MARC Record from marc_columbia

LEADER: 06981cam a2200865 i 4500
001 14750865
005 20220627133616.0
006 m o d
007 cr |||||||||||
008 190125s2019 flu ob 001 0 eng
010 $a 2020693314
035 $a(OCoLC)on1083342166
035 $a(NNC)14750865
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019 $a1228891731$a1275130378
020 $a9780429470417$qebook : alk. paper
020 $a042947041X
020 $a9780429893650$qebook
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020 $z9781138601031$qhardback : alk. paper
020 $a9780429893667
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020 $a9780429893643$q(electronic bk. ;$qMobipocket)
020 $a0429893647$q(electronic bk. ;$qMobipocket)
020 $z1138601039
024 7 $a10.1201/9780429470417.$2doi
035 $a(OCoLC)1083342166$z(OCoLC)1228891731$z(OCoLC)1275130378
037 $a9780429893650$bIngram Content Group
050 00 $aQC20
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072 7 $aSCI$x041000$2bisacsh
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082 00 $a530.15$223
049 $aZCUA
100 1 $aSerovajsky, Simon,$eauthor.
245 10 $aSequential models of mathematical physics /$cSimon Serovajsky.
264 1 $aBoca Raton, Florida :$bCRC Press,$c[2019]
300 $a1 online resource
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
504 $aIncludes bibliographical references and index.
588 $aDescription based on print version record.
505 0 $aCover; Half Title; Title Page; Copyright Page; Dedication; Contents; Preface; Author; Part I: Mathematical physics problems; Chapter 1: Classic models; 1.1 Mathematical analysis of a physical phenomenon; 1.2 Definition of a mathematical model; 1.3 Classic solution of the system; 1.4 Approximate solution of the system; 1.5 Validity of the classic method; 1.6 Conclusions; Chapter 2: Generalized models; 2.1 Generalized solution of the problem; 2.2 Determination of the generalized model; 2.3 Generalized derivatives; 2.4 Approximation of the generalized model
505 8 $a2.5 Validity of the generalized method2.6 Conclusions; Part II: Sequential method; Chapter 3: Convergence and Cauchy principle; 3.1 Definitions of the convergence; 3.2 Non-constructiveness of the limit; 3.3 Cauchy criterion of the convergence; 3.4 Picard's method for differential equations; 3.5 Banach fixed point theorem; 3.6 Conclusions; Chapter 4: Completeness and real numbers; 4.1 Inapplicability of the Cauchy criterion; 4.2 Complete metric spaces; 4.3 Completion problem; 4.4 Real numbers by Cantor; 4.5 Conclusions; Chapter 5: Real numbers and completion
505 8 $a5.1 Axiomatic definition of real numbers5.2 Weierstrass real numbers; 5.3 Properties of Weierstrass real numbers; 5.4 Properties of Cantor real numbers; 5.5 Completion of metric spaces; 5.6 Conclusions; Part III: Sequential objects; Chapter 6: p-adic numbers; 6.1 Comparisons of integers modulo; 6.2 Integer p-adic numbers; 6.3 General p-adic numbers; 6.4 p-adic metrics; 6.5 Sequential definition of p-adic numbers; 6.6 Conclusions; Chapter 7: Sequential controls; 7.1 Optimal control problems; 7.2 Insolvable optimal control problems; 7.3 Sequential controls
505 8 $a7.4 Extension of the easiest extremum problem7.5 Extension of the optimal control problem; 7.6 Non-uniqueness of the optimal control; 7.7 Tihonov well-posedness of the optimal control problems; 7.8 Conclusions; Chapter 8: Distributions; 8.1 Test functions; 8.2 Schwartz distributions; 8.3 Sequential distributions; 8.4 Sobolev spaces; 8.5 Conclusions; Part IV: Sequential models; Chapter 9: Sequential models of mathematical physics phenomena; 9.1 Sequential model of the heat transfer phenomenon; 9.2 Justification of sequential modeling; 9.3 Generalized model of the heat transfer phenomenon
505 8 $a9.4 Classic model of the heat transfer phenomenon9.5 Models of mathematical physics problems; 9.6 Conclusions; Bibliography; Index
520 $aThe equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, etc. In Sequential Models of Mathematical Physics, the author considers the justification of the process of constructing mathematical models. The book seeks to determine the classic, generalized and sequential solutions, the relationship between these solutions, its direct physical sense, the methods of its practical finding, and its existence. Features Describes a sequential method based on the construction of space completion, as well as its applications in number theory, the theory of distributions, the theory of extremum, and mathematical physics Presentation of the material is carried out on the simplest example of a one-dimensional stationary heat transfer process; all necessary concepts and constructions are introduced and illustrated with elementary examples, which makes the material accessible to a wide area of readers The solution of a specific mathematical problem is obtained as a result of the joint application of methods and concepts from completely different mathematical directions
506 1 $aLegal Deposit;$cOnly available on premises controlled by the deposit library and to one user at any one time;$eThe Legal Deposit Libraries (Non-Print Works) Regulations (UK).$5WlAbNL
540 $aRestricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.$5WlAbNL
650 0 $aMathematical physics.
650 0 $aMathematical models.
650 0 $aMathematics$xMethodology.
650 6 $aPhysique mathématique.
650 6 $aModèles mathématiques.
650 6 $aMathématiques$xMéthodologie.
650 7 $amathematical models.$2aat
650 7 $aSCIENCE$xEnergy.$2bisacsh
650 7 $aSCIENCE$xMechanics$xGeneral.$2bisacsh
650 7 $aSCIENCE$xPhysics$xGeneral.$2bisacsh
650 7 $aMATHEMATICS$xArithmetic.$2bisacsh
650 7 $aMATHEMATICS$xDifferential Equations.$2bisacsh
650 7 $aMATHEMATICS$xFunctional Analysis.$2bisacsh
650 7 $aMathematical models.$2fast$0(OCoLC)fst01012085
650 7 $aMathematical physics.$2fast$0(OCoLC)fst01012104
650 7 $aMathematics$xMethodology.$2fast$0(OCoLC)fst01012209
655 4 $aElectronic books.
776 08 $iPrint version:$aSerovajsky, Simon, author.$tSequential models of mathematical physics$dBoca Raton, Florida : CRC Press, [2019]$z9781138601031 (hardback : alk. paper)$w(DLC) 2018050822
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio14750865$zTaylor & Francis eBooks
852 8 $blweb$hEBOOKS