MAPLE Lesson1 Modau Pheptinhsohoc

NI DUNGGii thiu MapleHng dn s dng MapleMt s hm s hc c bnCc php tnh i sCc php tnh gii tch thi s tuyn tnhLp trnh vi Maple

TI LIU THAM KHOPhan c Chu, S dng Maple trong Ton s cp v Ton cao cp, NXB KHKT, 2005Nguyn Hu in, Hng dn s dng Maple, www.ebook.edu.vn

GII THIU MAPLECc phn mm ton hc ph dng: Mathematica, Matlab, Maple ,.Maplei hc Waterloo (Canada)c a ra ln u tin vo nm 1981 Nm 1988: c pht trin thnh mt sn phm thng mi ca cng ty Waterloo Maple Inc. (c bit n l Maplesoft). Kt hp ngn ng lp trnh vi giao din Cc chc nng ton hc c vit bi ngn ng Maple, bin dch bi Maple kernel. Maple kernel c vit bi ngn ng C.

HNG DN S DNG MAPLEMi trng lm vic ca MapleA Toolbar B Context barC Section headingD Maple InputE Maple OutputF Execution group G PromptH Section range blanketCc Palette:I Expresson paletteJ Vector paletteK Matrix palettteL Symbol palette

Mi trng lm vic ca Maple

HNG DN S DNG MAPLEMt s phn trn worksheet:Execution Group (EG)SpreadsheetParagraphsSectionHyperlinkTo ra cc phn trn worksheet: menu Insert ->chn phn tng ng

HNG DN S DNG MAPLEHyperlinkCho php lin kt n 1 file dng URL khc hay mt worksheet khc

HNG DN S DNG MAPLESectionCho php to vn bn theo ch VD: Tch phn>Int(sin(x),x); >int(sin(x),x); o hmTnh o hm ca hm x>Diff(x,x) = diff(x,x);

HNG DN S DNG MAPLEParagraphCho php son tho cc on vn bn ging nh cc ngn ng son tho vn bn khc: Cho php cn l, chn font, thay i kch thc, chn kiu hiu ng ch: nghing, m, gch chn,...La chn thuc tnh cho vn bn: dng menu FormatNh vy: Section, paragraph, hypelink cho php ta to vn bn v sp xp li

HNG DN S DNG MAPLESpreadsheet

ABC1ExpressionThe IntegralThe IntegralValue2cos(x)Int(~a2,x)int(~a2,x)3sin(x)Int(~a3,x)int(~a3,x)4exp(x)Int(~exp(x),x)int(~a4,x)5ln(x)Int(~a4,x)int(~a5,x)

HNG DN S DNG MAPLESpreadsheetKt qu:

HNG DN S DNG MAPLEExecution Group c th l 1 lnh, 1 nhm lnh hay l lnh kt hp vi text Kt thc lnh:Du ':' khng cho trnh by kt qu, l cc cu lnh trung gianDu ';' cho php trnh by kt qu3 cch to lnh:nh lnh trc tip VD: >3+5;8 >diff(x,x);1 >f:=3+5: >8+f; 16

Dng menu context to lnh (Menu ng cnh)>2*x;2x> R1:=int(2*x,x);x2Ni dung menu context ph thuc vo kt quExcution Group

Cch th 3 to lnh l copy:Copy cu lnh t v tr ny sang v tr khcKo kt qu vo dng lnh;Ko kt qu th vo thCch chy EX: a con tr vo phm vi EX, ri n EnterKt qu ca cu lnh c thc hin gn nht s lu trong b nh vi 1 bin c bitVD:>5^2;25>%;25

Excution Group

Excution Group

Cch nhm cc cu lnh thnh GroupDng Shift+Enter > x:=3;x:=10*x;y:=x+5;> x:=3; x:=10*x; y:=x+5; x:=3x:=30y:=35Excution Group

Gp cc nhm: Bi en cc nhm sau n F4> x:=3;>x:=10*x;>y:=x+5; > x:=3; >x:=10*x; >y:=x+5;Excution Group

Tch cc nhm: a con tr vo v tr cn tch sau n F3 > x:=3; >x:=10*x; >y:=x+5;> x:=3;>x:=10*x;>y:=x+5;Excution Group

HNG DN S DNG MAPLES dng tr gip Dng Help tra cu cch s dng cc cu lnh: ? tn_lnhF1, Ctrl + F1Nhp biu thcS dng Maple Notation: nhp vo lnh di dng c phpS dng Standard Math Notation: nhp lnh vo di dng k php (dng 4 palette)To trang lm vic miFile/ New M trang lm vic File/OpenGhi trang lm vic: *.mw

HNG DN S DNG MAPLECc lnh: cc lnh trong gi (package) v cc lnh kiu toplevel.(phn bit ch hoa v ch thng!)Sau mi lnh phi c du ( : ) hoc ( ; )Maple b qua dng c du # (dng lm ch thch)S dng lnh trong trong gicch1: Tn_gi [tn_hm] ()cch 2: Thc hin lnh with(tn_gi) trc.

HNG DN S DNG MAPLELnh ? c dng tra cu hng dn v cc lnh v cc gi lnh?cho bit thng tin v cc tnh nng tr gip (Help)?librarycho bit cc lnh v hm chun?indexcho bit mc lc cc tr gip?plotcho bit thng tin v lnh plot?plot[polar] cho bit thng tin s dng lnh plot vi ta ccXem cc gi lnh?index, package s dng cc lnh toplevel, cn xo b nh trong ca Maple bng lnh restart.

HNG DN S DNG MAPLECc ton t (?+)+, -, *, /, ^ hoc **, modCc hngPi, piinfinityIexp(1)egammaS Euler CatalanS Catalantruengfalsesai

MT S HM S HC C BNCc ton tCc hm vi s nguynCc hm vi s du phy ngTng, tch v hn v hu hnS phc v cc hm c bitCch nh biu thc trong Maple

Phn nguyn ca thng (Integer Quotient)>iquo(17,2);8>iquo(17,3,'r');5>r;2Phn d ca thng (Integer Remail)>irem(23,4);3>irem(-23,-4);-3Cc hm vi s nguyn

Phn tch ra tha s>ifactor (10!);(2)8(3)4(5)2(7)Khai trin>expand(%);3628800Cc hm tr kt qu nguyn>trunc(2.7);2Tr s nguyn gn nht v pha 0>trunc(-2.7);-2Cc hm vi s nguyn

>round(2.7);3>round(-2.7);-3Ngc hm trunc>floor (2.5);2>floor(-2.5);-3floor to s nguyn ln nht ceil(-2.5);-2>ceil(2.1);3ceil to s nguyn nh nht >=xCc hm vi s nguyn

Cc hm vi s nguynS nguyn tisprime(n): kim tra n c l s nguyn t hay khngnextprime(n): cho bit s nguyn t gn nht ng sau nprevprime(n): cho bit s nguyn t gn nht ng trc nTnh giai tha: n!c chung ln nht:igcd( )> igcd(6,8,10);2Bi chung nh nht:ilcm( ) > ilcm(3, 4, 5); 60

Cc hm vi s du phy ngL im mnh ca maple: Maple lu kt qu di dng k hiu ton hc trong qu trnh tnh tonMaple lu kt qu di dng du phy ng ch khi c yu cuMaple c kh nng biu din c hng trm ti hng nghn ch s sau du phy ngHm evalf cho ta gi tr ca x di dng du phy ng vi kt qu gm n ch s, ngm nh l 10evalf(x), evalf[n](x), evalf(x,n)

Tng hu hn(definite summation)sum(f, k) sum(f, k = m..n) sum(f, k = alpha) sum(f, k = expr)Sum(f, k) Sum(f, k = m..n) Sum(f, k = alpha) Sum(f, k = expr)Parameters f - expression k - name; summation index m, n - integers or arbitrary expressions alpha - RootOf expression expr - expression not containing 'k'

Tng v hn (indefinite summation)sum(f, k=n.. infinity) Sum(f, k=n.. infinity)

Parameters f - expression k - summation index n - integers or arbitrary expressions

Tch hu hn (definite product)product(f, k) product(f, k = m..n) product(f, k = alpha) product(f, k = expr)Product(f, k) Product(f, k = m..n) Product(f, k = alpha) Product(f, k = expr)

Parameters f - expression k - name, the product index m,n - integers or arbitrary expressions alpha - RootOf expr - expression not containing k

Tch v hn (indefinite summation)product(f, k=n.. infinity) Product(f, k=n.. infinity)

Parameters f - expression k - summation index n - integers or arbitrary expressions

Tng, tch mt dy sadd - add up a sequence of valuesadd(f, i = m..n)add(f, i = x)add(f, i in x)mul - multiply a sequence of valuesmul(f, i = m..n)mul(f, i = x)mul(f, i in x)Tham sf expressioni namem, n numerical valuesx expressionLu : Hm sum, product tnh tng/tch v hn/hu hn trn k hiu, c thit k tr v kt qu l mt cng thc, khng phi mt gi tr r rng.

Cc ton tCc hm vi s nguynCc hm vi s du phy ngTng, tch v hn v hu hnS phc v cc hm c bitCch nh biu thc trong MapleMT S HM S HC C BN

S phc (Complex number)Ch ci I i din cho s phc (I - the root of x^2 = -1)

Hm GAMMA (Gamma function)GAMMA(z) - Tr gi trgamma (z) - Vit cng thc vi ch thngGamma (z) - Vit cng thc vi ch hoaz - algebraic expression

Hng PI: vit ch hoaPi: Vit ch thng

Hm Beta (Beta function)Beta(x,y)Parameters x - algebraic expression y - algebraic expression

Cch nh biu thc trong mapleDng cch nh dng ca maple, Maple s gip ta nhn dng hm trong 1 biu thcVD: sin(x), cos(x), tan(x), cot(x), ln(x), exp(x)Dng ton t v cc hm c sn trong th vin maplenh biu thc dng cc ton t theo qui tc ca Maple

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MAPLE Lesson1 Modau Pheptinhsohoc