{VERSION 5 0 "IBM INTEL LINUX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 16 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Helvetica" 0 16 0 0 255 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "R3 Fo nt 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 0 9 0 0 0 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 0 9 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 0 {PARA 18 "" 0 "" {TEXT -1 28 "Maple f\374r \"Fortgesch rittene\"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 53 "Zuweisungen und verz\366gerte Zuw eisungen bei Funktionen" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Verz \366gerte Zuweisung " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x ->x^3+x^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(f(x),x); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "fs:=x->diff(f(x),x);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "fs(1);" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 98 "Bei Funktionsdefinition durch -> wird die Definiti on erst bei Verwendung der Funktion ausgewertet." }{MPLTEXT 1 0 0 "" } }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "Sofortige Zuweisung" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "fs:=unapply(diff(f(x),x),x);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "unapply(expr,x) entspricht x->ausw ertung von expr" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "fs(1);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 39 "Schl eifen und andere Kontrollstrukturen" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "for from to do od;" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "for i from 1 to 10 do print(`Hello World`);od;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 54 "for i from 1 to 10 do print(`Hello World Nr `| | i);od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "for i from 1 to 10 do evalf(Pi,i); od;" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 12 "whil e do od;" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "xneu:=2;xalt:=0 ;\nwhile abs(xneu-xalt)>10^(-20) do\n xalt:=xneu;\n xneu:=1/2*(x alt+2/xalt);\nod; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eval f(xneu,20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "evalf(xneu-s qrt(2),100);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 16 "if then else fi ;" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "r:=rand(10);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "if r()<5 then \n print(\"k leiner als 5\") \nelse \n print (\"gr\366\337er als 5\") \nfi;" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 6 "add();" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "x1:=[a,b,c,d,e,f,g];\nx2:=[1,2,3,4,5,6,7];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "add(x1[i],i=1..nops(x1));" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "add(x2[i],i=1..nops(x2)); " }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 27 "Selbstdefinierte Funktione n" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Pfeilnotation" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "norm2:=v->sqrt(add(v[k]^2,k=1..nops (v)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "norm2([1,2,3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:='a';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "norm2([a,b,c]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "v1:=vector([a,b,c]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "norm2(v1);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 " \"proc\"-Notation" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "norm2:= proc(v) \n sqrt(add(v[k]^2,k=1..nops(v)));\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "norm2([a,b,c]);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 10 "norm2(v1);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Zwischenergebnisse" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "s tdabw1:=x->[mu=add(x[l],l=1..nops(x))/nops(x),sigma=1/(nops(x)-1)*sqrt (add(((x[k]-(add(x[l],l=1..nops(x))/nops(x)))^2,k=1..nops(x))))];\n" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "xs:=[seq(rand(1000)()*0.01 ,i=1..100)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "stdabw1(xs) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "stdabw2:=proc(x) loca l i,m,n,s;\n n:=nops(x);\n m:=add(x[i],i=1..n)/n;\n s:=1/(n-1 )*sqrt(add((x[i]-m)^2,i=1..n));\n [mu=m, sigma=s];\nend;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "stdabw2(xs);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "Typ\374berpr\374fung" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "stdabw1(5);\nstdabw2(5);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 151 "stdabw3:=proc(x::list) local i,m,n,s;\n \+ n:=nops(x);\n m:=add(x[i],i=1..n)/n;\n s:=1/(n-1)*sqrt(add((x[i] -m)^2,i=1..n));\n [mu=m, sigma=s];\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "stdabw3(xs);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "stdabw3(5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "stdabw3([5]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 218 "std abw4:=proc(x::list) local i,m,n,s;\n n:=nops(x);\n m:=add(x[i],i =1..n)/n;\n if n>1 then \n s:=1/(n-1)*sqrt(add((x[i]-m)^2,i =1..n));\n else\n s:=`Undefiniert.`;\n fi;\n [mu=m, s igma=s];\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "stdabw4(x s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "stdabw4(5);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "stdabw4([5]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 200 "norm2:=proc(x::\{list,vector\}) lo cal l,n;\n if type(x,list) then\n l:=x;\n elif type(x,vec tor) then\n l:=convert(x,list);\n fi;\n \n n:=nops(l); \n sqrt(add(l[i]^2,i=1..n));\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "norm2([a,b,c]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "v1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "eval m(v1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "norm2(v1);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "norm2(5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "norm2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "eval(norm2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "eval(norm);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "interf ace(verboseproc=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "eval (norm);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "eval(abs);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "eval(int);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "Beispiel: Fibonacci-Zahlen" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "f1:=proc(n::nonnegint) \n if n<2 \+ then\n n;\n else\n f1(n-1)+f1(n-2);\n fi;\nend;\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "seq(f1(k),k=0..10);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f1(25);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 209 "f2:=proc(n::nonnegint) local x2,x1,x0,k;\n \+ x2:=0; \n x1:=1;\n for k from 2 to n do\n x0:=x1+x2;\n \+ x2:=x1;\n x1:=x0;\n od;\n if n<2 then \n n; \n else\n x0;\n fi;\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "seq(f2(k),k=0..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f2(25);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " time(f1(25));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "time(f2(25 ));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "time(f2(500));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "f3:=proc(n::nonnegint) \n \+ option remember;\n if n<2 then\n n;\n else\n f3(n-1)+ f3(n-2);\n fi;\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "s eq(f3(k),k=0..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "time( f3(25));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "time(f3(500)); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f:='f';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "f4_proto:=rsolve(\{f(n)=f(n-1)+f(n- 2),f(0)=0,f(1)=1\},f);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f 4:=m->normal(subs(n=m,f4_proto),expanded);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "seq(f4(k),k=0..10);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "time(f4(25));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "time(f4(500));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(combinat);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " f5:=k->fibonacci(k);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "seq (f5(k),k=0..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "time(f5 (25));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "time(f5(500));" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "time(f5(10^5));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "time(f2(10^5));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eval(fibonacci);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}{MARK "0 1 0 0" 6 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }