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The Resource Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz
Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz
Resource Information
The item Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 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
 1 online resource (xi, 285 pages)
 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
 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
 Dewey number
 570.1/51
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QH323.5
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Modeling and Simulation in Science, Engineering and Technology,
 Label
 Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 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
 Dimensions
 unknown
 Extent
 1 online resource (xi, 285 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319051406
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 SpringerLink
 Other control number
 10.1007/9783319051406
 Other physical details
 illustrations (some color).
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)878120950
 (OCoLC)ocn878120950
 Label
 Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 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
 Dimensions
 unknown
 Extent
 1 online resource (xi, 285 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319051406
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 SpringerLink
 Other control number
 10.1007/9783319051406
 Other physical details
 illustrations (some color).
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)878120950
 (OCoLC)ocn878120950
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/Methodsofsmallparameterinmathematical/snn0pPhA3eE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/Methodsofsmallparameterinmathematical/snn0pPhA3eE/">Methods of small parameter in mathematical biology, Jacek Banasiak, Mirosław Lachowicz</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>