(y=x,f));subs({x=y,y=x},f);L:=[x,y,z];op(3,L);subsop(3=w,L);subsop(3=NULL,L);MAPLE as a programming language has several attributes common to object oriented languages (e.g. C++).In particular variables and procedure parameters can hold any valid MAPLE object. In principle MAPLEhas no declarations so it is up to the user to specify restrictions. For this one can test or define TYPESwhattype(4.5);whattype(567);whattype(x*y+y^6-8*x);type(x*y+y^6-8*x,polynom);TOPIC 3: PROCEDURES AND BASIC PROGRAMMINGAn important component of MAPLE is its programming language which can be used to do iteration,write procedures, use parameters and do recursive calls. Here are a few examples that illustrate the keypoints of the language. You need to practice yourself by attempting the homework exercises.Here is a procedure to compute the FIBONACCI NUMBERS. The purpose of the option rememberis to tell the system to store computed values as it proceeds.F:=proc(n) option remember; if n<2 then n else F(n):=F(n-1)+F(n-2) fi; end:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEiI0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVE7fk5PV35XRX5DQUxMflRIRX5QUk9DRURVUkVGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRic=seq(F(i),i=1..10);HERE is a routine to compute the STANDARD DEVIATION of a LIST OF NUMBERS. Notethat in this example we make a clear distinction which variables are used locally.sigma:=proc(data) local mean, n, s, x; n:=nops(data); if n <2 then ERROR(`input must contain at least 2 values`) fi; mean:=0; for x in data do mean := mean +x; od: mean:=mean/n; s:=0; for x in data do s:=s+(x-mean)^2; od; sqrt(s/(n-1));end;sigma([1,2,3,4,5,6]);LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=