**Maintainer:**admin

Basic multivariable calculus. Should be mostly review from Calculus 3 or A/B.

*1*Reversing the order of integration¶

A seemingly impossible integral involving e, and a simple region in two dimensions.

*1.1*General solution¶

Have to change the order of integration. After that it should be a breeze.

*1.2*Examples¶

*2*Change of variables over a region¶

Notes: For the Jacobian: new variables go on the bottom, but take the inverse of that because otherwise it's hard to compute (so 1 over the value). Also positive (since, abs value etc)

*2.1*Examples¶

- Assignment 1, questions 1-3
- Winter 2006 final, question 3
- Winter 2010 final, question 2

*3*Deriving surface area in a specific coordinate system¶

Won't need to do this (no proofs etc)

*3.1*Examples¶

- Assignment 1, question 4

*4*Integrating using spherical coordinates¶

Basically a surface integral. Parametrise it, take the cross-product of the two partial derivatives, use that as the integrand and integrate over the limits of the region.