From c8a164d2681c40d84bdb9dda09471a690cdec142 Mon Sep 17 00:00:00 2001 From: Martin Kennedy Date: Mon, 17 Feb 2025 15:01:13 -0500 Subject: [PATCH] format: number the derivations We borrowed the command from https://tex.stackexchange.com/a/42728. --- Lab1.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/Lab1.tex b/Lab1.tex index 8aae194..05af4a7 100644 --- a/Lab1.tex +++ b/Lab1.tex @@ -14,6 +14,8 @@ \usepackage[a4paper, total={6in, 8in}]{geometry} \usepackage{amsmath} +\newcommand\numberthis{\addtocounter{equation}{1}\tag{\theequation}} + \usepackage{cancel} \usepackage{graphicx} @@ -103,7 +105,7 @@ expressed as: &= V_{m}\sqrt{\frac{1}{T} \left[ \frac{t}{2} + \frac{1}{4\omega} \sin{(2\omega t)} \right]_{0}^T} \\ &= V_{m}\sqrt{\frac{1}{T} \left( \frac{T}{2} + \frac{1}{4\omega} \cancel{\sin{(2\omega T)}} - \frac{1}{4\omega} \cancel{\sin{(0)}} \right)} \\ &= V_{m}\sqrt{\frac{1}{\cancel{T}} \frac{\cancel{T}}{2}} \\ - &= \frac{V_{m}}{\sqrt{2}}. + &= \frac{V_{m}}{\sqrt{2}}. \numberthis \label{deriv:ac} \end{align*} \subsection{Signal type ~\ref{type:acoffset}} @@ -127,7 +129,7 @@ expressed as: &= V_{m}\sqrt{\frac{1}{T} \left( \frac{T}{2} + \frac{1}{4\omega} \cancel{\sin{(2\omega T)}} + \frac{2 V_{b}}{\omega V_{m}} \cancel{\sin{(\omega T)}} + T \left( \frac{V_{b}}{V_{m}} \right)^{2} - \frac{1}{4\omega} \cancel{\sin{(0)}} - \frac{2 V_{b}}{\omega V_{m}} \cancel{\sin{(0)}}\right)} \\ &= V_{m}\sqrt{\frac{1}{\cancel{T}} \left( \cancel{T} \right) \left( \frac{1}{2} + \left( \frac{V_{b}}{V_{m}} \right)^{2} \right)} \\ &= V_{m}\sqrt{\frac{1}{2} + \left( \frac{V_{b}}{V_{m}} \right)^{2}} \\ - &= \sqrt{\frac{V_{m}^{2}}{2} + V_{b}^{2}}. + &= \sqrt{\frac{V_{m}^{2}}{2} + V_{b}^{2}}. \numberthis \label{deriv:acoffset} \end{align*} \section{Numerical Modeling Results}