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In my first semester of university I learned using substitution for integrals (I study physics not math). Now I took a math class where we were introduced to transformation, for example polar coordinates, etc. I already knew polar coodinates from physics but for me it seemed like just a good substitution. Now I wonder if substitution and transformation are the same thing or not.

I appreciate an explanation.

Lizzi
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  • If you integrate a function of two variables over circle in cartesian coordinates and use polar substitution, domain of integration “unrolls” into rectangle with sides on $r$ and $\varphi$ axes. – Yalikesifulei Mar 09 '21 at 13:02

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