MediumChange of variables

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.2 Change to Better Coordinates, #16 · Multivariable Calculus · Change of variables

Draw the … region … that corresponds in 17–22 to the …

Change four-sided regions to squares.

A nonlinear term $uv$ was needed in Problem 15. Which regions $R$ could change to the square $S$ with a linear $x = a u + b v$ , $y = c u + d v$ ?

Draw the $x y$ region $R$ that corresponds in 17–22 to the $uv$ square $S$ with corners $(0, 0)$ , $(1, 0)$ , $(0, 1)$ , $(1, 1)$ . Locate the corners of $R$ and then its sides (like a jigsaw puzzle).

This exercise builds on another exercise in its source book, which isn't shown here.

~8 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.2 Change to Better Coordinates, #16

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.