Borrow it
Coverart for item
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)

Creator
Author
Contributor
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
Language
eng
Work
Publication
Extent
1 online resource (xi, 285 pages)
Isbn
9783319051390
Instance
Label
Methods of small parameter in mathematical biology
Title
Methods of small parameter in mathematical biology
Statement of responsibility
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
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)
Instantiates
Publication
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
10.1007/978-3-319-05140-6
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)
Publication
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
10.1007/978-3-319-05140-6
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

Subject

Member of

Library Locations

Library Links

Structured data from the Bibframe namespace is licensed under the Creative Commons Attribution 4.0 International License by University of Liverpool. Additional terms may apply to data associated with third party namespaces.
Processing Feedback ...