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  • A Practical Course in Differential Equations and Mathematical Modelling :classical and new methods, nonlinear mathematical models, symmetry and invariance principles
  • 點閱:230
  • 作者: by Nail H. Ibragimov
  • 出版社:Higher Education Press
  • 出版年:c2009
  • ISBN:978-7-04-027603-9 ; 7-04-027603-8
  • 格式:PDF
  • 附註:簡體字版

A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book -- which aims to present new mathematical curricula based on symmetry and invariance principles -- is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. 

  • 1 Selected topics from analysis(第1頁)
    • 1.1 Elementary mathematics(第1頁)
    • 1.2 Differential and integral calculus(第14頁)
    • 1.3 Vector analysis(第26頁)
    • 1.4 Notation of differential algebra(第32頁)
    • 1.5 Variational calculus(第38頁)
    • Problems to Chapter 1(第40頁)
  • 2 Mathematical models(第45頁)
    • 2.1 Introduction(第45頁)
    • 2.2 Natural phenomena(第46頁)
    • 2.3 Physics and engineering sciences(第53頁)
    • 2.4 Diffusion phenomena(第72頁)
    • 2.5 Biomathematics(第76頁)
    • 2.6 Wave phenomena(第79頁)
    • Problems to Chapter 2(第88頁)
  • 3 Ordinary di erential equations: Traditional approach(第91頁)
    • 3.1 Introduction and elementary methods(第91頁)
    • 3.2 First-order equations(第99頁)
    • 3.3 Second-order linear equations(第108頁)
    • 3.4 Higher-order linear equations(第120頁)
    • 3.5 Systems of first-order equations(第124頁)
    • Problems to Chapter 3(第133頁)
  • 4 First-order partial differential equations(第135頁)
    • 4.1 Introduction(第135頁)
    • 4.2 Homogeneous linear equation(第136頁)
    • 4.3 Particular solutions of non-homogeneousequations(第138頁)
    • 4.4 Quasi-linear equations(第139頁)
    • 4.5 Systems of homogeneous equations(第142頁)
    • Problems to Chapter 4(第145頁)
  • 5 Linear partial differential equations of the second order(第149頁)
    • 5.1 Equations with several variables(第149頁)
    • 5.2 Classification of equations in two independentvariables(第153頁)
    • 5.3 Integration of hyperbolic equations in twovariables(第159頁)
    • 5.4 The initial value problem(第169頁)
    • 5.5 Mixed problem. Separation of variables(第172頁)
    • Problems to Chapter 5(第177頁)
  • 6 Nonlinear ordinary di erentialequations(第179頁)
    • 6.1 Introduction(第179頁)
    • 6.2 Transformation groups(第180頁)
    • 6.3 Symmetries of first-order equations(第188頁)
    • 6.4 Integration of first-order equations usingsymmetries(第193頁)
    • 6.5 Second-order equations(第201頁)
    • 6.6 Higher-order equations(第218頁)
    • 6.7 Nonlinear superposition(第235頁)
    • Problems to Chapter 6(第251頁)
  • 7 Nonlinear partial di erential equations(第255頁)
    • 7.1 Symmetries(第255頁)
    • 7.2 Group invariant solutions(第262頁)
    • 7.3 Invariance and conservation laws(第274頁)
    • Problems to Chapter 7(第286頁)
  • 8 Generalized functions or distributions(第291頁)
    • 8.1 Introduction of generalized functions(第291頁)
    • 8.2 Operations with distributions(第295頁)
    • 8.3 The distribution △(r2-n)(第298頁)
    • 8.4 Transformations of distributions(第301頁)
    • Problems to Chapter 8(第304頁)
  • 9 Invariance principle and fundamental solutions(第307頁)
    • 9.1 Introduction(第307頁)
    • 9.2 The invariance principle(第308頁)
    • 9.3 Cauchy’s problem for the heat equation(第313頁)
    • 9.4 Wave equation(第316頁)
    • 9.5 Equations with variable coefficients(第325頁)
    • Problems to Chapter 9(第325頁)
  • Answers(第327頁)
  • Bibliography(第337頁)
  • Index(第341頁)
紙本書 NT$ 3150
單本電子書
NT$ 2205

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