From d165d17c3c98d1c4cc9507d4aa58de2fd1a1be4c Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Mon, 12 Aug 2019 14:46:59 +1000 Subject: [PATCH] [methods] corrections & layout of collated notes --- methods/{temp => }/calculus.tex | 8 +- methods/circ-functions.tex | 6 +- methods/methods-collated.pdf | Bin 431585 -> 431179 bytes methods/methods-collated.tex | 456 ++++++++++++------------- methods/{temp => }/stuff.tex | 2 +- methods/temp/inverse.tex | 72 ---- methods/temp/polynomials.tex | 211 ------------ methods/{temp => }/transformations.tex | 34 -- 8 files changed, 232 insertions(+), 557 deletions(-) rename methods/{temp => }/calculus.tex (98%) rename methods/{temp => }/stuff.tex (98%) delete mode 100644 methods/temp/inverse.tex delete mode 100644 methods/temp/polynomials.tex rename methods/{temp => }/transformations.tex (78%) diff --git a/methods/temp/calculus.tex b/methods/calculus.tex similarity index 98% rename from methods/temp/calculus.tex rename to methods/calculus.tex index 541a8c0..4478faa 100644 --- a/methods/temp/calculus.tex +++ b/methods/calculus.tex @@ -86,10 +86,10 @@ Type \(x\) value to solve for a point. Return to show equation for line. \subsection*{Stationary points} -\emph{Stationary point} - i.e. -\(f^\prime(x)=0\)\\ -\emph{Point of inflection} - max \(|\)gradient\(|\) (i.e. -\(f^{\prime\prime} = 0\)) +\begin{align*} + \textbf{Stationary point:} && f^\prime(x) &= 0 \\ + \textbf{Point of inflection:} && f^{\prime\prime} &= 0 +\end{align*} \begin{tikzpicture} \begin{axis}[xmin=-21, xmax=21, ymax=1400, ymin=-1000, ticks=none, axis lines=middle] diff --git a/methods/circ-functions.tex b/methods/circ-functions.tex index a2d85bf..7580791 100644 --- a/methods/circ-functions.tex +++ b/methods/circ-functions.tex @@ -91,8 +91,8 @@ \begin{tikzpicture} \begin{axis}[yticklabel style={yshift=1.0pt, anchor=north east},x=0.1cm, y=1cm, ymax=2, ymin=-2, xticklabels={}, ytick={-1.5708,1.5708},yticklabels={\(-\frac{\pi}{2}\),\(\frac{\pi}{2}\)}] \addplot[color=orange, smooth] gnuplot [domain=-35:35, unbounded coords=jump,samples=350] {atan(x)} node [pos=0.5, above left] {\(\tan^{-1}x\)}; - \addplot[->, gray, dotted, thick, domain=-35:35] {1.5708}; - \addplot[->, gray, dotted, thick, domain=-35:35] {-1.5708}; + \addplot[gray, dotted, thick, domain=-35:35] {1.5708} node [black, font=\footnotesize, below right, pos=0] {\(y=\frac{\pi}{2}\)}; + \addplot[gray, dotted, thick, domain=-35:35] {-1.5708} node [black, font=\footnotesize, above left, pos=1] {\(y=-\frac{\pi}{2}\)}; \end{axis} \end{tikzpicture} @@ -122,7 +122,7 @@ where: \item Asymptotes at \(x=\frac{(2k+1)\pi}{2n}\) \end{description} -\textbf{Asymptotes should always have equations and arrow pointing up} +\textbf{Asymptotes should always have equations} \subsection*{Solving trig equations} diff --git a/methods/methods-collated.pdf b/methods/methods-collated.pdf index 808c3b5e4c720d8bce63ecbe446dba546cddd599..acdd213f7b5a629d240207140dbf1d93941fdadf 100644 GIT binary patch delta 245957 zcmZU3V{D)e&~4kT?X7Lww(afKwzgY8wQZYQ+qP}nw!imFZgO*Te@t?cnPle2WHM*w z?3UwrCDJYPoi0EMiX`1cDtt#;#Z!;_?7@hl@r=ksV4@cz0m&uM8G z%fOS<^8R`pgJ^e*C9~xut`-pd|YhTKOV0a5#42r*go%@GPX7f<<|#e<4Lj}2`mD76?y{i7is_a zThH}R^PXt&IVC)Y8E`TIk>)dz5L#0Wv}>GclgKP)4|)> zp7(phFSlY1N3>eG$Kq>yK{neDm%BC5_cz4Fp3GEvUmM$giV`a)@#E!*df{ zU(m93lj5xX81UpMT@3`hJ*5bK+X(_?9XhE$+ofkW>(L2{FDRa88p!`T>Ddmwo+2Bt zP&7r1-&8W(8)ASDg4px-A4V;OZ+L0m=c_`Bp2)RE6$J?K;hp^=b3v zl)o+nW`uR_AK)XfJwyhrJZWcPHkVh6t8=lrQp$w%cQ#a(1r_gHv@J}ZHBa&!9$Sn0 zbTsiYr%iQ5uZ5ypRqmdDzK$;A_3I%;r;u72nNOGB_s9l$hsCcWnFDtS&$C*WLhj3p zR{i@CfLp)!hvQ65L7zX~svjLbc|eAN@@WBk!xXaN&B+Tetu%r8k>>2Eo5dG(w*Lf1| zZtD0Zx|Cn1FYmvW8HXeXYAW`W-S~KEXJd#$OFvNN2UkV&^;F7L-BR>h;t^uKLS$1jUz2F@>Sy}DJZ{mm!t&pnv!9It6!^6E?hIL>_P6%&rNrH%7RBO7@K zXS0IL>=5Q7s#7stg3c4vFOfYQ=jGHvpxqiRdf&La)(PtG^g%5E= zXY(g-bu#8QHZNSZAU(fl=O(FDB$4Ciqti=t>+`M^N}l-75Tgw8!6n>9#x%jDyV|=K zOhv0~)Z%|>EOVTFY~bj02KC(5WVsdfU~EMBr=hP2Vh$x>te61jAN z;ywI5105}a=EIB79ScI?s9%{2GWMGGVMIfz$HFbb&q(n%P5Qgd!*wycX-OBJ_QqQj zE=$H=bY)cM>VOYnb;y)>UEz8IAk?)V`^rO-X{Oa@V1Q?I9-IGo6Z5Hk%kbju*Zo5L z{*1x$VH+}(v0WP51+|`>`?<@SFXP+at3sY)dF&z`$!7a!Nb&sXmwo5et?oI;%xTe*^C?gfpsUlHZ}Ct8*PpZD05M8TW02T%*7WkNmKdzw)*1tG<3wv^vyr_^zUV$-VlN%$Zs;KC= zeMgthj!f!g|1b+TYq}5@l$^xfdIKw1)p)F!goyyr*hnUfz@H{&@b8%Q#Pe|+5@?GS z;Ji7G%*NTKqz11ijbRSsYX!VZwl^az48C$%FLdLh^BrYtxr8$o07B{k2_-JcPdv>5 zrr8OFHWeWOS6D(UPDa%X335E;&6q>QfEOzd zlr%76&q^~@9b99r0t%tOWmGo?+&moE$a`ex&_CrWLhHeg8yd)Wq!+~GDn#e$f}He& z!)F71ld%bN^_{REzzRmA-SH}<3wTpu2F&0Y)>)>&KcC9s0~+OOU53EK8$`qg1D(K- zbr1+zWGteA@qMN(6HQ-J7|aA@h}o@WW__JMJ~dQZ^8#frlb7 z>AXg)scE%<4P>K>681?gg#nV1RzgHi(11pGef)Su&jg+MU;*5y(0~1;Z(OD!V8p?c zlPD&qMS@l^h)_pNHyIyun;IBf6B!%<>2}1;PjJ;Qa-CqzOULw)Wq}@9`wtN$ORiUgPZY&IJhh8(!gY^Aj|lZp(h;BE*IfyrhP%SH+)1EGf}%>i4Um><1~YAe3^hE00}ZIW&iQUh6(KzM%DJz$ynQ!+HQtZ%Lu~2Xp7B+ zgS7&%5%#V?w>I%`F(K(SOU;uT_H}QhI2*VEO)0=v6*@zQG{}q(V*l6VKSYa|#Up&* zH&SbM6QD*9Wt~6J9%$+Rv>Lb|E&@&=HBTty95BnIBu7$_hA?ZpCO{4|D>0u=qKeoQ zV0apt=0AE^u}dUvDxAb;i=iNGUKJBuKbr`IcAN25q=h{Qy6nxURM5f4+#*KoSgOWy zm1f0xfg4IC!i#WGCXxM)0aZrj*<-SV4_6};KpF~UV9F#;cN|=a?QhmOK|4i9h3}`K z$9L$F{FfsWHdzsPz#l!iL<9{y zYK*|if$=kdAXZ?4X~Cs4W2=jobnY$61-2Z}dLb|rAZ(O@O`y+<(A7=6iqMb-Ot7$2 z1h)8x+*Q;l8!{1nir)jda@rKxkV84;}h=!o) z{mf(4DVQrxKyqcF#j>M8^(Jjfd+zXM^B`EUF%eh6DZt5h#T^8C;2_R-xC3=4Zau-W zhd=t&hmGhRqK0Pf!e-gvx1H&+=4*yfm|+kx?jtSz82YgaQA}Ts`1q`t}uII zP(bV?vJ1I<#9-9BMFLEsh@7&Yx{lbDaE379gIimqQc>LBAXzNII&+xcz|%dtiEO(d?PEbLp%lffWO zq%i1_V9~xe%UqU0T=dp(D0|2_j@lq1vZ<3610#x1u);mCSlYVkJkZ)xdOE~pQ0?JN z(^y3qK0RupvA0sB9)$ry$iXh+$+HfZHHgS$19wutT|h*|z=p`*9O-~|1`etdp@JlG zwg6ZVp&o3J%iJe7vBDnD0mwDT28pF`DpB)V!s!#j-D-m^X;?XEUUVWN9A*)ssXMBb z2w_YyS^4Ns7&^0BrQnWH=a3%(C?%NtQxICh5;;~UsK|uyj>t<>bLLn>WM0Dqc_;^7 zEbFndMLP8!hq)L+s)ztLY*xZi(Mz<2<;ca5nvsdWznc|%Rwk0vHgT9x*&fty*bP#V zX3Kmx*#UcPT4+C#m1t_c0}WK_EGAK^@dl zh}3E^jyS}yv1Z6VNHS1tQ8rNY!zmL;YNYt&d!;h{y3CZf$UuPvXnquTP;n6vT|?}l z*ux$%zu&bN8b-ez8u6c7rJ{$)mQfzS{0wy>11E*RA*E|>TKas7l``k1 zury=vzZ1FENNS@hccEEKPBA7->>ft^tSuoVz%U(+v^)W^W^g|f^|@-f$y{8btsdwf zs`(b~Pps@WoFG4UQQlZJfK87_vo8M<8c#EGHcN`O4uRP z##_1AP(=Ve9}yT?0ap1Ry{d7)G<;TM@p>bAh_mrxE$H8#bQqXImeS^tzTAUZka5Hi z^+9UH;m`qQs%<`+ENUh-EY1%X(8797Ix#zhr@nEjNpzg;0})z}HI2P5^pHlHN~U{*#vH+zvcuh3mqOJReA=~DU1Nq%)%uQ8H;f>)D?m75vV{$Y3`)z zLtLp^kmT$iQ*pT{tvo_l6k)67evHV<;hAJBRBWx_7V^uX>TGPI$f*%3i3R~|m64|R zD)2MXvyocNN`pEwVZL?&qs=5%GjtMIADO4hSV>gEzJ~K+czCk1B-HXqP(gmc-be$8 zrzY?ZZ0M)-goCK*rbw0Zgig@$Pii&`>gyW3-G=!hJVOv0tz#ixT-i;LARb+f)O;}z zGjuvMOH496T4tS@=4U;VB7>r$(7g3n!$@U5I%^c3I@exBfx92s`)ISR$wEU*6$`02 zeIOMe24o*S0hood*f+k$%22RLVZ!dDT%JINOq^7$59uW9d1NL@a>7iJRyNFwMbR1f zL}?K`c)@_W$-2#;WMXh8ciIFV8mqBubnaTBNQ#^ADbtN|W#}o7Z7^3dllquhcp9Q9 zG_x05gmr2ORoz9A1v*xh^`8g~x=UN?C1U+z8DYqne0@Kn2jfmKw;W}XyMKLkc; 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