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

Chapter11Double Integrals

Objectives

This unit covers the following ideas.

  1. Explain how to setup and compute a double integral. Show how to interchange the bounds of integration.

  2. For planar regions, find area, mass, centroids, center of mass, moments of inertia, and radii of gyration.

  3. Explain how to change coordinate systems in integration, in particular to polar coordinates.

  4. Explain what the Jacobian is, and show how to use it.

  5. Explain how to use Green's theorem to compute flow along and flux across a curve.

Wrap Up

You've finished the chapter! Look at the objectives at the beginning of the chapter. Can you now do all the things you were promised?

Review Guide Creation

Your assignment: organize what you've learned into a small collection of examples that illustrates the key concepts. I'll call this your chapter review guide. I'll provide you with a template which includes the chapter's key concepts from the objectives at the beginning. Once you finish your review guide, scan it into a PDF document (use any scanner on campus or photo software) and upload it to Gradescope.

As you create this review guide, consider the following:

  • Before each Celebration of Knowledge we will devote a class period to review. With well created lesson plans, you will have 4-8 pages(for 2-4 Chapters) to review for each, instead of 50-100 problems.

  • Think ahead 2-5 years. If you make these lesson plans correctly, you'll be able to look back at your lesson plans for this semester. In about 20-25 pages, you can have the entire course summarized and easy for you to recall.