Askkud n Tayluṛ (Taylor)

Amnni ad icqqa ad t tfhmt ! Amnni ad gis kra n iwalwn nna ur iẓḍaṛ yan ad tn ifhm iɣ ur issin ɣ umawal iẓlin n tutlayt taclḥiyt tatrart. Mad igan afssay ? Fad ad tfhmt mad gis illan tzḍart ad tawst i yixf nnk s umawal lli illan ɣ izddar akkʷ n tasna. Iɣ t ur tufit, tzḍart ad nn taggʷt ɣ imawaln d isgzawaln.

Ɣ tusnakt, slawan akkʷ ɣ taslṭ, Askkud n Taylor nɣ Tanfalit n Taylor, s yism n amusnak angliz Brook Taylor nna st iɛdln ɣ usggʷwas n 1715, ar tmmal tanfalit ad mas kra n tasɣnt itwazlamn ɣaydd n twal nẓḍar ad as naf yan ugtful nna iṭṭafn imuskirn itɛtamadn ɣar f izllumn n tasɣnt ann ɣ yat tanqqiṭ. Agtful ad ar as ittaẓ ɣ tidjiwṛa n tanqqiṭ ann. Tasɣnt tagtfult ad ar as nttini lbɛḍ n twal Agtful n Taylor.

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

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 $n\geq 1.$

S man aya, i kraygat $x$ illan ɣ $I$, darnɣ tanfalit n Taylor-Young:

$$f(x)=f(a)+{\frac {f'(a)}{1!}}(x-a)+{\frac {f^{(2)}(a)}{2!}}(x-a)^{2}+\cdots +{\frac {f^{(n)}(a)}{n!}}(x-a)^{n}+R_{n}(x)$$

nɣ s tɣarast yaḍnin :

$$\displaystyle f(x)=\sum _{k=0}^{n}{\frac {f^{(k)}(a)}{k!}}(x-a)^{k}+R_{n}(x)$$

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:

$$f(a+h)=f(a)+{\frac {f'(a)}{1!}}h+{\frac {f^{(2)}(a)}{2!}}h^{2}+\cdots +{\frac {f^{(n)}(a)}{n!}}h^{n}+R_{n}(h)$$

nɣ s tɣarast yaḍnin :

$$\displaystyle f(a+h)=\sum _{k=0}^{n}{\frac {f^{(k)}(a)}{k!}}h^{k}+R_{n}(h)$$

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]