Estimation Of Probability Distributions For Individual Parameters Using Aggregate Population Observations
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Mathematical and Experimental Modeling of Physical and Biological Processes
Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why a model is needed and what goals can be achieved with the model. Exploring what mathematics can reveal about applications, the book focuses on the design of appropriate experiments to validate the development of mathematical models. It guides students through the modeling process, from empirical observations and formalization of properties to model analysis and interpretation of results. The authors also describe the hardware and software tools used to design the experiments so faculty/students can duplicate them. Integrating real-world applications into the traditional mathematics curriculum, this textbook deals with the formulation and analysis of mathematical models in science and engineering. It gives students an appreciation of the use of mathematics and encourages them to further study the applied topics. Real experimental data for projects can be downloaded from CRC Press Online.
Estimation of Probability Distributions for Individual Parameters Using Aggregate Population Observations
In this paper we discuss a general methodology for estimating the distribution of individual growth rates in a size-structured population using aggregate population data. The method, for which rigorous theoretical formulations have been developed, is presented in the context of an inverse problem methodology and its use in illustrated with application to mosquitofish, Gambusia affinis, population in rice fields.
Modeling and Inverse Problems in the Presence of Uncertainty
Modeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation i