Skip to main content\(\newcommand{\doubler}[1]{2#1}
\newcommand{\definiteintegral}[4]{\int_{#1}^{#2}\,#3\,d#4}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Chapter 3 A Bit of Math \(y=mx+b\)
This paragraph has some inline math, a Diophantine equation, \(x^2 +
\doubler{y^2} = z^2\text{.}\) And some display math about infinite series:
\begin{equation}
\sum_{n=1}^\infty\,\frac{1}{n^2} = \frac{\pi^2}{6}.\tag{3.0.1}
\end{equation}
Look at the XML source to see how LaTeX macros are employed.
And a bit of multi-line display math:
\begin{align}
\frac{d}{dx}\definiteintegral{a}{x}{f(t)}{t}&=\frac{d}{dx}\left(F(x)-F(a)\right)\tag{3.0.2}\\
&=\frac{d}{dx}F(x)-\frac{d}{dx}F(a)\notag\\
&=f(x)-0 = f(x)\text{.}\tag{3.0.3}
\end{align}
And multi-line math with an embedded cross-reference to a figure:
\begin{align*}
x^2 + y^2 &= z^2&&\knowl{./knowl/xref/complete-graph.html}{\text{Figure 4.1.3}}\\
a^2 + b^2 &= c^2&&
\end{align*}
Nice.
Theorem 3.0.1 (Newton, Leibniz). Fundamental Theorem of Calculus.
Let \(f\) be a continuous function on the interval \([a,b]\text{.}\) If \(F\) is an antiderivative for \(f\) on \([a,b]\text{,}\) then
\begin{equation*}
\int_a^b f(t)\, dt = F(b)-F(a)\text{.}
\end{equation*}
Outcomes
