Basic multivariable calculus. Should be mostly review from Calculus 3 or A/B.
1Reversing the order of integration¶
A seemingly impossible integral involving e, and a simple region in two dimensions.
Have to change the order of integration. After that it should be a breeze.
2Change 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)
3Deriving surface area in a specific coordinate system¶
Won't need to do this (no proofs etc)
- Assignment 1, question 4
4Integrating 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.