000 05767cam a2200661Ki 4500
001 9780429470417
003 FlBoTFG
005 20220509193131.0
006 m o d
007 cr cnu---|nuuu
008 190125s2019 flu ob 001 0 eng d
040 _aOCoLC-P
_beng
_erda
_epn
_cOCoLC-P
020 _a9780429470417
_q(electronic bk.)
020 _a042947041X
_q(electronic bk.)
020 _a9780429893667
020 _a0429893663
020 _a9780429893650
_q(electronic bk. : EPUB)
020 _a0429893655
_q(electronic bk. : EPUB)
020 _a9780429893643
_q(electronic bk. : Mobipocket)
020 _a0429893647
_q(electronic bk. : Mobipocket)
020 _z9781138601031
020 _z1138601039
035 _a(OCoLC)1083342166
035 _a(OCoLC-P)1083342166
050 4 _aQC20
_b.S47 2019eb
072 7 _aSCI
_x024000
_2bisacsh
072 7 _aSCI
_x041000
_2bisacsh
072 7 _aSCI
_x055000
_2bisacsh
072 7 _aMAT
_x004000
_2bisacsh
072 7 _aMAT
_x007000
_2bisacsh
072 7 _aMAT
_x037000
_2bisacsh
072 7 _aPB
_2bicssc
082 0 4 _a530.15
_223
100 1 _aSerovajsky, Simon,
_eauthor.
245 1 0 _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
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
588 _aOCLC-licensed vendor bibliographic record.
650 0 _aMathematical physics.
650 0 _aMathematical models.
650 0 _aMathematics
_xMethodology.
650 7 _aSCIENCE / Energy
_2bisacsh
650 7 _aSCIENCE / Mechanics / General
_2bisacsh
650 7 _aSCIENCE / Physics / General
_2bisacsh
650 7 _aMATHEMATICS / Arithmetic
_2bisacsh
650 7 _aMATHEMATICS / Differential Equations
_2bisacsh
650 7 _aMATHEMATICS / Functional Analysis
_2bisacsh
856 4 0 _3Taylor & Francis
_uhttps://www.taylorfrancis.com/books/9780429470417
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
999 _c130572
_d130572