Partial Differential Equations in Classical Mathematical Physics
$114.00 (X)
- Authors:
- Isaak Rubinstein, Ben-Gurion 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 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.
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...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.
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