Mathematics of the Living Body

The Mathematics of the Living Body, Volume 1: Cardiovascular PhysiologyThis is a physiology book written in equations.Not a mathematics textbook that uses the heart as a worked example - the physiology comes first, always. Every equation in the book emerges from a named protein, a measurable cellular event, or a conservation law that the biology makes necessary. The mathematics follows because it is the only honest way to describe what the system is doing.The central argumentThe cardiovascular system is a control architecture. It is not a collection of organs with properties to memorise. It is a set of feedback loops, setpoints, and dynamical subsystems - a pressure-controlled pump connected to a resistance network, regulated by a proportional-integral controller in the brainstem, a hormonal cascade in the kidney, and local autoregulation in every organ. Once you see it this way, the pharmacology, the pathology, and the clinical decision-making all follow from the same framework.That framing is not new to physiology research. It is almost entirely absent from medical education.Each chapter opens with the molecular biology - named genes, named proteins, named mechanisms - before any equation appears. Each carries an explicit Model Assumptions box distinguishing core physical principles from useful approximations from empirical fits. Worked examples report ranges, not single numbers.The reader is a medical student who already knows basic physiology and wants to know why, a biomedical engineering student who wants clinical grounding, or a quantitatively minded clinician who prefers mechanism-first explanations. It is a companion text, not a primary medical textbook - strongest for readers who want the first-principles framework underneath the clinical vocabulary they already have.Where physiology ends, mathematics begins.