$$ \def\ab{\boldsymbol{a}} \def\bb{\boldsymbol{b}} \def\cb{\boldsymbol{c}} \def\db{\boldsymbol{d}} \def\eb{\boldsymbol{e}} \def\fb{\boldsymbol{f}} \def\gb{\boldsymbol{g}} \def\hb{\boldsymbol{h}} \def\kb{\boldsymbol{k}} \def\nb{\boldsymbol{n}} \def\tb{\boldsymbol{t}} \def\ub{\boldsymbol{u}} \def\vb{\boldsymbol{v}} \def\xb{\boldsymbol{x}} \def\yb{\boldsymbol{y}} \def\Ab{\boldsymbol{A}} \def\Bb{\boldsymbol{B}} \def\Cb{\boldsymbol{C}} \def\Eb{\boldsymbol{E}} \def\Fb{\boldsymbol{F}} \def\Jb{\boldsymbol{J}} \def\Lb{\boldsymbol{L}} \def\Rb{\boldsymbol{R}} \def\Ub{\boldsymbol{U}} \def\xib{\boldsymbol{\xi}} \def\evx{\boldsymbol{e}_x} \def\evy{\boldsymbol{e}_y} \def\evz{\boldsymbol{e}_z} \def\evr{\boldsymbol{e}_r} \def\evt{\boldsymbol{e}_\theta} \def\evp{\boldsymbol{e}_r} \def\evf{\boldsymbol{e}_\phi} \def\evb{\boldsymbol{e}_\parallel} \def\omb{\boldsymbol{\omega}} \def\dA{\;d\Ab} \def\dS{\;d\boldsymbol{S}} \def\dV{\;dV} \def\dl{\mathrm{d}\boldsymbol{l}} \def\bfzero{\boldsymbol{0}} \def\Rey{\mathrm{Re}} \def\Real{\mathbb{R}} \newcommand{\dds}[1]{\frac{d{#1}}{ds}} \newcommand{\ddy}[2]{\frac{\partial{#1}}{\partial{#2}}} \newcommand{\ddt}[1]{\frac{d{#1}}{dt}} \newcommand{\DDt}[1]{\frac{\mathrm{D}{#1}}{\mathrm{D}t}} $$
Preamble
These are the lecture notes for MATH 2031 Analysis in Many Variables for Michaelmas Term 2023/24. I will generally follow these notes in the lectures, although not word for word.
If you do spot any significant discrepancies, or typos in the notes, then please let me know!
Many aspects of the notes draw on those inherited from previous lecturers on the course including Emma Coutts, Ian Vernon, Patrick Dorey and Sam Fearn. I have also made use of other publicly-available lecture notes from David Tong, Andrea Moiola, Stephen Cowley and Oliver Knill. You may also find these useful to look at.
In these notes, remarks like this are “non-examinable” extra information.
The notes are formatted with Quarto (https://quarto.org/docs/books).