Growth and diffusion phenomena : mathematical frameworks and applications
著者
書誌事項
Growth and diffusion phenomena : mathematical frameworks and applications
（Texts in applied mathematics, 14）
Springer-Verlag, c1994
- : gw
- : us
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注記
Includes bibliographical references (p. [429]-443) and indexes
内容説明・目次
内容説明
Diffusion and growth phenomena abound in the real world
surrounding us. Someexamples: growth of the world's
population, growth rates of humans, public interest in news
events, growth and decline of central city populations,
pollution of rivers, adoption of agricultural innovations,
and spreading of epidemics and migration of insects. These
and numerous other phenomena are illustrations of typical
growth and diffusion problems confronted in many branches of
the physical, biological and social sciences as well as in
various areas of agriculture, business, education,
engineering medicine and public health. The book presents a
large number of mathematical models to provide frameworks
forthe analysis and display of many of these. The models
developed and utilizedcommence with relatively simple
exponential, logistic and normal distribution functions.
Considerable attention is given to time dependent growth
coefficients and carrying capacities. The topics of discrete
and distributed time delays, spatial-temporal diffusion and
diffusion with reaction are examined. Throughout the book
there are a great many numerical examples. In addition and
most importantly, there are more than 50 in-depth
"illustrations" of the application of a particular framework
ormodel based on real world problems. These examples
provide the reader with an appreciation of the intrinsic
nature of the phenomena involved. They address mainly
readers from the physical, biological, and social sciences,
as the only mathematical background assumed is elementary
calculus. Methods are developed as required, and the reader
can thus acquire useful tools for planning, analyzing,
designing,and evaluating studies of growth transfer and
diffusion phenomena. The book draws on the author's own
hands-on experience in problems of environmental diffusion
and dispersion, as well as in technology transfer and
innovation diffusion.
目次
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.
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