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Modeling and Inverse Problems in the Presence of Uncertainty (Paperback): H.T. Banks, Shuhua Hu, W. Clayton Thompson Modeling and Inverse Problems in the Presence of Uncertainty (Paperback)
H.T. Banks, Shuhua Hu, W. Clayton Thompson
R1,855 Discovery Miles 18 550 Ships in 12 - 17 working days

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 itself. After a useful review of relevant probability and statistical concepts, the book summarizes mathematical and statistical aspects of inverse problem methodology, including ordinary, weighted, and generalized least-squares formulations. It then discusses asymptotic theories, bootstrapping, and issues related to the evaluation of correctness of assumed form of statistical models. The authors go on to present methods for evaluating and comparing the validity of appropriateness of a collection of models for describing a given data set, including statistically based model selection and comparison techniques. They also explore recent results on the estimation of probability distributions when they are embedded in complex mathematical models and only aggregate (not individual) data are available. In addition, they briefly discuss the optimal design of experiments in support of inverse problems for given models. The book concludes with a focus on uncertainty in model formulation itself, covering the general relationship of differential equations driven by white noise and the ones driven by colored noise in terms of their resulting probability density functions. It also deals with questions related to the appropriateness of discrete versus continuum models in transitions from small to large numbers of individuals. With many examples throughout addressing problems in physics, biology, and other areas, this book is intended for applied mathematicians interested in deterministic and/or stochastic models and their interactions. It is also s

A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering (Paperback): H.T. Banks A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering (Paperback)
H.T. Banks
R1,753 Discovery Miles 17 530 Ships in 12 - 17 working days

A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional analysis can be the basis of modern partial differential equation (PDE) and delay differential equation (DDE) techniques. Recent Examples of Functional Analysis in Biology, Electromagnetics, Materials, and MechanicsThrough numerous application examples, the book illustrates the role that functional analysis-a classical subject-continues to play in the rigorous formulation of modern applied areas. The text covers common examples, such as thermal diffusion, transport in tissue, and beam vibration, as well as less traditional ones, including HIV models, uncertainty in noncooperative games, structured population models, electromagnetics in materials, delay systems, and PDEs in control and inverse problems. For some applications, computational aspects are discussed since many problems necessitate a numerical approach.

Modeling and Inverse Problems in the Presence of Uncertainty (Hardcover): H.T. Banks, Shuhua Hu, W. Clayton Thompson Modeling and Inverse Problems in the Presence of Uncertainty (Hardcover)
H.T. Banks, Shuhua Hu, W. Clayton Thompson
R5,297 Discovery Miles 52 970 Ships in 12 - 17 working days

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 itself. After a useful review of relevant probability and statistical concepts, the book summarizes mathematical and statistical aspects of inverse problem methodology, including ordinary, weighted, and generalized least-squares formulations. It then discusses asymptotic theories, bootstrapping, and issues related to the evaluation of correctness of assumed form of statistical models. The authors go on to present methods for evaluating and comparing the validity of appropriateness of a collection of models for describing a given data set, including statistically based model selection and comparison techniques. They also explore recent results on the estimation of probability distributions when they are embedded in complex mathematical models and only aggregate (not individual) data are available. In addition, they briefly discuss the optimal design of experiments in support of inverse problems for given models. The book concludes with a focus on uncertainty in model formulation itself, covering the general relationship of differential equations driven by white noise and the ones driven by colored noise in terms of their resulting probability density functions. It also deals with questions related to the appropriateness of discrete versus continuum models in transitions from small to large numbers of individuals. With many examples throughout addressing problems in physics, biology, and other areas, this book is intended for applied mathematicians interested in deterministic and/or stochastic models and their interactions. It is also s

A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering (Hardcover, New): H.T. Banks A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering (Hardcover, New)
H.T. Banks
R3,054 Discovery Miles 30 540 Ships in 12 - 17 working days

A Modern Framework Based on Time-Tested MaterialA Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional analysis can be the basis of modern partial differential equation (PDE) and delay differential equation (DDE) techniques. Recent Examples of Functional Analysis in Biology, Electromagnetics, Materials, and MechanicsThrough numerous application examples, the book illustrates the role that functional analysis-a classical subject-continues to play in the rigorous formulation of modern applied areas. The text covers common examples, such as thermal diffusion, transport in tissue, and beam vibration, as well as less traditional ones, including HIV models, uncertainty in noncooperative games, structured population models, electromagnetics in materials, delay systems, and PDEs in control and inverse problems. For some applications, computational aspects are discussed since many problems necessitate a numerical approach.

Estimation Techniques for Distributed Parameter Systems (Paperback, Softcover reprint of the original 1st ed. 1989): H.T.... Estimation Techniques for Distributed Parameter Systems (Paperback, Softcover reprint of the original 1st ed. 1989)
H.T. Banks, K. Kunisch
R1,475 Discovery Miles 14 750 Ships in 10 - 15 working days

The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations. Our attempts to apply control theory techniques to such prob lems in several areas of science convinced us that in the need for better and more detailed models of distributed/ continuum processes in biology and mechanics lay a rich, interesting, and challenging class of fundamen tal questions. These questions, which involve science and mathematics, are typical of those arising in inverse or parameter estimation problems. Our efforts on inverse problems for distributed parameter systems, which are infinite dimensional in the most common realizations, began about seven years ago at a time when rapid advances in computing capabilities and availability held promise for significant progress in the development of a practically useful as well as theoretically sound methodology for such problems. Much of the research reported in our presentation was not begun when we outlined the plans for this monograph some years ago. By publishing this monograph now, when only a part of the originally intended topics are covered (see Chapter VII in this respect), we hope to stimulate the research and interest of others in an area of scientific en deavor which has exceeded even our optimistic expectations with respect to excitement, opportunity, and stimulation. The computer revolution alluded to above and the development of new codes allow one to solve rather routinely certain estimation problems that would have been out of the question ten years ago."

Modeling and Control in the Biomedical Sciences (Paperback): H.T. Banks Modeling and Control in the Biomedical Sciences (Paperback)
H.T. Banks
R1,425 Discovery Miles 14 250 Ships in 10 - 15 working days

These notes are based on (i) a series of lectures that I gave at the 14th Biennial Seminar of the Canadian Mathematical Congress held at the University of Western Ontario August 12-24, 1973 and (li) some of my lectures in a modeling course that I have cotaught in the Division of Bio-Medical Sciences at Brown during the past several years. An earlier version of these notes appeared in the Center for Dynamical Systems Lectures Notes series (CDS LN 73-1, November 1973). I have in this revised and extended version of those earlier notes incorporated a number of changes based both on classroom experience and on my research efforts with several colleagues during the intervening period. The narrow viewpoint of the present notes (use of optimization and control theory in biomedical problems) reflects more the scope of the CMC lectures given in August, 1973 than the scope of my own interests. Indeed, my real interests have included the modeling process itself as well as the contributions made by investiga tors who employ the techniques and ideas of control theory, systems analysis, dif ferential equations, and stochastic processes. Some of these contributions have quite naturally involved application of optimal control theory. But in my opinion many of the interesting efforts being made in modeling in the biomedical sciences encompass much more than the use of control theory."

Mathematical and Experimental Modeling of Physical and Biological Processes (Hardcover): H.T. Banks, H. T. Tran Mathematical and Experimental Modeling of Physical and Biological Processes (Hardcover)
H.T. Banks, H. T. Tran
R2,823 Discovery Miles 28 230 Ships in 12 - 17 working days

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.

The Visitors' Centennial Guide to the Capitol - Gives a Brief History of the Capitol, Together with a Specific... The Visitors' Centennial Guide to the Capitol - Gives a Brief History of the Capitol, Together with a Specific Description... (Paperback)
H.T. Banks
R377 Discovery Miles 3 770 Ships in 10 - 15 working days
Estimation Techniques for Distributed Parameter Systems (Hardcover, 1989 ed.): H.T. Banks, K. Kunisch Estimation Techniques for Distributed Parameter Systems (Hardcover, 1989 ed.)
H.T. Banks, K. Kunisch
R2,159 Discovery Miles 21 590 Out of stock

The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations. Our attempts to apply control theory techniques to such prob­ lems in several areas of science convinced us that in the need for better and more detailed models of distributed/ continuum processes in biology and mechanics lay a rich, interesting, and challenging class of fundamen­ tal questions. These questions, which involve science and mathematics, are typical of those arising in inverse or parameter estimation problems. Our efforts on inverse problems for distributed parameter systems, which are infinite dimensional in the most common realizations, began about seven years ago at a time when rapid advances in computing capabilities and availability held promise for significant progress in the development of a practically useful as well as theoretically sound methodology for such problems. Much of the research reported in our presentation was not begun when we outlined the plans for this monograph some years ago. By publishing this monograph now, when only a part of the originally intended topics are covered (see Chapter VII in this respect), we hope to stimulate the research and interest of others in an area of scientific en­ deavor which has exceeded even our optimistic expectations with respect to excitement, opportunity, and stimulation. The computer revolution alluded to above and the development of new codes allow one to solve rather routinely certain estimation problems that would have been out of the question ten years ago.

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