HTSEFP: Multivariable calculus CC-BY-NC

Maintainer: admin

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.

1.1General solution

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.