michaeljdklein

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PYTHAGORAS’ THEOREM a² + b² = c² _Pythagoras, 530 BC_ -------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------ --------- LOGARITHMS logxy = logx + logy _John Napier, 1610_ CALCULUS $ f}{ t} = {h}$ _Newton, 1668_ LAW OF GRAVITY $F = G {r^2}$ _Newton, 1687_ THE SQUARE ROOT OF MINUS ONE i² = −1 _Euler, 1750_ EULER’S FORMULA FOR POLYHEDRA V − E + F = 2 _Euler, 1751_ NORMAL DISTRIBUTION $\psi(x) = {} e^{2~\rho^2}$ _C. F. Gauss, 1810_ WAVE EQUATION ${\partial t^2} = c^2 {\partial x^2}$ _J. D‘Ambert, 1746_ FOURIER TRANSFORM f(ω)=∫−∞∞f(x)e−2 π i x ωdx _J. Fourier, 1822_ NAVIER-STOKES EQUATION $\rho \left ( }{\partial t} + \cdot \nabla \right ) = - \nabla p + \nabla \cdot T + f$ _C. Navier, G. Stokes, 1845_ MAXWELL’S EQUATIONS ∇ ⋅ E = 0 _J. C. Maxwell, 1865_ $\nabla \times E = - {e} {\partial t}$ ∇ ⋅ H = 0 $\nabla \times H = {e} {\partial t}$ SECOND LAW OF THERMODYNAMICS dS ≥ 0 _L. Boltzmann, 1874_ PAYWALL RELATIVITY E = mc² _Einstein, 1905_ PAYWALL SCHRÖDINGER’S EQUATION $ \hbar {\partial t} \psi = H \psi$ _E. Schrödinger, 1927_ PAYWALL INFORMATION THEORY H = −∑p(x)logp(x) _C. Shannon, 1949_ PAYWALL CHAOS THEORY xt + 1 = k xt(1 − xt) _Robert May, 1975_ PAYWALL BLACK-SCHOLES EQUATION ${2} \sigma^2 S^2 {\partial S^2} + r S {\partial S} + {\partial t} - r V = 0$ _F. Black, M. Scholes, 1990_ PAYWALL EULER’S TRANSFORMATION $^\infty (-1)^n a_n = ^\infty (-1)^n {2^{n+1}}$ _Euler, 1755_ PAYWALL RUSSELL’S PARADOX Let R = {x ∣ x ∉ x}, then R ∈ R ⇔ R ∉ R _Russell, 1902_ GÖDEL’S INCOMPLETENESS THEOREM G(x):=¬Prov(sub(x, x)) ⇒ PA ⊢ G(⌜G⌝) ↔ ¬Prov(⌜G(⌜G⌝)⌝) _Gödel, 1931_

Authorea Help

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SUPPORTED LATEXFEATURES Authorea features LaTeXML for the web view. The continually updated list of packages supported by LaTeXML includes, at the time of writing, 286 class and style files. This is an up to date list. How to include a LaTeX package in your document To add a LaTeX package to your document, follow these instructions. In a nutshell: click on the Document Settings and select EDIT MACROS. What is supported? When writing LaTeX inside Authorea documents (here’s how), the following class and style files _should_ be supported (rendering LaTeX on the web is not easy so we cannot always guarantee everything will work): -- -------------------- ------------------ --------------------- ----------------- ----------------- ----------------- AMSAfontencoding AMSBfontencoding AmSTeX.pool BibTeX.pool JHEP.cls JHEP2.cls JHEP3.cls LGRfontencoding LaTeX OmniBus.cls SIunits TeX a0poster a0size a4 a4wide aa aasupport aasmacros.sty aassupport.sty aasms aaspp aastex acronym amssupport amsart amsbook amsbsy amscd amsfonts amsgen.sty.ltxml amsmath amsopn amsppt.sty amsproc amsrefs amssymb amstex amstex.tex amstext amsthm amsxtra apjfonts applemac.def array article attachfile.sty authblk.sty avant babel babel.def balance.sty bbm bbold beton bm book bookman booktabs braket breakurl.sty calc.sty cancel caption.sty ccfonts chancery charter circuitikz.sty cite citesort cmbright color colordvi colortbl comment concmath courier cp852.def crop.sty cropmark csquotes dcolumn deluxetable.sty doublespace dsfont eTeX ellipsis elsart.cls elsart.sty elsartsupport elsarticle.cls emulateapj emulateapj5 enumerate.sty epigraph epsf epsfig epstopdf esint eucal eufrak euler eulervm eurosym.sty euscript exscale fancyhdr.sty fix-cm fixltx2e flafter fleqn float floatfig floatflt floatpag fontenc fontspec footmisc fourier framed frenchb.ldf fullpage gen-j-l gen-m-l gen-p-l geometry german graphics graphicx grffile helvet hepunits here hhline html hyperref hyperxmp ifluatex ifpdf ifthen.sty ifvtex ifxetex inputenc insertfirst instsupport iopams.sty iopart.cls iopartsupport keyval latexml latexsym latin10.def lineno listings listingsutf8 llncs.cls lmodern.sty longtable lscape luximono lxRDFa ly1fontencoding makeidx marvosym.sty mathbbol.sty mathpazo mathpple mathptm mathptmx mathrsfs mathtools mn.cls mn2e.cls mn2esupport multicol.sty multido.sty multirow nameref natbib newcent newlfont.sty.ltxml ngerman nicefrac ntheorem numprint ot4fontencoding palatino paralist pdfTeX pdflscape pdfsync pgf.sty pgfkeys.code.tex pgfplots.sty pgfsyslatexmldriver pifont placeins preview psfig psfig.tex pslatex pspicture pst-grad.sty pxfonts relsize report revsymb.sty revtex.cls revtex.sty revtex3support revtex4.cls revtex4.sty revtex4support rotate rotating rsfs scalefnt setspacing showkeys.sty siunitx slashed slides soul srcltx stmaryd subfig.sty subfigure.sty subfloat supertabular svg svjour.cls svmult.cls svsupport t1enc.def t1enc.sty t1fontencoding t2afontencoding t2bfontencoding t2cfontencoding tabularx tabulary textcomp texvc theorem threeparttable tikz-3dplot.sty tikz.sty times tocbibind transparent ts1fontencoding txfonts type1cm.def ulem units upgreek upref url -- -------------------- ------------------ --------------------- ----------------- ----------------- -----------------