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Teaching and applying mathematical modelling

Mathematical In medicine, Pp 252, £14-65. 1983. This book aims to show that interesting mathematical problems can arise from questions in Physiology and Medicine. Finding the best strategy to be used in drug therapy, the use of radiation in diagnosis or in treatment leads via mathematical formulation to corresponding problems in what is now called Optimal Control Theory. The techniques introduced here are those of (extended) Calculus of Variations and of Dynamic Programming. Although sections appear elementary the book is not an introduction to Control Theory nor a textbook. It is an invitation to professional Mathematicians, Physicists and Engineers to join the study of optimal treatment in Medicine with an assurance that they will meet hard but congenial problems there. Physical scientists with a knowledge of Systems Theory will be interested by this book. Readers with no background in control will have to skim judiciously to follow the text. There are gaps in the development of theory and in presenting the equations describing the therapy while some simple manipulations are fully described. The mathematical background assumed is very uneven—how many people do you know who are familiar with uniform boundedness but do not know about matrices and eigenvalues? The book is unlikely to be helpful in giving a first introduction to the use of mathematics in Medicine for those unfamiliar with Systems Theory or related mathematical subjects.