Mapleda nomli va nomsiz buyruqlar bajartirilishining ikki XIL o`suli Standart funktsiyalar

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Maple muhitida hisoblashlar

Standart funktsiyalar.

Maple da standart funktsiyalarning ayrimlarini ro’yxatini keltiramiz:

N	funktsiya	Maple da	N	funktsiya	Maple da
1		exp(x)	12	cosecx	cosec(x)
2	lnx	ln(x)	13	arcsinx	arcsin(x)
3	lgx	lg10(x)	14	arccosx	arcos(x)
4		log[a](x)	15	arctgx	arctg(x)
5		sqrt(x)	16	arcctgx	arcctg(x)
6		abs(x)	17	shx	sh(x)
7	sinx	sin(x)	18	chx	ch(x)
8	cosx	cos(x)	19	thx	th(x)
9	tgx	tg(x)	20	cthx	cth(x)
10	ctgx	ctg(x)	21	-Dirak funktsiyasi	Dirac(x)
11	secx	sec(x)	22	-Xevisayd funktsiyasi	Heaviside(x)

Maple ga juda katta miqdorda maxsus funktsiyalar ham kiritilgan. Ular Bessel, Eylerning beta-, gamma-funktsiyalari, xatoliklar integrali, elliptik integrallar, har xil ortogonal ko’phadlar va hokazo. Eyler soni ye=2.718281828…. exp(x) orqali quyidagicha hisoblanadi: exp(1).

Topshiriq №1.3.
1. Matnli rejimda Amaliy topshiriq №2 deb yozing.
2. ni hisoblang.\\(t.10-2-58;j:0;1;-1;0.5;-0.5)
Komandani 1-to’g’ri o`sul bilan bajaramiz:
> a:=cos(12*Pi*(log[2](0.25)+log[0.25](2))/5);\\a:=1.
3. ifodani hisoblang.
Komandani smart o`sul (o’ngdagi jadval kontekst menyu)bilan bajaramiz:

>b:=(sin(Pi/8))^2+(cos(3*Pi/8))^2+(sin(5*Pi/8))^2+(cos(7*Pi/8))^2;

> R3 := evalf[5]( sin(1/8*Pi)^2+cos(3/8*Pi)^2 +sin(3/8*Pi)^2+cos(1/8*Pi)^2 ); \\R3:=2.0000

Komandani to’g’ri o`sul bilan tekshirib ko’ramiz:

> simplify(b); \\2

Ayrim ko’p uchraydigan buyruqlar va ularga doir misollar keltiramiz.

	Komanda	Ma’nosi	Parametrlaning ma’nosi
1	expand(eq)	Qavslarni ochib yoyish	eq-ifoda
2	fastor(eq)	Ko’phadni ko’paytuvchilarga ajratish
3	normal(eq)	Kasrni normal ko’rinishga keltirish
4	collect(eq, var)	O’xshash hadlarni ixchamlash	var-o’zgaruvchi
5	simplify(eq {,option})	Ifodalarni soddalashtirish	option-parametr
6	combine(eq, param)	Darajalarni birlashtirish yoki trigonometrik ifodalarni darajalarini pasaytirish	param=trig, param=power,
7	radnormal(eq)	Ildiz, darajali ifodalarni soddalashtirish
8	convert(eq,param)	Ifoda param tipli ifodaga almashtiriladi	param- tip parametr param=sincos, param=tan, param=vector, param=string, param=termin
9	subs(g(x)=t, f)	f(x) da g(x)=t deb o’zgaruvchini almashtirish

Topshiriq 1.4.
1. Qavslarni ochib yoyish.
>eq:=(x+1)*(x-1)*(x^2-x+1)*( x^2+x+1); \\ >expand(eq); \\x^6-1
2. Ko’phadni ko’paytuvchilarga ajratish (99-10-7)
> p:=a^5+a^4-2*a^3-2*a^2+a+1; \\
>p:=factor(a^5+a^4-2*a^3-2*a^2+a+1);\\
3. Kasrni normal ko’rinishga keltirish (96-3-74)
> q:=(x^3+2*x^2+x)/(x+1)^2; \\
> normal(%); \\ x
4. Ifodalarni soddalashtirish
> simplify((a^3-b^3)/(a^2+a*b+b^2)); \\a-b
> expand((a+b)*(a^2-a*b+b^2)); \\
> normal(y/x+1/x^2); \\
> collect(x^2+3*x^2+4*x+4*x+y,x); \\
> simplify(2*a/sqrt(a^2),assume(a<0)); \\-2
> combine((x^(1/2))*x^(3/2)); \\
_5. Irratsional ifodalarni ratsionallashtirib soddalashtirish
> f:=((sqrt(x)+1)/(x*sqrt(x)+x+sqrt(x)))*(x^2-sqrt(x));

> g:=subs(sqrt(x)=a,x^2=a^4,x^(3/2)=a^3,x=a^2,f);

> R2 := simplify( (a+1)*(a^4-a)/(a^3+a^2+a), 'assume=real' );

Oldingi o’zgaruvchiga qaytib x-1 javobni olamiz.
_6. Trigonometrik ifodalarni soddalashtirish
> simplify(cos(x)^2+sin(x)^2); \\1
> expand(cos(x+y)); \\cos(x)cos(y)-sin(x)sin(y)
> expand(cos(2*x)); \\
> expand(sin(2*x)); \\ 2sin(x)cos(x)
> combine(4*cos(x)^3); \\ cos(3x)+3cos(x)
> combine(8*sin(x)^4); \\ 3+cos(4x)-4cos(2x)
> expand(cos(5*x)); \\
_{>combine(4*sin(x)^3,trig); \\-sin(3x)+3sin(x)}
_7. Ildiz, darajali ifodalarni soddalashtirish
> a:=sqrt(3+sqrt(3)+(10+6*sqrt(3))^(1/3)):
> a1:=radnormal(a);\\
8.> b:=(m^2-(2+m^4)/(m^2-1))/((m^2+2)/(m-1)):
> b1:=simplify(b);\\b1:=-1/(m+1).
9. > c:=(a^(3/2)-b^(3/2))/(a^(1/2)-b^(1/2))-(a^(3/2)+b^(3/2))/(a^(1/2)+b^(1/2));

> c1:=simplify(c); \\
> a:=8*sqrt(2):b:=4*sqrt(2):
> c1:=simplify(c); \\c1:=16
10. > a:=(sqrt(192)-sqrt(108)+sqrt(243)/3);\\ (99-6-36)

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