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Some in-house expertise

  • Scientific publishing assistance
    • Patent documentation
    • Audio/Video production
  • Optics bench demonstrations
  • Photomicroscopy: brightfield, Fluorescence, DIC, polarization
  • Full electronics bench (Tektronix/Keysight)
  • Software
    • Scientific software: MATLAB, Python
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    • Database platform: MySQL
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  • AI Enhanced Projects: ChatGPT, Claude, CoPilot, and Gemini
  • Multimedia: Adobe Creative Suite, Universal Audio

WPMathPub WordPress Math Plugin

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From now on :

Definition : (u_{n})_{n in bbN} converges to l ~ doubleleftright ~ forall epsilon{gt}0, ~ exists p in bbN such that forall n{ge}p delim{|}{u_{n}-l}{|}{le}epsilon

Remark : in the case of a vector sequence, just replace delim{|}{u_{n}-l}{|} by delim{vert}{u_{n}-l}{vert}

Taylor series with integral remainder :

If f is a class, ~ C^{n+1} is a class over the interval : f(x)=f(0)+xf{prime}(0)+{x^{2}}/{2!}f{prime prime}(0)+...+{x^{n}}/{n!}f^{n}(0)+int{0}{x}{{(x-t)^{n}}/{n!}f^{(n+1)}(t)dt}

Fourier series :

Definition : Then we call the Fourier series of f : S(f)(t)=a_{0}+sum{n=1}{+infty}{a_{n} cos(n omega t)+b_{n} sin(n omega t)} with omega={2pi}/{T}

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Some in-house expertise