Diffusion and growth phenomena abound in the real worldsurrounding us. Someexamples: growth of the world'spopulation, growth rates of humans, public interest in newsevents, growth and decline of central city populations,pollution of rivers, adoption of agricultural innovations,and spreading of epidemics and migration of insects. Theseand numerous other phenomena are illustrations of typicalgrowth and diffusion problems confronted in many branches ofthe physical, biological and social sciences as well as invarious areas of agriculture, business, education,engineering medicine and public health. The book presents alarge number of mathematical models to provide frameworksforthe analysis and display of many of these. The modelsdeveloped and utilizedcommence with relatively simpleexponential, logistic and normal distribution functions.Considerable attention is given to time dependent growthcoefficients and carrying capacities. The topics of discreteand distributed time delays, spatial-temporal diffusion anddiffusion with reaction are examined. Throughout the bookthere are a great many numerical examples. In addition andmost importantly, there are more than 50 in-depth"illustrations" of the application of a particular frameworkormodel based on real world problems. These examplesprovide the reader with an appreciation of the intrinsicnature of the phenomena involved. They address mainlyreaders from the physical, biological, and social sciences,as the only mathematical background assumed is elementarycalculus. Methods are developed as required, and the readercan thus acquire useful tools for planning, analyzing,designing,and evaluating studies of growth transfer anddiffusion phenomena. The book draws on the author's ownhands-on experience in problems of environmental diffusionand dispersion, as well as in technology transfer andinnovation diffusion.
1 Introduction.- 2 Some Basic Frameworks.- 3 Some Additional Frameworks.- 4 Phenomena with Variable Growth Coefficients.- 5 Phenomena with Variable Carrying Capacities.- 6 Phenomena with Time Delays.- 7 Phenomena with Spatial Diffusion.- 8 Conclusion.- References.- Author Index.
Series: Texts in Applied Mathematics
Number Of Pages: 455
Published: 22nd December 1993
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.4 x 15.6
Weight (kg): 0.84