Mathematical Techniques for Biology and Medicine

For many years statistics has been regarded as the essential mathematical preparationfor biologists. Recently, however, it has become necessary to broaden this background to includeadvanced techniques such as linear differential equations. The difficulty with this has been thatmost courses in differential equations are designed for engineering students. This book is designedfor biologists. It was developed in a graduate course at the University of Rochester School ofMedicine but the approach is such that it will be useful at either the undergraduates or thegraduate level. The only prerequisite is elementary calculus, and the assumption is that the studenthas probably forgotten much of what he learned in that course.The book begins with a review of theconcepts of elementary calculus and shows how physiological problems can be formulated in terms ofdifferential equations. It then proceeds quickly but in an entirely self-contained way to developthree techniques for the solution of differential equations: solution by Laplace transform, solutionby inspection of the physical problem, and numerical solutions. These are applied to the types ofproblems most often encountered in physiology: compartmental problems, regulations, diffusion, flowmeasurements, and curve fitting. The terminology used in the problems and examples will be familiarto biologists. In each chapter the problems range from routine to fairly difficult.The first editionof this book was published in hardcover in 1972 with the title Mathematical Techniques forPhysiology and Medicine. This revised contains a new chapter, on tracer experiments, and twoadditional appendixes. Many new problems (and their solutions) have also been added.