Holdings: Methods of small parameter in mathematical biology

Methods of small parameter in mathematical biology:

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Bibliographic Details
Main Authors:	Banasiak, Jacek 1959- (Author), Lachowicz, Mirosław (Author)
Format:	Electronic eBook
Language:	English
Published:	Cham [u.a.] Birkhäuser 2014
Series:	Modeling and simulation in science, engineering and technology
Online Access:	DE-634 DE-861 DE-91 DE-384 DE-19 DE-703 DE-20 DE-739 Volltext Inhaltsverzeichnis Abstract
Physical Description:	1 Online-Ressource
ISBN:	9783319051406
DOI:	10.1007/978-3-319-05140-6

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MARC


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adam_text	METHODS OF SMALL PARAMETER IN MATHEMATICAL BIOLOGY / BANASIAK, JACEK : 2014 TABLE OF CONTENTS / INHALTSVERZEICHNIS 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 DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. METHODS OF SMALL PARAMETER IN MATHEMATICAL BIOLOGY / BANASIAK, JACEK : 2014 ABSTRACT / INHALTSTEXT 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 DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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author	Banasiak, Jacek 1959- Lachowicz, Mirosław
author_GND	(DE-588)141516585 (DE-588)1058418297
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author_sort	Banasiak, Jacek 1959-
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dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
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dewey-tens	510 - Mathematics
discipline	Biologie Mathematik
doi_str_mv	10.1007/978-3-319-05140-6
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spelling	Banasiak, Jacek 1959- Verfasser (DE-588)141516585 aut Methods of small parameter in mathematical biology Jacek Banasiak ; Miroslaw Lachowicz Cham [u.a.] Birkhäuser 2014 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Modeling and simulation in science, engineering and technology Lachowicz, Mirosław Verfasser (DE-588)1058418297 aut Erscheint auch als Druckausgabe 978-3-319-05139-0 https://doi.org/10.1007/978-3-319-05140-6 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027310334&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027310334&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract
spellingShingle	Banasiak, Jacek 1959- Lachowicz, Mirosław Methods of small parameter in mathematical biology
title	Methods of small parameter in mathematical biology
title_auth	Methods of small parameter in mathematical biology
title_exact_search	Methods of small parameter in mathematical biology
title_full	Methods of small parameter in mathematical biology Jacek Banasiak ; Miroslaw Lachowicz
title_fullStr	Methods of small parameter in mathematical biology Jacek Banasiak ; Miroslaw Lachowicz
title_full_unstemmed	Methods of small parameter in mathematical biology Jacek Banasiak ; Miroslaw Lachowicz
title_short	Methods of small parameter in mathematical biology
title_sort	methods of small parameter in mathematical biology
url	https://doi.org/10.1007/978-3-319-05140-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027310334&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027310334&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT banasiakjacek methodsofsmallparameterinmathematicalbiology AT lachowiczmirosław methodsofsmallparameterinmathematicalbiology

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