The Resource Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz, (electronic book)
Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz, (electronic book)
Resource Information
The item Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant and preserves the salient features of the dynamics. The aim of this book is to present a systematic way of deriving the socalled limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools described allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in appled and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis
 Language
 eng
 Label
 Methods of small parameter in mathematical biology
 Title
 Methods of small parameter in mathematical biology
 Statement of responsibility
 Jacek Banasiak, Mirosław Lachowicz
 Language
 eng
 Summary
 This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant and preserves the salient features of the dynamics. The aim of this book is to present a systematic way of deriving the socalled limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools described allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in appled and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Banasiak, J
 Dewey number
 570.1/51
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QH323.5
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Lachowicz, Mirosław
 Series statement
 Modeling and Simulation in Science, Engineering and Technology,
 http://library.link/vocab/subjectName

 Biomathematics
 Biology
 Label
 Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz, (electronic book)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Color
 multicolored
 Control code
 SPR878120950
 Dimensions
 unknown
 Extent
 1 online resource (xi, 285 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319051390
 Level of compression
 unknown
 Other control number
 10.1007/9783319051406
 Other physical details
 illustrations (some color).
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
 Label
 Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz, (electronic book)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Color
 multicolored
 Control code
 SPR878120950
 Dimensions
 unknown
 Extent
 1 online resource (xi, 285 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319051390
 Level of compression
 unknown
 Other control number
 10.1007/9783319051406
 Other physical details
 illustrations (some color).
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Methodsofsmallparameterinmathematical/VAK2M_Q0LA/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Methodsofsmallparameterinmathematical/VAK2M_Q0LA/">Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz, (electronic book)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>