evaluating multiple integrals: polar coordinates
(1.3 hours to learn)
A common trick for computing double integrals is to transform them into a polar coordinate representation. Canonical examples include integrating a Gaussian and computing moments of inertia.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ MIT Open Courseware: Multivariable Caclulus (2010)
Video lectures for MIT's introductory multivariable calculus class.
→ Multivariable Calculus
An introductory multivariable calculus textbook.
Location: Section 14.4, "Double integrals in polar coordinates," pages 961-966
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location: Section 7.3, "Polar, cylindrical, and spherical coordinates," pages 288-296
- This trick can be generalized to three dimensions:change of variables .
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