\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fmodern\fprq1 Lucida Sans Typewriter;}{\f3\fswiss\fprq2 Trebuchet MS;}{\f4\fswiss\fprq2 System;}} {\colortbl\red0\green0\blue0;\red255\green0\blue0;\red0\green0\blue255;} \deflang1033\pard\ri4\plain\f3\fs36\cf0 Chapter 7 A brief introduction to programming\plain\f3\fs28\cf0 \par \par 7.1 Variables again \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}reset(): \par {\pntext\f1\'b7\tab}A := 1.23: \par {\pntext\f1\'b7\tab}B := A: \par {\pntext\f1\'b7\tab}A := A*100: \par {\pntext\f1\'b7\tab}C := 200: \par {\pntext\f1\'b7\tab}C := C+1: \par \pard\ri4\plain\f3\fs28\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs28\cf1 {\pntext\f1\'b7\tab}A\plain\f2\fs28\cf1 , B, C \par {\pntext\f1\'b7\tab}(x.i := i^2) $ i=1..10000: \par {\pntext\f1\'b7\tab}x1, x23, x567, x9999 \par {\pntext\f1\'b7\tab}(x234 + x456)/x76 \par {\pntext\f1\'b7\tab}Functions := (a.i := x^i) $ i=1..10: \par {\pntext\f1\'b7\tab}plotfunc2d(Functions, x=0..1) \par {\pntext\f1\'b7\tab}(a[n] := n/(n+1)) $ n=1..10 \par {\pntext\f1\'b7\tab}a[4], a[7], a[21] \par {\pntext\f1\'b7\tab}b[1] := 123: \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 b[2] := 234: \par b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}a[1] := x^2: \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 a[2] := (x -> x^2): \par a \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}subs(a[1], x=2) \par {\pntext\f1\'b7\tab}a[2](2) \par \pard\ri4\plain\f3\fs28\cf0 \par >>>>>>>>>> Time for Exercise 7.1 \par \par 7.2 Procedures \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}mean := (x,y) -> (x+y)/2 \par \pard\li50\ri6\plain\f2\fs28\cf2\protect 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000000FB02E8FE0000000000009001010000020700000054696D6573204E657720526F6D616E00 D89FF377E19FF3772020F577EE0B6679040000002D010A00040000002D01040007000000210501 00790033019D06040000002D010300070000002105010032008A02B305040000002D0105000400 00002D0106000700000021050100C5008E01BB040700000021050100C5008E0163050700000021 050100C5008E010B060700000021050100C5008E01900608000000FA0200000000000000000000 040000002D010B0004000000F001000007000000FC020000FFFFFF000000040000002D01000004 000000F00101001C000000FB021000070000000000BC02000000000102022253797374656D0000 270D0AE438E91200D89FF377E19FF3772020F577EE0B6679040000002D010100040000002701FF FF04000000F001020004000000F001030004000000F001040004000000F001050004000000F001 060004000000F001070004000000F001080004000000F001090004000000F0010A000400000027 01FFFF030000000000 }\plain\f2\fs28\cf2\protect \par \pard\li50\ri2\plain\f2\fs28\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}Mean := proc(x,y) \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 local u; \par begin \par u := (x+y)/2; \par return(u) \par end_proc: \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}Mean(123,456), mean(123,456) \par {\pntext\f1\'b7\tab}test := proc(a,b) \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 begin \par return(a); \par return(b) \par end_proc: \par \pard\ri4\plain\f3\fs28\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}test(1,2) \par \pard\ri4\plain\f3\fs28\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}sequence := proc(n,m) \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 local temp; \par begin \par temp := k/(k+1)*(-1)^k $ k=n..m; \par return(temp) \par end_proc: \par \pard\ri4\plain\f3\fs28\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}sequence(9,15) \par {\pntext\f1\'b7\tab}sequence(1500,1505) \par {\pntext\f1\'b7\tab}// Program to draw pattern of squares, \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 // June 2nd, 2005 \par // ----------------------------------------------------------------------------------------------------------------------------- \par // procedure to draw a square with given side \par // ----------------------------------------------------------------------------------------------------------------------------- \par square := proc(side) \par local T; \par begin \par T:=plot::Turtle(); \par T::forward(side); T::right(PI/2); \par T::forward(side); T::right(PI/2); \par T::forward(side); T::right(PI/2); \par T::forward(side); T::right(PI/2); \par return(T) \par end_proc: \par // -------------------------------------------------- \par // procedure to make 4 copies of a pattern \par // note: pattern must be a list or set of \par // graphical objects \par // -------------------------------------------------- \par fourCopies := proc(pattern, distance) \par begin \par s1 := op(pattern): \par s2 := plot::Translate2d([distance,0], s1): \par s3 := plot::Translate2d([0,distance], s1): \par s4 := plot::Translate2d([distance,distance], s1): \par return(s1,s2,s3,s4) \par end_proc: \par // here we start using our procedures \par // develop a list of squares \par squares := [(square(i) $ i=1..10)]: \par // develop the final pattern \par myPattern := fourCopies(squares, 11): \par // finally plot the whole pattern \par plot(myPattern) \par \pard\ri4\plain\f3\fs28\cf0 \par >>>>>>>>>> Time for Exercise 7.2 \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}READPATH := "d:\\\\My Documents\\\\MuPAD": \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 WRITEPATH := "d:\\\\My Documents\\\\MuPAD": \par // here you can put more statements if \par // you need them \par print("My configuration of MuPAD.") \par \pard\ri4\plain\f3\fs28\cf0 \par 7.4 Creating user libraries \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}MyPI := 3.14159: \par {\pntext\f1\'b7\tab}toDeg := proc(x) \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 begin \par return(float(x*180/PI)) \par end: \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}toRad := proc(x) \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 begin \par return(PI*x/180) \par end: \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}information := proc() \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 begin \par print("Trigonometric procedures: toDeg,toRad") \par end: \par \pard\ri4\plain\f3\fs28\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}toDeg(2*PI/4) \par {\pntext\f1\'b7\tab}toRad(361) \par {\pntext\f1\'b7\tab}information() \par {\pntext\f1\'b7\tab}write(Text,"tryg.mu",MyPI,toRad,toDeg,information) \par {\pntext\f1\'b7\tab}read("tryg.mu") \par {\pntext\f1\'b7\tab}information() \par {\pntext\f1\'b7\tab}toDeg(PI/3) \par {\pntext\f1\'b7\tab}toRad(120) \par \pard\ri4\plain\f3\fs28\cf0 \par >>>>>>>>>> Time for Exercise 7.4 \par \par 7.5 Control structures \par \par 7.5.1 Logical conditions \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f3\fs28\cf1 {\pntext\f1\'b7\tab}1\plain\f2\fs28\cf1 > 2, 10 >= 5, sin(x) < 1, x^2 + y^2 > 1 \par {\pntext\f1\'b7\tab}is(1 > 2), is(10 >= 5) \par {\pntext\f1\'b7\tab}not(TRUE and FALSE) and not(TRUE or FALSE) \par {\pntext\f1\'b7\tab}FALSE or TRUE \par {\pntext\f1\'b7\tab}is(sin(x) < 1) \par {\pntext\f1\'b7\tab}is(x^2 + y^2 > 1) \par {\pntext\f1\'b7\tab}is( subs(x^2+y^2>1, x=1/3, y=1/2) ) \par {\pntext\f1\'b7\tab}is( subs(x^2+y^2>1, x=1, y=1) ) \par {\pntext\f1\'b7\tab}FALSE and UNKNOWN \par {\pntext\f1\'b7\tab}TRUE or UNKNOWN \par {\pntext\f1\'b7\tab}TRUE and UNKNOWN \par {\pntext\f1\'b7\tab}not(TRUE and UNKNOWN) and not(TRUE or UNKNOWN) \par \pard\ri4\plain\f3\fs28\cf0 \par >>>>>>>>>> Time for Exercise 7.5.1 \par \par 7.5.2 Making decisions \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}f := x -> sin(x)/x \par {\pntext\f1\'b7\tab}f(PI), f(12.45), f(-34.98) \par {\pntext\f1\'b7\tab}f(0) \par {\pntext\f1\'b7\tab}f := x -> if x=0 then 0 else sin(x)/x end_if: \par {\pntext\f1\'b7\tab}f(PI), f(12.45), f(-34.98), f(0) \par {\pntext\f1\'b7\tab}F := proc(x) \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 local result; \par begin \par if x=0 then \par result:=0 \par else \par result:=sin(x)/x \par end_if; \par return(result) \par end_proc: \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}F(PI), F(12.45), F(-34.98), F(0) \par \pard\ri4\plain\f3\fs28\cf0 \par Technical comment: \par ================= \par The programming construction described here is known as an \par if-then-else control structure, or a conditional structure or an \par if structure for short. The if structure can be used in a simplified \par form such as if..then..end_if. \par \par Technical comment: \par ================= \par While writing programs in MuPAD and other \par programming languages, it is convenient to use indents. This is the \par best way to highlight the structure of the program. For instance, \par the statement if x=0 then result:=0 else result:=sin(x)/x end_if \par contains two further statements, result:=0 and result:=sin(x)/x. \par By using indents we are able to show the dependency between \par successive statements. In this book, we usually use three spaces \par for indents. \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}a := 1: b := 4: c := 2: \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 if a<>0 then \par delta := b^2 - 4*a*c; \par if delta >= 0 then \par x1 := (-b + sqrt(delta))/(2*a); \par x2 := (-b - sqrt(delta))/(2*a); \par x1, x2 \par else \par print("No real results") \par end_if \par else \par if b<>0 then \par x1 := -c/b \par else \par print("No results") \par end_if \par end_if \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}Quadratic := proc(a,b,c) \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 local delta, x1, x2; \par begin \par if a<>0 then \par delta := b^2-4*a*c; \par if delta >= 0 then \par x1 := (-b + sqrt(delta))/(2*a); \par x2 := (-b - sqrt(delta))/(2*a); \par return(x1, x2) \par else \par print("No real results") \par end_if \par else \par if b<>0 then \par x1 := -c/b; \par return(x1) \par else \par print("No results") \par end_if \par end_if \par end_proc: \par \pard\ri4\plain\f3\fs28\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}Quadratic(1,3,1) \par \pard\ri4\plain\f3\fs28\cf0 \par >>>>>>>>>> Time for Exercise 7.5.2 \par \par 7.5.3 Iterations \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}psum := 0: \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 for k from 1 to 10 do \par term := k/(k+1)*(-1)^k; \par psum := psum + term; \par end_for \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}psum := 0: \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 points := []: \par for k from 0 to 50 do \par term := k/(k+1)*(-1)^k; \par psum := psum + term; \par points := points.[[k,psum]] \par end_for: \par graph := plot::Polygon2d(points): \par plot(graph) \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}SumPlot := proc(n) \par \pard\li600\ri1\fi-300\plain\f2\fs28\cf1 local psum, points, k, term; \par begin \par psum := 0: \par points := []: \par for k from 0 to n do \par term := k/(k+1)*(-1)^k; \par psum := psum + term; \par points := points.[[k,psum]] \par end_for: \par return(plot::Polygon2d(points, YGridVisible=TRUE)): \par end_proc: \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f2\fs28\cf1 {\pntext\f1\'b7\tab}plot(SumPlot(100)) \par \pard\ri4\plain\f3\fs28\cf0 \par \plain\f3\fs36\cf0 The Animated Circles Example\plain\f3\fs28\cf0 \par {\object\objemb{\*\objclass VCam.Graphics.3}{\*\objname Object1}\objw5669\objh5669\objscalex99\objscaley99{\*\objdata 01050000 02000000 10000000 5643616D2E47726170686963732E3300 00000000 00000000 00B40200 D0CF11E0A1B11AE1000000000000000000000000000000003E000300FEFF090006000000000000 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