Skip to main content
\(\renewcommand{\chaptername}{Unit} \newcommand{\derivativehomeworklink}[1]{\href{http://db.tt/cSeKG8XO}{#1}} \newcommand{\chpname}{unit} \newcommand{\sageurlforcurvature}{http://bmw.byuimath.com/dokuwiki/doku.php?id=curvature_calculator} \newcommand{\uday}{ \LARGE Day \theunitday \normalsize \flushleft \stepcounter{unitday} } \newcommand{\sageworkurl}{http://bmw.byuimath.com/dokuwiki/doku.php?id=work_calculator} \newcommand{\sagefluxurl}{http://bmw.byuimath.com/dokuwiki/doku.php?id=flux_calculator} \newcommand{\sageworkfluxurl}{http://bmw.byuimath.com/dokuwiki/doku.php?id=both_flux_and_work} \newcommand{\sagelineintegral}{http://bmw.byuimath.com/dokuwiki/doku.php?id=line_integral_calculator} \newcommand{\sagephysicalpropertiestwod}{http://bmw.byuimath.com/dokuwiki/doku.php?id=physical_properties_in_2d} \newcommand{\sagephysicalpropertiesthreed}{http://bmw.byuimath.com/dokuwiki/doku.php?id=physical_properties_in_3d} \newcommand{\sageDoubleIntegralCheckerURL}{http://bmw.byuimath.com/dokuwiki/doku.php?id=double_integral_calculator} \newcommand{\myscale}{1} \newcommand{\ds}{\displaystyle} \newcommand{\dfdx}[1]{\frac{d#1}{dx}} \newcommand{\ddx}{\frac{d}{dx}} \newcommand{\ii}{\vec \imath} \newcommand{\jj}{\vec \jmath} \newcommand{\kk}{\vec k} \newcommand{\vv}{\mathbf{v}} \newcommand{\RR}{\mathbb{R}} \newcommand{\R}{ \mathbb{R}} \newcommand{\inv}{^{-1}} \newcommand{\im}{\text{im }} \newcommand{\colvec}[1]{\begin{bmatrix}#1\end{bmatrix} } \newcommand{\cl}[1]{ \begin{matrix} #1 \end{matrix} } \newcommand{\bm}[1]{ \begin{bmatrix} #1 \end{bmatrix} } \DeclareMathOperator{\rank}{rank} \DeclareMathOperator{\rref}{rref} \DeclareMathOperator{\vspan}{span} \DeclareMathOperator{\trace}{tr} \DeclareMathOperator{\proj}{proj} \DeclareMathOperator{\curl}{curl} \newcommand{\blank}[1]{[14pt]{\rule{#1}{1pt}}} \newcommand{\vp}{^{\,\prime}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)

ColophonColophon

Edition Web-Enhanced Edition

Website faculty.valpo.edu/calculus3ibl

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. You may copy, distribute, display, and perform this copyrighted work, but only if you give credit to Ben Woodruff and Karl R. B. Schmitt, and all derivative works based upon it must be published under the Creative Commons Attribution-Share Alike 4.0 International License (or an updated equivalent). Please attribute this work to Ben Woodruff, Mathematics Faculty at Brigham Young University--Idaho, woodruffb@byui.edu and Karl R. B. Schmitt, Mathematics and Statistics Faculty at Valparaiso University karl.schmitt@valpo.edu.