From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Sun, 29 Sep 2019 11:08:38 +0000 (+1000)
Subject: [spec/methods] formatting fixes
X-Git-Tag: yr12~23
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/41eacf2b65512b5d0bfdedd85b5f2231b77e6c3e?ds=sidebyside

[spec/methods] formatting fixes
---

diff --git a/methods/calculus.tex b/methods/calculus.tex
index 72b8bdb..05bab2b 100644
--- a/methods/calculus.tex
+++ b/methods/calculus.tex
@@ -53,8 +53,14 @@ Not differentiable at:
 (\(m_{{tan}} \cdot m_{\operatorname{norm}} = -1\))\\
 \textbf{Secant} \(={{f(x+h)-f(x)} \over h}\)
 
-\colorbox{cas}{On CAS:} \\ Action \(\rightarrow\) Calculation
-\(\rightarrow\) Line \(\rightarrow\) \texttt{tanLine} or \texttt{normal}
+\begin{cas}
+  \textbf{In main}: Interactive \(\rightarrow\) Calculation \(\rightarrow\) Line \\
+  \-\hspace{1em} \texttt{tanLine(f(x), x, p)} \\
+  \-\hspace{1em} \texttt{normal(f(x), x, p)} \\
+  where \texttt{p} is the \(x\)-value of the coordinate
+
+  \textbf{In graph}: define function, then Analysis \(\rightarrow\) Sketch \(\rightarrow\) (Normal \textbar{} Tan line). Type \(x\) value to solve for a point. Return to show equation for line.
+\end{cas}
 
 \subsection*{Strictly increasing/decreasing}
 
@@ -67,15 +73,6 @@ For \(x_2\) and \(x_1\) where \(x_2 > x_1\):
   \item Endpoints are included, even where gradient \(=0\)
 \end{itemize}
 
-\begin{cas}
-  \colorbox{cas}{\textbf{In main}}: type function. Interactive
-  \(\rightarrow\) Calculation \(\rightarrow\) Line \(\rightarrow\) (Normal
-  \textbar{} Tan line)\\
-  \colorbox{cas}{\textbf{In graph}}: define function. Analysis
-  \(\rightarrow\) Sketch \(\rightarrow\) (Normal \textbar{} Tan line).
-  Type \(x\) value to solve for a point. Return to show equation for line.
-\end{cas}
-
 \subsection*{Stationary points}
 
 \begin{align*}
diff --git a/methods/methods-collated.pdf b/methods/methods-collated.pdf
index 35e900e..6737a92 100644
Binary files a/methods/methods-collated.pdf and b/methods/methods-collated.pdf differ
diff --git a/methods/methods-collated.tex b/methods/methods-collated.tex
index 4a0403a..b7accd1 100644
--- a/methods/methods-collated.tex
+++ b/methods/methods-collated.tex
@@ -7,9 +7,10 @@
 \usepackage{dblfloatfix}
 \usepackage{enumitem}
 \usepackage{fancyhdr}
-\usepackage[a4paper,margin=2cm]{geometry}
+\usepackage[a4paper,margin=1.8cm]{geometry}
 \usepackage{graphicx}
 \usepackage{harpoon}
+\usepackage{keystroke}
 \usepackage{listings}
 \usepackage{makecell}
 \usepackage{mathtools}
@@ -96,8 +97,8 @@
 \definecolor{peach}{HTML}{e6beb2}
 \definecolor{lblue}{HTML}{e5e9f0}
 
-\newtcolorbox{cas}{colframe=cas!75!black, title=On CAS, left*=3mm}
-\newtcolorbox{warning}{colback=white!90!black, leftrule=3mm, colframe=important, coltext=important, fontupper=\sffamily\bfseries}
+\newtcolorbox{cas}{colframe=cas!75!black, fonttitle=\sffamily\bfseries, title=On CAS, left*=3mm}
+\newtcolorbox{warning}{colback=white!90!black, leftrule=3mm, colframe=important, coltext=darkgray, fontupper=\sffamily\bfseries}
 \newtcolorbox{theorembox}[1]{colback=green!10!white, colframe=blue!20!white, coltitle=black, fontupper=\sffamily, fonttitle=\sffamily, #1}
 
 
@@ -121,15 +122,11 @@
 \subsection*{One to one functions}
 
 \begin{itemize} \tightlist
-  \item
-    \(f(x)\) is \emph{one to one} if \(f(a) \ne f(b)\) if
-    \(a, b \in \operatorname{dom}(f)\) and \(a \ne b\)\\
-    \(\implies\) unique \(y\) for each \(x\) (\(\sin x\) is not 1:1,
-    \(x^3\) is)
-  \item
-    horizontal line test
-  \item
-    if not one to one, it is many to one
+  \item \(f(x)\) is 1:1 if \(f(a) \ne f(b) \> \forall \>\{a,b\} \in \operatorname{dom}(f)\) \\
+        \(\implies\) unique \(y\) for each \(x\)
+  \item e.g. \(\sin x\) is not 1:1, \(x^3\) is
+  \item horizontal line test
+  \item if not one to one, it is many to one
 \end{itemize}
 
 \subsection*{Odd and even functions}
@@ -258,8 +255,10 @@ For \(x^n\), parity of \(n \equiv\) parity of function
       \begin{figure*}[ht]
         \centering
 
-        \begin{tabularx}{\textwidth}{r|Y|Y}
+        \begin{tabularx}{\textwidth}{|r|Y|Y|}
 
+          \hline
+          \rowcolor{lblue}
           & \(n\) is even & \(n\) is odd \\ \hline
 
           \centering \(x^n, n \in \mathbb{Z}^+\) & 
diff --git a/methods/statistics-ref.tex b/methods/statistics-ref.tex
index 8731999..ec728d8 100644
--- a/methods/statistics-ref.tex
+++ b/methods/statistics-ref.tex
@@ -24,11 +24,17 @@ Independent events:
 
 \subsection*{Combinatorics}
 
-\begin{itemize} \tightlist
-  \item Arrangements \({n \choose k} = \frac{n!}{(n-k)}\)
-  \item \colorbox{highlight}{Combinations} \({n \choose k} = \frac{n!}{k!(n-k)!}\)
-  \item Note \({n \choose k} = {n \choose k-1}\)
-\end{itemize}
+\begin{align*}
+  \text{Arrangements} && {n \choose k} & = \frac{n!}{(n-k)} \\
+  \text{Combinations} && {n \choose k} & = \frac{n!}{k!(n-k)!}
+\end{align*}
+
+Note \({n \choose k} = {n \choose k-1}\)
+
+\begin{cas}
+  Keyboard \(\rightarrow\) Advance \(\rightarrow\) \keystroke{nCr}/\keystroke{nPr} \\
+  \-\hspace{1em} \texttt{nCr(n, r)} or \texttt{nPr(n, r)}
+\end{cas}
 
 \subsection*{Distributions}
 
diff --git a/methods/transformations.tex b/methods/transformations.tex
index 00428e3..96b520a 100644
--- a/methods/transformations.tex
+++ b/methods/transformations.tex
@@ -17,12 +17,11 @@
 \item
   if \(a<0\), graph is reflected over \(x\)-axis
 \item
-  translation of \(k\) units parallel to \(y\)-axis or from \(x\)-axis
+  translation of \(k\) units \(\parallel y\)-axis/from \(x\)-axis
 \item
-  translation of \(h\) units parallel to \(x\)-axis or from \(y\)-axis
+  translation of \(h\) units \(\parallel x\)-axis/from \(y\)-axis
 \item
-  for \((ax)^n\), dilation factor is \(1 \over a\) parallel to
-  \(x\)-axis or from \(y\)-axis
+  for \((ax)^n\), dilation factor is \(1 \over a \> \parallel x\)-axis/from \(y\)-axis
 \item
   when \(0 < |a| < 1\), graph becomes closer to axis
 \end{itemize}
diff --git a/spec/spec-collated.pdf b/spec/spec-collated.pdf
index 7b998a9..1a67419 100644
Binary files a/spec/spec-collated.pdf and b/spec/spec-collated.pdf differ
diff --git a/spec/spec-collated.tex b/spec/spec-collated.tex
index 94d6187..e084adb 100644
--- a/spec/spec-collated.tex
+++ b/spec/spec-collated.tex
@@ -1,5 +1,6 @@
 \documentclass[a4paper]{article}
 \usepackage[dvipsnames, table]{xcolor}
+\usepackage{adjustbox}
 \usepackage{amsmath}
 \usepackage{amssymb}
 \usepackage{array}
@@ -7,7 +8,7 @@
 \usepackage{dblfloatfix}
 \usepackage{enumitem}
 \usepackage{fancyhdr}
-\usepackage[a4paper,margin=2cm]{geometry}
+\usepackage[a4paper,margin=1.8cm]{geometry}
 \usepackage{graphicx}
 \usepackage{harpoon}
 \usepackage{hhline}
@@ -52,11 +53,11 @@
 \usepgflibrary{arrows.meta}
 \pgfplotsset{compat=1.16}
 \pgfplotsset{every axis/.append style={
-  axis x line=middle,    % put the x axis in the middle
-  axis y line=middle,    % put the y axis in the middle
-  axis line style={->}, % arrows on the axis
-  xlabel={$x$},          % default put x on x-axis
-  ylabel={$y$},          % default put y on y-axis
+  axis x line=middle,
+  axis y line=middle,
+  axis line style={->},
+  xlabel={$x$},
+  ylabel={$y$},
 }}
 
 \psset{dimen=monkey,fillstyle=solid,opacity=.5}
@@ -81,6 +82,7 @@
 
 \newcolumntype{L}[1]{>{\hsize=#1\hsize\raggedright\arraybackslash}X}%
 \newcolumntype{R}[1]{>{\hsize=#1\hsize\raggedleft\arraybackslash}X}%
+\newcolumntype{Y}{>{\centering\arraybackslash}X}
 
 \definecolor{cas}{HTML}{e6f0fe}
 \definecolor{important}{HTML}{fc9871}
@@ -876,13 +878,25 @@
                   \emph{Point of inflection} - max \(|\)gradient\(|\) (i.e.
                   \(f^{\prime\prime} = 0\))
 
+                  \subsubsection*{Strictly increasing/decreasing}
+
+                  For \(x_2\) and \(x_1\) where \(x_2 > x_1\):
+
+                  \textbf{Strictly increasing}\\
+                  \hspace{1em}where \(f(x_2) > f(x_1)\) or \(f^\prime(x)>0\)
+                  \textbf{strictly decreasing}\\
+                  \hspace{1em}where \(f(x_2) < f(x_1)\) or \(f^\prime(x)<0\)
+                  \begin{warning}
+                    Endpoints are included, even where gradient \(=0\)
+                  \end{warning}
+
 
                   \begin{table*}[ht]
                     \centering
-                    \begin{tabularx}{\textwidth}{rXXX}
+                    \begin{tabularx}{\textwidth}{rYYY}
                       \hline
                       \rowcolor{shade2}
-                      & \centering\(\dfrac{d^2 y}{dx^2} > 0\)  & \centering \(\dfrac{d^2y}{dx^2}<0\) & \(\dfrac{d^2y}{dx^2}=0\) (inflection) \\[1.5em]
+                      & \adjustbox{margin=0 1ex, valign=m}{\centering\(\dfrac{d^2 y}{dx^2} > 0\)}  & \adjustbox{margin=0 1ex, valign=m}{\centering \(\dfrac{d^2y}{dx^2}<0\)} & \adjustbox{margin=0 1ex, valign=m}{\(\dfrac{d^2y}{dx^2}=0\) (inflection)} \\
                       \hline
                       \(\dfrac{dy}{dx}>0\) &
                       \makecell{\\\begin{tikzpicture}\begin{axis}[axis x line=none, axis y line=none, xmin=-3,  xmax=0.8, scale=0.2, samples=50, unbounded coords=jump] \addplot[blue] {(e^(x)};  \addplot[red] {x/2.5+0.75}; \end{axis}\end{tikzpicture} \\Rising (concave up)}&