This is an old revision of the document!
We derived the transport equation; we reviewed the visualisation of scalar and vector-valued functions.
We reviewed key notions of Riemann integration (the idea of adding up infinitesimal elements), then started investigating the notion of a scalar line integral.
We covered the computation of scalar integrals and work integrals, doing examples for both. We also covered various properties of curves (reversability, for instance) and wrote down properties of line integrals that will be attempted as part of the homework.
We discussed the definition of conservative fields, and covered the important (BIG) theorem on conservative forces, and discussed its importance in the computation of work integrals. We ended with a result linking work integrals with change in kinetic energy (to be completed in lecture 5).