Preface

Welcome. These are the interactive notes for Mathematical Methods and Modelling I — a living, evolving book rather than a static PDF. They combine my own material, contributions and notes from colleagues, embedded video lectures, and worked examples, and they will keep growing throughout the semester: new sections, simulations, and exercises will be added as we go.

Every chapter follows the same rhythm you’ll meet again and again in this course: motivate \(\to\) formulate \(\to\) solve \(\to\) interpret. Wherever possible I’ve tried to lead with a real question before the mathematics, because differential equations are far more interesting — and far easier to remember — when you know why someone needed them in the first place.

This book is a collaborative effort, and it improves every year because students tell me what’s confusing, what’s missing, or what’s just plain wrong. If you spot a typo, an unclear explanation, or an error, please let me know — you’ll be helping the next cohort as much as yourself.

I hope you enjoy the journey from “what is a differential equation?” to being able to look at a real, messy situation and see the equation hiding inside it.

AHC