From 70cc3f400b678561173925bef7f4c5517fab4b56 Mon Sep 17 00:00:00 2001 From: Charlie Root Date: Tue, 10 Mar 2026 16:09:00 -0300 Subject: [PATCH] How to model periodic things. --- calculus.pdf | Bin 843785 -> 821824 bytes calculus.tex | 46 +++++++++++++++++++++++++++++++++++++++++++++- 2 files changed, 45 insertions(+), 1 deletion(-) diff --git a/calculus.pdf b/calculus.pdf index ce6f7b7ad0bf4b95a397b1918f2e33974d0e5ba2..4600265d00e8926adc8cd01b9034d4ce7a7a7666 100644 GIT binary patch delta 342877 zcmZs?V~;Khw5;2*dq$BqMQvtSh|vU%5{}M9S1)7f`_i`bYom`=U*{Xg@e}pt4KSg6w4~E2GC3W?SVbpt*yUK) znFe#rIt@7YS67r0R_0zaB@pXQJTgmbj|@pbdPg*a(@#}iI!-}aKd}( ziGZ8!Gf`rL$GK=*10rRpl?t34oH^vQnO1mmY5_(wqQjpGAT%+cXtA$+EjoMTd3l;K@Qs-EvL6h zowt0@WP5+A0aK?gLeO!9EN;IQ4iwM5=70D925sqI#ro}Qt^8^R*cYk;$ZPGMg9crp zv;dNa1Mje)oIV4^w&owNn{FD~Qe zrsnLrdnp-GqT!h33i(Whq<%0%_F^7&>1r>QK@k2IA+ZN;K{|J;(>wN+UBt=%;}vF70^?P!I(TQ zYj7R(Zktu|;lIo}ZiBw%hSRMy80zz}gx2H^*Ma-NCcmr=8a1>m*KGsyw77h%r3I_M z=s)xaS|smpcacXXcIU!}z>$A)*rx7;#Bam9rK%AC?DNCu$ld9|T>oiU;?!@qS#@Kx zTYb-jqUSL8^g9$xPQs~jG zyu_Yj82(D^_{o{c31m1n z*<011;>3L;)&Cu?^iXET_K=1f?eR>lzte@mg(kG*< z)O4hX?)tt5gbt>8aJ1U=!iL+uq8R2iPnm18%T^%8r_0|m6HxjZN!}V33U|!abPjpRp=T$cITA6OrqpjX> z9?EB06rBxbHuYAd39-Gl7eCDT>5D?0h1A{!A7w-Qj1E@OqPc679UeDS1Jcg#Jyqmu z6mmnu%7t#RXv1+ZUw(70B$^xm#-Qv(a)i`9Nt13=2E=z_fW#HNez^x58p2^ZH-kV} zQf6H(;~7YeA_h#OU9BaXWrlCQHI2!tSDImJ%<{hp(LeFgt>YAT>2STi&H}}cXEtie zNsBV97HK%`_9amZB(Auij#kSw4x2G-+xja^7BG_s#EL5kL;LH8ee&JBpoNH!=VDRq}SKL(E+g6g%o-3;@J3M`_#{v?J8i};&FfL8-`E5KqRXcADD|WGdAAW`je{HTA zl%3Pa&u_k`8T!35Z~hL9Xy@JTXm%pb3wF#Seg@A|T<8!OwtuiKFE;$1e*-Z|*a*;?rfH@xN;@(!@;^M|z zrG$#CI$+Qrc~4~VQS+=MDgaE|Sb)X=+Ya!qG|G0nX@%%AJbrz-w~9A`qu*}lNUN`r zn;R%-y?m9o$HfK>Uk7K?q^}^-4w4R8#>Sbk3!imA5UwA~kN@o($SR1rez@?P_0}0K zSnU3hkmLQ2QEHrld#ogf-eMxLvK~`jOVP70SFWV~Y*jBXxCDWMARr08_8w?2@)i2^ z=<_~?tijr;donTNpNb@!90V`3On*T4^&i=|;=DAtWH8(Gfy0Zol9z$y+C0Bg^V zU+0tZgr$HlI#0!wv|T>($^bXJ&J*dL7FC<5Tuqu}EFh5(KK=+sX5wum&_Iv9bLRzW z0Q*OPL~w8nj`$+e5}>6fQteqjm)N7YM`eu*_O3&YJ$ut{Zv1&ju+>Mr9pCo!tTG)y z;f9OZ=Y%T(eoFczfL9)h8pJ$N0nA#b7g{hx5<~i^*$6!uA(?<^H-_jVH2N1B8xn~j zXy8O1Gei#yVmD+(-Q{v&dgAOtYSOm!Szx)~!x2hF41KX(1i)EsyU|(-;>{W2$GhEL z=Ik_dLIX3JM(IeHNRT0;T(n{bA?oktDrxiMwtg`P6s1f~$OeuxY{e84rjrsLr2PeUh^s3fg;j-f##M>wt}dGe)}Ik+7BWkfKv26>JYxp4 z^QzfT<%nT&lMEYgcP@lklaT#J;$r*AGuC{%1B6jXIsHvA;wI~VcfUi15%FD#I%pI6 zS`Mc-&hy6^Uc4Lge&yur7kCZ{21YboW2UxGNg%d2DgNcay5ok6O<)4Nbfu8g457gU zM=BJ$q}t6KX7fg*AUz-1z#((}e6m7XI(bUj9r+C`@JbX=wLk9=hB|reZnEcavs$S{ z0TzM!Hn~n$(_5o)6_E4N)IMgl=C)v$?4 zF1m#k-f}&jyF~5f43vZhnF||ZVrpt*D*ITqPgyWP7&G-~r-Y;~BkdW^6D*_VxiwF7 z{1A0nT5}2>!3OXM*rnWZ3c`e6$CAZW*u4;!{M^IkgxV$F%*BRplE79(9dgFm0fiQO zYoD_w#ww5thq>|lNx48W?#4VA@-On>?OoN5{bG?E6XHh zns&5o{W~;480uNcyrReg^sps0TpQv)p$f;XSNzWhJ;?ybAAfDKpFW+9wFd%Q zL}7VBeltQ#X_U?VhL;5&fKjFprh-9KFGqH;@Vr?gtjS{2w%oR|4V$NkWVR~*KB%B* zIRR&)w*lpkh+;OFYxz~qDUp%kc%%!TJk^W=X-clSl7rJKCa0UlM+i1y)@5EFV`V^VA6&p#Hu>6drb&pWN?Eha!%6-}T^p)SZf zPKOyLrH;!M^n82C0}IzR0NQ0NoGY=jLK-y?3ebe6wPe^lCTUU|-=q4uF zsd~uTmbO$C`}snBa&JVei7FAAtp)Egnx-ag^Nb&gP!d-27GAo!o!iK>-~a0ywEywV z4-)6g>*)wXJG0?Jh9t5ruw;tb5!g5T2k-AUv8IHd13&81;UWQc>G9!M zv!Yit%3))iFk}uRxlyTnVzS=w8{IIF9iVLpLP#-B5^Wl^S}bMIHxQ?#HIadcjgxQ7tB z3351-ScYo#FR^8SX)YIn^z0BvK#>`fNS@6;3zf_V+>LQWD7G#FI zje9v!bU3FfwItAkkEIGmIegBIj}XfHJanSb8K|cj;_qK;Fk0>gkc;<_uKqyO)lf^8 zck(+M9cG+Jr6Q=aAhNI-ah&8NPJl@Y_S@wgF%5)E0Tv@zh=r=;AW)YBBH)*!0O_|o zRp#1WJCf?!U|dElff^m6tqAnH&rB$^Pu0rD;$PW!qX37fTLP(FEEwD%zInFE^-W;r zWxrqExeHxfvrmwbA9gQ;IZIy)_nR4^P!)3hpu0SQ%*rx`R;BV|8+tJsCE(mH0}9$j zl0UC_&<3i;_`v?I35q3SiwkqAxlZamQhJ&Jw2WIzI|@*=RFakq7}ie9!Y#UBJHpYx zSC}PT^G(cxh5_bgqB%6i8yOoOUXuJhUH(Q2x=oYU7H}6o1Nfy%YnN6KIgaY)y&xRG>*pO*U1O-1R8&M6=?r`#?|u44 zFrVPHW_iFU%>ZeYn1Nc2hMo7tB1Ef;2r}=-*|WA3#GWoY_sO)H{!_O{_4|i?wP5^^ zl+VaFtoQHXB7>ieV)BS4o}Od`w%8o@FWm=f6Vm+6z?{OVPhrAY6Tr>LY}lBu$k-^7 z)2uH^hlgl1{CC+i{<^P@z}BM6@r)`6ul*h9iKJcLQy-E=NA2XG=g)~7gK5TIfSL6P zFAg;x=>$pZ!3dKGkE!SRDMnDFshmU*S~8T$twMRGfGDT`{ZYRE>`FOksfp3kgt~K^ zNVeyT)<0@wvflt;8vrCoc3heL~X${5pBmfED7eAss@x}DK51QL8$NS7nA?6#j6b;3RoL=3s z1T^%A4}qiEJ5$GW@YCzen(=<2tR0OP8ZfkLW4{K)9^&Yz^|>K9>7-h zk=~qho|z<7RfXL!GHotTEy5=VyH58TsxtV52rycB(rf&?Eegto)PGQz^w4+Ts(K`8D6RlPE=-wU% zN6(gG3;EAmIo8RQVXDnbIfIrP^W;I?*uyDEr3aZcP@G|fWL{qap>EMt!qjL)OdCrf z1pu`9CDT+;voGv+a8FahW;R9Lb5k{jiU5qF^Ob}#d%vTbG(#V8w8}@Y=Sn0&*w8mp zE>v0>HaIegXqtY>_HQ~yBmP;V31plQ1zFu;ia=$A4+wP2OS5(N;FT{uI{#o3oOa2Z zaMNa}(sD^)>+^m9R3s4+uaY(xI_+AZ2LS3kZ2sKk4}}$v$?FG7N~Fg}65@25WdX&&J2ILLg z^TRKpaoeSRx&;IURfv!09L5Kz%^GvPyXB0u4b@X#CBYXjT0W(Z6!F!OuP7Wc+#1TA zT4ls#n=Nf^NtY{{Wy73;u8kHDZC(eI$%PZXy+Z~ib*R$auaTtbg-y9f0;-kzY-P+* z2pMP0G}ea|L0M-`vps)7Qz}}C(f=1@Vqs1eMn(nZNLP9QrUB$)k0))mJ>S&NB~~@F zfq7CK2PaR-sk@A+jf@ZHg6fF0?vp@cBk}70e00I1l~VZTG)_X?0SW9~M=wk-Qfz;H zF{Iwl67GKAsVY09Y_ytZ+6xFc;IwGkcUL~z?f%P-ADu2gVyyGr)K6m{_cx%)nJ?3+S96bG}5{36Za`MMi;XDH7W(dkxa)1RDqsaj~Ttmk}jp zr1;2dU*2h(wGmvAKyUU=S%PTMdxsQZ=hS@#_crZ}IL|`eWr4V@p`29q;N$h*IEsI5nh02)u!m$vU`KGOwqe%e2vNY-w4L|8

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