The Resource Methods of Small Parameter in Mathematical Biology, by Jacek Banasiak, Mirosław Lachowicz, (electronic resource)
Methods of Small Parameter in Mathematical Biology, by Jacek Banasiak, Mirosław Lachowicz, (electronic resource)
Resource Information
The item Methods of Small Parameter in Mathematical Biology, by Jacek Banasiak, Mirosław Lachowicz, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Methods of Small Parameter in Mathematical Biology, by Jacek Banasiak, Mirosław Lachowicz, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
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
 Extent
 XI, 285 pages 17 illustrations, 9 illustrations in color.
 Contents

 1 Small parameter methods
 basic ideas
 2 Introduction to the ChapmanEnskog method
 linear models with migrations
 3 TikhonovVasilyeva theory
 4 The Tikhonov theorem in some models of mathematical biosciences
 5 Asymptotic expansion method in a singularly perturbed McKendrick problem
 6 Diffusion limit of the telegraph equation
 7 Kinetic model of alignment
 8 From microscopic to macroscopic descriptions.  9 Conclusion
 Isbn
 9783319051406
 Label
 Methods of Small Parameter in Mathematical Biology
 Title
 Methods of Small Parameter in Mathematical Biology
 Statement of responsibility
 by 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
 ITFiEUI
 http://library.link/vocab/creatorName
 Banasiak, J
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Lachowicz, Mirosław.
 SpringerLink (Online service)
 Series statement

 Modeling and Simulation in Science, Engineering and Technology,
 Springer eBooks
 http://library.link/vocab/subjectName

 Mathematics
 Differential equations
 Genetics
 Label
 Methods of Small Parameter in Mathematical Biology, by Jacek Banasiak, Mirosław Lachowicz, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 1 Small parameter methods  basic ideas  2 Introduction to the ChapmanEnskog method  linear models with migrations  3 TikhonovVasilyeva theory  4 The Tikhonov theorem in some models of mathematical biosciences  5 Asymptotic expansion method in a singularly perturbed McKendrick problem  6 Diffusion limit of the telegraph equation  7 Kinetic model of alignment  8 From microscopic to macroscopic descriptions.  9 Conclusion
 Control code
 9783319051406
 Dimensions
 unknown
 Extent
 XI, 285 pages 17 illustrations, 9 illustrations in color.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319051406
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319051406
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1048130287
 Label
 Methods of Small Parameter in Mathematical Biology, by Jacek Banasiak, Mirosław Lachowicz, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 1 Small parameter methods  basic ideas  2 Introduction to the ChapmanEnskog method  linear models with migrations  3 TikhonovVasilyeva theory  4 The Tikhonov theorem in some models of mathematical biosciences  5 Asymptotic expansion method in a singularly perturbed McKendrick problem  6 Diffusion limit of the telegraph equation  7 Kinetic model of alignment  8 From microscopic to macroscopic descriptions.  9 Conclusion
 Control code
 9783319051406
 Dimensions
 unknown
 Extent
 XI, 285 pages 17 illustrations, 9 illustrations in color.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319051406
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319051406
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1048130287
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/MethodsofSmallParameterinMathematical/F5k5zROAWik/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/MethodsofSmallParameterinMathematical/F5k5zROAWik/">Methods of Small Parameter in Mathematical Biology, by Jacek Banasiak, Mirosław Lachowicz, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Methods of Small Parameter in Mathematical Biology, by Jacek Banasiak, Mirosław Lachowicz, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/MethodsofSmallParameterinMathematical/F5k5zROAWik/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/MethodsofSmallParameterinMathematical/F5k5zROAWik/">Methods of Small Parameter in Mathematical Biology, by Jacek Banasiak, Mirosław Lachowicz, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>