Functio periodica Exempla | Tabula navigationis

Mathematica


mathematicafunctioNumerus realisfunctionis




Functio periodica in mathematica dicitur functio cui valor quidam iterum iterumque tempore periodico repetitur. Numerus realis Tdisplaystyle T; quidem appellatur functionis f periodus si dominium Df⊆Rdisplaystyle mathcal D_fsubseteq mathbb R habetur ut:


  • pro x∈Df⟺x+T∈Df∀x∈Rdisplaystyle xin mathcal D_fLongleftrightarrow x+Tin mathcal D_fquad forall xin mathbb R

  • f(x+T)=f(x)∀x∈Dfdisplaystyle f(x+T)=f(x)quad forall xin mathcal D_f


Exempla |


  • Functiones sin⁡(x)displaystyle sin(x) et cos⁡(x)displaystyle cos(x) periodicae sunt et periodus utroque casu est 2π.displaystyle 2pi .

  • Functio tan⁡xdisplaystyle tan x periodica est et periodus est πdisplaystyle pi .



Periodus fractionis exempli gratia in numeris 1/3 = 0,3333333... = 0,3 vel 299/333 = 897/999 = 0,897897897897897... = 0,897 invenitur, nam 3 in prima aut sequentia numerorum 8 9 7 in altera fractione decimaliter reddita usque ad infinitatem proveniunt.







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