$$ \def\ab{\boldsymbol{a}} \def\bb{\boldsymbol{b}} \def\cb{\boldsymbol{c}} \def\db{\boldsymbol{d}} \def\eb{\boldsymbol{e}} \def\fb{\boldsymbol{f}} \def\gb{\boldsymbol{g}} \def\hb{\boldsymbol{h}} \def\kb{\boldsymbol{k}} \def\nb{\boldsymbol{n}} \def\tb{\boldsymbol{t}} \def\ub{\boldsymbol{u}} \def\vb{\boldsymbol{v}} \def\xb{\boldsymbol{x}} \def\yb{\boldsymbol{y}} \def\Ab{\boldsymbol{A}} \def\Bb{\boldsymbol{B}} \def\Cb{\boldsymbol{C}} \def\Eb{\boldsymbol{E}} \def\Fb{\boldsymbol{F}} \def\Jb{\boldsymbol{J}} \def\Lb{\boldsymbol{L}} \def\Rb{\boldsymbol{R}} \def\Ub{\boldsymbol{U}} \def\xib{\boldsymbol{\xi}} \def\evx{\boldsymbol{e}_x} \def\evy{\boldsymbol{e}_y} \def\evz{\boldsymbol{e}_z} \def\evr{\boldsymbol{e}_r} \def\evt{\boldsymbol{e}_\theta} \def\evp{\boldsymbol{e}_r} \def\evf{\boldsymbol{e}_\phi} \def\evb{\boldsymbol{e}_\parallel} \def\omb{\boldsymbol{\omega}} \def\dA{\;d\Ab} \def\dS{\;d\boldsymbol{S}} \def\dV{\;dV} \def\dl{\mathrm{d}\boldsymbol{l}} \def\rmd{\mathrm{d}} \def\bfzero{\boldsymbol{0}} \def\Rey{\mathrm{Re}} \def\Real{\mathbb{R}} \def\grad{\boldsymbol\nabla} \newcommand{\dds}[2]{\frac{d{#1}}{d{#2}}} \newcommand{\ddy}[2]{\frac{\partial{#1}}{\partial{#2}}} \newcommand{\pder}[3]{\frac{\partial^{#3}{#1}}{\partial{#2}^{#3}}} \newcommand{\deriv}[3]{\frac{d^{#3}{#1}}{d{#2}^{#3}}} \newcommand{\ddt}[1]{\frac{d{#1}}{dt}} \newcommand{\DDt}[1]{\frac{\mathrm{D}{#1}}{\mathrm{D}t}} \newcommand{\been}{\begin{enumerate}} \newcommand{\enen}{\end{enumerate}}\newcommand{\beit}{\begin{itemize}} \newcommand{\enit}{\end{itemize}} \newcommand{\nibf}[1]{\noindent{\bf#1}} \def\bra{\langle} \def\ket{\rangle} \renewcommand{\S}{{\cal S}} \newcommand{\wo}{w_0} \newcommand{\wid}{\hat{w}} \newcommand{\taus}{\tau_*} \newcommand{\woc}{\wo^{(c)}} \newcommand{\dl}{\mbox{$\Delta L$}} \newcommand{\upd}{\mathrm{d}} \newcommand{\dL}{\mbox{$\Delta L$}} \newcommand{\rs}{\rho_s} $$
Preamble
These are the lecture notes for MATH 2031 Analysis in Many Variables for Epiphany Term 2024/25. 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 Anne Taormina as well as Andrew Krause, Andreas Muench and Derek Moulton. It borrows heavily form the style of Anthony Yeates in term 1.
The notes are formatted with Quarto (https://quarto.org/docs/books).