rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Sequential models of mathematical physics
  title info:
    title: MATHnetBASE
  name:
    name part: Serovajsky, Simon
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: flu
    date issued: 2019
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: The equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, et cetera 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
  table of contents: Cover; 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
  table of contents: 2.5 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
  table of contents: 5.1 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
  table of contents: 7.4 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
  table of contents: 9.4 Classic model of the heat transfer phenomenon9.5 Models of mathematical physics problems; 9.6 Conclusions; Bibliography; Index
  note: Simon Serovajsky.
  subject:
    topic: Mathematical physics
  subject:
    topic: Mathematical models
  subject:
    topic: Mathematics
    topic: Methodology
  subject:
    topic: SCIENCE / Energy
  subject:
    topic: SCIENCE / Mechanics / General
  subject:
    topic: SCIENCE / Physics / General
  subject:
    topic: MATHEMATICS / Arithmetic
  subject:
    topic: MATHEMATICS / Differential Equations
  subject:
    topic: MATHEMATICS / Functional Analysis
  classification: QC20 .S47 2019eb
  classification: 530.15
  identifier: 9780429470417
  identifier: 042947041X
  identifier: 9780429893667
  identifier: 0429893663
  identifier: 9780429893650
  identifier: 0429893655
  identifier: 9780429893643
  identifier: 0429893647
  identifier: 9781138601031
  identifier: 1138601039
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCoLC-P
    record creation date: 190125
    record change date: 20220613180037.0
    record identifier: in00004581986
    language of cataloging:
      language term: eng