Partial Differential Equations in Classical Mathematical Physics
$99.00 (X)
 Authors:
 Isaak Rubinstein, BenGurion University of the Negev, Israel
 Lev Rubinstein, Hebrew University of Jerusalem
 Date Published: April 1998
 availability: Available
 format: Paperback
 isbn: 9780521558464

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 problemselliptic, parabolic, and hyperbolicas 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.
Read more 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)
Reviews & endorsements
"...A rigorous, systematic treatment of mathematics applied in classical physics." The American Mathematical Monthly
See more reviews"...a comprehensive account of the basic principles and applications of the classical theory of partial differential equations in mathematical physics...wellwritten 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 firstorder partial differential equations
4. Classification of secondorder 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 secondorder linear hyperbolic equation with two independent variables. Riemann's method
7. Cauchy problem for a 2dimensional wave equation. The VolterraD'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 boundaryvalue problems. Elements of potential theory
13. Cauchy problem for heatconduction 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 boundaryvalue problems in heatconduction 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 boundaryvalue problems
Appendix I. Elements of vector analysis
Appendix II. Elements of theory of Bessel functions
Appendix III. Fourier's method and SturmLiouville equations
Appendix IV. Fourier integral
Appendix V. Examples of solution of nontrivial engineering and physical problems
References
Index.
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