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With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.

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Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces - all in a single study. Detailed analyses. Problems. Bibliography. Index.

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This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models t...

This book is based on a one semester course that the authors have been teaching for several years, and includes two sets of case studies.  The first includes chemostat models, predator-prey interaction, competition among species, the spread of infectious diseases, and oscillations arising from bifurcations.  In developing these topics, readers will also be introduced to the basic theory of ordinary differential equations, and how to work with ...

Considers models that are described by systems of partial differential equations, focusing on modelling rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing.

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This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to a variety of problems in partial differential equations. It covers Cauchy and Goursat problems, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. 1963 edition

Intended for students who have already completed a one-year course in elementary calculus, this two-part treatment advances from functions of one variable to those of several variables. Solutions. 1971 edition.

Largely self-contained, this three-part treatment focuses on elliptic and evolution equations, concluding with a series of independent topics directly related to the methods and results of the preceding sections. 1969 edition.

This book presents mathematical models that arise in current photographic science. The book contains seventeen chapters, each dealing with one area of photographic science, and a final chapter containing exercises. Each chapter, except the two introductory chapters, begin with general background information at a level understandable by graduate and undergraduate students. It then proceeds to develop a mathematical model, using mathematical too...

The 9th volume in Avner Friedmans collection of Mathematics in Industrial problems. Fostering interaction between industry and mathematics at the "grass roots" level, the problems presented here arise from models developed by industrial scientists engaged in R&D, of new or improved products. Topics explored in this volume include diffusion in porous media and in rubber/glass transition, coating flows, solvation of molecules, semiconductor proc...

This is the tenth volume in the series "Mathematics in Industrial Prob­ lems. " The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level, " that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob­ lems ha...

This is the eighth volume in the series "Mathematics in Industrial Prob­ lems." The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level", that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob­ lems hav...

Advanced graduate-level text examines variational methods in partial differential equations and illustrates their applications to free-boundary problems. Features detailed statements of standard theory of elliptic and parabolic operators. 1982 edition.

Building a bridge between mathematicians and industry is both a chal­ lenging task and a valuable goal for the Institute for Mathematics and its Applications (IMA). The rationale for the existence of the IMA is to en­ courage interaction between mathematicians and scientists who use math­ ematics. Some of this interaction should evolve around industrial problems which mathematicians may be able to solve in "real time." Both Industry and Mathem...

This is the sixth volume in the series "Mathematics in Industrial Prob­ lems. " The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level", that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob­ lems hav...