simvolli (analitik) amallar

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1352360167_32197.doc 9 x 2 y 6 + ( ) x y x 27 1 := e + + - - ( ) cos x 5 ( ) sin x 4 2 ( ) cos x 2 2 ( ) sin x 2 ( ) cos 2 x + ( ) cos x 5 ( ) cos x 4 := w - 5 b 2 a 5 - b 2 a b 5 - a x 4 y 2 x 2 y x 2 y ni , f x proc ( ) := local ; i description ; "chiziqsiz tenglamalarni yechish" ; := i - x / f ( ) diff , f x ( ) unapply , i x end proc , f x proc ( ) local ; i description ; "chiziqsiz tenglamalarni yechish" ; := i - x / f ( ) diff , f x ( ) …

> simplify(sqrt(x^4*y^2)); bunday hollarda kerakli aniqliklarni kiritib soddalashtirishga erishish mumkin > simplify(sqrt(x^4*y^2),assume=real); > simplify(sqrt(x^4*y^2),assume=positive); bu yerda o`zgaruvchilar birinchi holda real deb, ikkinchi holda musbat deb aniqlashtirildi. simvolli amallarni dasturlashni f(x)=0 ko`rinishidagi chiziqsiz tenglamalarni npyutonning iteratsiyalar usuli bilan yechish misolida ko`raylik. maolumki npyuton usuli quyidagi formulaga asosan iteratsion hisoblashlarga asoslangan: xi+1=x1+f(x1)/f`(x1). uni simvolli ko`rinishda dasturlaymiz: > ni := proc( f,x ) description "chiziqsiz tenglamalarni yechish"; local i; > i:=x-f/diff(f,x); > unapply(i,x) end; > print( ni ); bu yerda iteratsion formulani analitik ko`rinishda olish uchun unapply funksiyasi ishlatilgan. endi yechilishi zarur bo`lgan ifoda berilsa yechimning analitik ifodasini olish mumkin: > f:=sin(x)^2-0.5; > t:=ni(f,x); so`ngra x uchun boshlanich yaqinlashishni x=x0 ko`rinishida berib qator iteratsiyalar uchun hisoblash natijalarini olish mumkin: > x0:=0.2; > to 8 do x0:=t(x0);od; bu misoldan boshlanich sakrashlardan keyin tezlik bilan aniq yechimga yaqinlashilganligini ko`rish mumkin. ushbu usul yordamida tenglamaning faqat bitta ildizini topish mumkin. boshqa ildizlar boshlanich shartni o`zgartirish yo`li …

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"simvolli (analitik) amallar" haqida

1352360167_32197.doc 9 x 2 y 6 + ( ) x y x 27 1 := e + + - - ( ) cos x 5 ( ) sin x 4 2 ( ) cos x 2 2 ( ) sin x 2 ( ) cos 2 x + ( ) cos x 5 ( ) cos x 4 := w - 5 b 2 a 5 - b 2 a b 5 - a x 4 y 2 x 2 y x 2 y ni , f x proc ( ) := local ; i description ; "chiziqsiz tenglamalarni yechish" ; := i - x / f ( ) diff , f x ( ) unapply , i x end …

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