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Obesity Expertise · Book 2

Mathematics for modelling and inferenceRung 1 · Introductory

Reading the equations in a paper instead of skipping them

Dr. Harsh Maheshwari · Version 1.1 · updated 24 September 2026 · CC BY-NC-SA 4.0

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Why this book

Most papers on body weight carry a few equations, and most readers skip them. The argument is often in those lines. Book 0 named the derivative and the integral and asked you to work out neither. This book asks you to work them out, on body stores rather than on made-up curves. It adds the few tools that the equations in these papers keep using: tables of numbers multiplied together, the arithmetic of chance, and the point where a changing system stops changing.

How to read it

Read Book 0 and Book 1 first, or at least the sections this book names as it goes. Then read this one in order: each section assumes everything before it. Do the practice problems in each section before you read on, with a pen and a calculator. Keep a notebook open as you go. By the end it should hold ten equations from papers you have read, each written out in words. What this book does not teach yet: the product and chain rules, partial derivatives, likelihood, confidence intervals, hypothesis tests, regression and causal inference. Later books in the series take them up; “inference” in the title is where this subject’s rungs are heading.

1 Reading the symbols in a methods section

2 The derivative: the rate at an instant, computed

3 The few rules that do the differentiating

4 The number e, natural logarithms and change proportional to amount

5 The integral of a rate is the change in the stock

6 Undoing a derivative: antiderivatives and the fundamental theorem

7 A differential equation: a rule that gives the rate from the state

8 Equilibrium: where the rate is zero

9 Highest and lowest points: slope zero and curvature

10 Vectors as data rows, and the weighted sum

11 A matrix, and what multiplying by one does

12 A column that is a weighted sum of other columns

13 A random variable and its distribution

14 Expectation

15 Variance, and why independent errors add as squares

16 Following a derivation without skipping

17 Four kinds of equation, and the notebook entry

References 157
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