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Partial Differential Equations in Classical Mathematical Physics

Partial Differential Equations in Classical Mathematical Physics

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textbook
  • Date Published: April 1998
  • availability: Available
  • format: Paperback
  • isbn: 9780521558464

$ 99.00 (X)
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About the Authors
  • This book considers the theory of partial differential equations as the language of continuous processes in mathematical physics. This is an interdisciplinary area in which the mathematical phenomena are reflections of their physical counterparts. The authors trace the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems--elliptic, parabolic, and hyperbolic--as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by students and researchers in applied mathematics and mathematical physics.

    • PDEs are an essential topic in applied maths, natural science and engineering
    • Successful hardback edition
    • Unique style, employing a motivated approach
    • Very experienced authors (father and son team known to most applied mathematicians)
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    Reviews & endorsements

    "...A rigorous, systematic treatment of mathematics applied in classical physics." The American Mathematical Monthly

    "...a comprehensive account of the basic principles and applications of the classical theory of partial differential equations in mathematical physics...well-written for graduate students in physics, engineering, and applied mathematics sequences, and scientists and engineers whose projects require knowledge of equations of mathematical physics...extremely valuable appendixes review important mathematical concepts. Recommended." Choice

    "I enjoy paging through books like this one....[The authors] have succeeded in their goal of treating this field from an interdisciplinary, but unified standpoint. It is a nice book." SIAM Review

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    Product details

    • Date Published: April 1998
    • format: Paperback
    • isbn: 9780521558464
    • length: 696 pages
    • dimensions: 243 x 169 x 36 mm
    • weight: 1.094kg
    • contains: 80 b/w illus.
    • availability: Available
  • Table of Contents

    Preface
    1. Introduction
    2. Typical equations of mathematical physics. Boundary conditions
    3. Cauchy problem for first-order partial differential equations
    4. Classification of second-order partial differential equations with linear principal part. Elements of the theory of characteristics
    5. Cauchy and mixed problems for the wave equation in R1. Method of travelling waves
    6. Cauchy and Goursat problems for a second-order linear hyperbolic equation with two independent variables. Riemann's method
    7. Cauchy problem for a 2-dimensional wave equation. The Volterra-D'Adhemar solution
    8. Cauchy problem for the wave equation in R3. Methods of averaging and descent. Huygens's principle
    9. Basic properties of harmonic functions
    10. Green's functions
    11. Sequences of harmonic functions. Perron's theorem. Schwarz alternating method
    12. Outer boundary-value problems. Elements of potential theory
    13. Cauchy problem for heat-conduction equation
    14. Maximum principle for parabolic equations
    15. Application of Green's formulas. Fundamental identity. Green's functions for Fourier equation
    16. Heat potentials
    17. Volterra integral equations and their application to solution of boundary-value problems in heat-conduction theory
    18. Sequences of parabolic functions
    19. Fourier method for bounded regions
    20. Integral transform method in unbounded regions
    21. Asymptotic expansions. Asymptotic solution of boundary-value problems
    Appendix I. Elements of vector analysis
    Appendix II. Elements of theory of Bessel functions
    Appendix III. Fourier's method and Sturm-Liouville equations
    Appendix IV. Fourier integral
    Appendix V. Examples of solution of nontrivial engineering and physical problems
    References
    Index.

  • Authors

    Isaak Rubinstein, Ben-Gurion University of the Negev, Israel

    Lev Rubinstein, Hebrew University of Jerusalem

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