Mathematical Techniques For Physiology And Medicine

Mathematical Techniques For Physiology and Medicine

Suitable for both graduate and undergraduate courses, this text recalls basic concepts of calculus and shows how problems can be formulated in terms of differential equations. Fully worked-out solutions to selected problems. Fourth edition.

This book is intended for medical students and advanced undergraduates such as physicists and mathematicians with inter-disciplinary interests, biophysicists, medical physicists, applied mathematicians and others who wish to understand medicine in mathematical terms as well as current mathematical applications in physiology and medicine. The mathematical presentation is clear and self-contained.This book, representing 15 years of work at RAND Corporation and USC on chemotherapy, pharmacokinetics and nuclear medicine, attempts to direct medical scientists towards mathematical aspects of problems in medicine. The book begins with an introduction to compartmental models and matrix theory, highlighting the advantages of the approach. Discussions on how questions in observations and testing lead to multi-point boundary value problems are presented. The potentials of the digital computer in the bio-medical field are examined. A new approach — dynamic programming — to overcome clinical constraints is covered in detail. The reader should obtain a broad impression of where future research opportunities in the biochemical field lie.

The aim of this book is to introduce the subject of mathematical modeling in the life sciences. It is intended for students of mathematics, the physical sciences, and engineering who are curious about biology. Additionally, it will be useful to students of the life sciences and medicine who are unsatisfied with mere description and who seek an understanding of biological mechanism and dynamics through the use of mathematics. The book will be particularly useful to premedical students, because it will introduce them not only to a collection of mathematical methods but also to an assortment of phenomena involving genetics, epidemics, and the physiology of the heart, lung, and kidney. Because of its introductory character, mathematical prerequisites are kept to a minimum; they involve only what is usually covered in the first semester of a calculus sequence. The authors have drawn on their extensive experience as modelers to select examples which are simple enough to be understood at this elementary level and yet realistic enough to capture the essence of significant biological phenomena drawn from the areas of population dynamics and physiology. Because the models presented are realistic, the book can serve not only as an introduction to mathematical methods but also as a mathematical introduction to the biological material itself. For the student, who enjoys mathematics, such an introduction will be far more stimulating and satisfying than the purely descriptive approach that is traditional in the biological sciences.

Introduces concepts from nonlinear dynamics using an almost exclusively biological setting for motivation, and includes examples of how these concepts are used in experimental investigations of biological and physiological systems. One novel feature of the book is the inclusion of classroom-tested computer exercises. This book will appeal to students and researchers working in the natural and physical sciences wanting to learn about physiological systems from a mathematical perspective.

First multi-year cumulation covers six years: 1965-70.