*Academic Year 2022 - 2023*

*Semester 2*

This is a module on the calculus of functions of several real variables, applications of which abound in mathematics, the physical sciences and engineering. The aim is for students to acquire computational skills, ability for 2- and 3-D visualisation and to understand conceptually fundamental results such as Green’s Theorem, Stokes’ Theorem and the Divergence Theorem. Major topics Euclidean distance and elementary topological concepts in Rn, limit and continuity, implicit functions. Partial differentiation, differentiable functions, differentials, chain rules, directional derivatives, gradients, mean value theorem, Taylor’s formula, extreme value theorem, Lagrange multipliers. Multiple integrals and iterated integrals, change of order of integration, applications, Jacobian matrix, change of variables in multiple integrals. Line integrals and Green’s theorem. Surface integrals, Stokes’ Theorem, Divergence Theorem.

This module is taught by Prof Zhang Tengren. There are 3 assignments, a midterm and a final. The assignments were challenging and fun enough. I panicked during the midterm but I recollected myself and scored 48/50. The final is relatively easy for me.

I maybe attended 20% of the lectures and perhaps just 3 tutorial sessions. I went for my friend’s tutorial session instead of the one I registered for. I found this module easy and almost negligible workload because I have learnt most of the stuff during NS by self-studying the Oxford Maths course equivalent.

The only difficult part about this module is the high risk of carelessness. It is a very computational module, with little to no proving. I implore students to use a GC and check each step correctly. Are your bounds correct? Is the solid you identified the correct one? Are you missing a constant? Did you miss out the Jacobian?

What I liked about Prof Zhang (or rather what I learnt from him) is that he is a good artist. The 3D graphs he draws are so helpful for visualisation. My drawing skills for this module improved and this is actually very useful when doing questions. Prof Zhang is also very dedicated. He even gave lectures (albeit at a different time) whilst serving his reservist training.

I would recommend students who need to clear MA2104 to take it under Prof Zhang Tengren.