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changed fonts because previous one was ugly
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kangzhe-xyz committed Jul 12, 2019
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20 changes: 10 additions & 10 deletions content/chapter01.tex
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Expand Up @@ -70,28 +70,28 @@
\subsection{Vector Analysis}
Vectors can be added by using the trigonometric method or the graphical method.

\peqn{Components}{A two-dimensional vector \(\vec{\mathbf{v}}\) can be broken down into components \(\vec{\mathbf{v}}_x\) and \(\vec{\mathbf{v}}_y\), with magnitudes of}{\vec{\mathbf{v}}_x = \mathbf{v} \cos \theta, \, \vec{\mathbf{v}}_y = \mathbf{v} \sin \theta}
\peqn{Components}{A two-dimensional vector \(\vb{v}\) can be broken down into components \(v_x\) and \(v_y\), with magnitudes of}{v_x = \abs{\vb{v}} \cos \theta, \ v_y = \abs{\vb{v}} \sin \theta}

\peqn{Magnitude of Vectors}{
The magnitude of a vector \(\vec{\mathbf{v}}\) with components \(\vec{\mathbf{v}}_x\) and \(\vec{\mathbf{v}}_y\) is given by}{\left|\vec{\mathbf{v}}\right| = \sqrt{\left|\vec{\mathbf{v}}_x\right|^2 + \left|\vec{\mathbf{v}}_y\right|^2}}
The magnitude of a vector \(\vb{v}\) with components \(v_x\) and \(v_y\) is given by}{\left|\vb{v}\right| = \sqrt{v_x^2 + v_y^2}}

\begin{center}
\begin{tikzpicture}
\draw [line width=0.5mm, -latex] (0,0) -- (2,2) node[anchor=south east, pos=0.5]{\(\vec{\mathbf{v}}\)};
\draw [line width=0.25mm, dashed, -latex] (0,0) -- (2,0) node[anchor=north, pos=0.5] {\(\vec{\mathbf{v}}_x\)};
\draw [line width=0.25mm, dashed, -latex] (0,0) -- (0,2) node[anchor=east, pos=0.5] {\(\vec{\mathbf{v}}_y\)};
\draw [line width=0.5mm, -latex] (0,0) -- (2,2) node[anchor=south east, pos=0.5]{\(\vb{v}\)};
\draw [line width=0.25mm, dashed, -latex] (0,0) -- (2,0) node[anchor=north, pos=0.5] {\(v_x\)};
\draw [line width=0.25mm, dashed, -latex] (0,0) -- (0,2) node[anchor=east, pos=0.5] {\(v_y\)};
\draw (0.5,0) arc (0:45:0.5) node[pos=0.5, anchor=west] {\(\theta\)};
\end{tikzpicture}
\end{center}

Observer that when you add the two components together, they form the vector itself.
\begin{center}
\begin{tikzpicture}
\draw [line width=0.5mm, -latex] (0,0) -- (1,2) node[anchor=south east, pos=0.5] {\(\vec{\mathbf{u}}\)};
\draw [line width=0.2mm, dotted, -latex] (2,-3) -- (3,-1) node[anchor=north west, pos=0.5] {translated \(\vec{\mathbf{u}}\)};
\draw [line width=0.5mm, -latex] (0,0) -- (2,-3) node[anchor=north east, pos=0.5] {\(\vec{\mathbf{v}}\)};
\draw [line width=0.2mm, dotted, -latex] (1,2) -- (3,-1) node[anchor=south west, pos=0.5] {translated \(\vec{\mathbf{v}}\)};
\draw [line width=0.5mm, ->>] (0,0) -- (1.5,-0.5) node[anchor=north] {\(\vec{\mathbf{u}} + \vec{\mathbf{v}}\)};
\draw [line width=0.5mm, -latex] (0,0) -- (1,2) node[anchor=south east, pos=0.5] {\(\vb{u}\)};
\draw [line width=0.2mm, dotted, -latex] (2,-3) -- (3,-1) node[anchor=north west, pos=0.5] {translated \(\vb{u}\)};
\draw [line width=0.5mm, -latex] (0,0) -- (2,-3) node[anchor=north east, pos=0.5] {\(\vb{v}\)};
\draw [line width=0.2mm, dotted, -latex] (1,2) -- (3,-1) node[anchor=south west, pos=0.5] {translated \(\vb{v}\)};
\draw [line width=0.5mm, ->>] (0,0) -- (1.5,-0.5) node[anchor=north] {\(\vb{u} + \vb{v}\)};
\draw [line width=0.5mm] (1.5,-0.5) -- (3,-1);
\end{tikzpicture}
\begin{framed}
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4 changes: 2 additions & 2 deletions content/chapter02.tex
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Expand Up @@ -69,9 +69,9 @@
xlabel = \(t\),
ylabel = \(v\)
]
\addplot [name path=x, domain=0:10] {0};
\addplot [name path=x, domain=0:5] {0};
\addplot [domain=0:10] {3*x^2};
\addplot [name path=v, domain=0:5] {3*x^2} \closedcycle;
\addplot [name path=v, domain=0:5] {3*x^2};
\addplot [
fill = gray,
fill opacity = 0.5,
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6 changes: 2 additions & 4 deletions main.tex
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Expand Up @@ -14,14 +14,12 @@
\usepackage{multicol}
\usepackage{tabularx}
\usepackage{parskip}
\usepackage{unicode-math}
\usepackage{hyperref}
\usepackage{physics}
\usepackage[math]{iwona}
\usepackage{framed}
\usepackage[version=4]{mhchem}

\setmainfont{STIX Two Text}
\setmathfont{STIX Two Math}

\tcbuselibrary{skins}
\tcbuselibrary{breakable}

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