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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)

Label
Methods of Small Parameter in Mathematical Biology
Title
Methods of Small Parameter in Mathematical Biology
Statement of responsibility
by Jacek Banasiak, Mirosław Lachowicz
Creator
Contributor
Author
Subject
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 so-called 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
Member of
Cataloging source
IT-FiEUI
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)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-05140-6
Instantiates
Publication
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 Chapman--Enskog method -- linear models with migrations -- 3 Tikhonov--Vasilyeva 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
978-3-319-05140-6
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, non-commercial 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
10.1007/978-3-319-05140-6
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)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-05140-6
Publication
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 Chapman--Enskog method -- linear models with migrations -- 3 Tikhonov--Vasilyeva 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
978-3-319-05140-6
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, non-commercial 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
10.1007/978-3-319-05140-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1048130287

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