Askkud n Tayluṛ (Taylor)

Asmdya n tasɣnt n ikspununsyal (s uzggʷaɣ) d agtful nns n Taylor s tfsna 4 ɣ tabkkit n 0.

Ɣ tusnakt, slawan akkʷ ɣ asfsi, Askkud n Taylor nɣ Tanfalit n Taylor, s ism n amusnak angliz Brook Taylor nna st iskrn ɣ usggʷas n 1715, ar tmmal tanfalit ad mas kra n tasɣnt itwazlamn ɣaydd n twal nẓḍaR ad as naf yan ugtful nna iṭṭafn imuskirn ittbddadn ɣar f izllumn n tasɣnt ann ɣ yat tabkkit . Agtful ad ar as ittaẓ ɣ imnala n tabkkit ann. Tasɣnt tagtfult ad ar as nttini kra n tikkal Agtful n Taylor.

Asnml

Tanfalit tanawayt

S yat tɣarast tanɣaṭ, ad ig:

• $I$ yan uzilal ilaw ;
• $a$ yan ufrdis n $I$ ;
• $E$ yan usayrar amaway alugan ilaw ;
• $f$ yat tasɣnt zɣ $I$ ar $E$ ittuzlamn ɣ $a$ ar yat tfsna bḍḍbṭ $n\ge 1.$

S man aya, i kraygat $x$ illan ɣ $I$, darnɣ tanfalit n Taylor-Young:$$f(x)=f(a)+\frac{f^{\prime }(a)}{1!}(x-a)+\frac{f^{(2)}(a)}{2!}(x-a{)}^2+\cdots +\frac{f^{(n)}(a)}{n!}(x-a{)}^n+R_n(x)$$nɣ s tɣarast yaḍnin :

$$f(x)=\sum _{k=0}^n\frac{f^{(k)}(a)}{k!}(x-a{)}^k+R_n(x)$$maɣ asagur $R_n(x)$ lli d iciḍn iga tasɣnt tawzizt taman $(x-a{)}^n$ ɣ tidjiwṛa n $a$, s unamk n ur da tbayyan tasɣnt ad taman tisɣnin yaḍni li tt izwarn yɛni ur teṭṭaf yan usnfl imqqurn ɣ ammas n tasɣnt.

Tinfaliyin yaḍnin

S yan ubddl n umutti irxan, nẓḍar ad nara tanfalit n Taylor-Young s tɣarast ddaw as:

$$f(a+h)=f(a)+\frac{f^{\prime }(a)}{1!}h+\frac{f^{(2)}(a)}{2!}{h}^2+\cdots +\frac{f^{(n)}(a)}{n!}{h}^n+R_n(h)$$nɣ s tɣarast yaḍnin :

$$f(a+h)=\sum _{k=0}^n\frac{f^{(k)}(a)}{k!}{h}^k+R_n(h)$$maɣ asagur $R_n(x)$ lli d iciḍn iga tasɣnt tawzizt taman $h^n$ ɣ tidjiwṛa n 0.

Talɣa y'ad ar sis nswurri lbɛḍ n twal iɣ nlla taman tidjiwṛa n $a$ (aynna issumkn i $h$ mẓẓiyn).

Ẓṛ uggar

• Alugaritm agaman
• Asnful n Nyuṭun
• Targadda n Cauchy Schwarz
• Tanfalit n Stirling

Amawal

Tiguriwin

• Taslṭ = analyse
• Tasɣnt = fonction
• Itwazlamn = derivable
• Tidjiwṛa = voisinage
• Agtful = polynome
• Imuskirn = coefficients
• Asmdya = representation
• Asayrar = espace
• Amaway = vectoriel
• Alugan = norme
• Tawzizt = negligeable
• Asagur = restes

Imawaln n tusnakt n tmaziɣt

Amawal umniḍ DGLAi n Asinag Agldan n Tussna Tamaziɣt, s kraḍ tutlayin (tamaziɣt tatrart tamɣribit - tafransist - taɛrabt) [Alink nns]

Amawal Tafsut n tusnakt - MCB Alger, Tiwi Uzzu s sin tutlayin (tamaziɣt taqbaylit - tafransist) [Alink nns]