Potentials And Partial Differential Equations
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| Author | : S. L. Sobolev |
| Publisher | : Courier Corporation |
| Total Pages | : 452 |
| Release | : 1964-01-01 |
| Genre | : Science |
| ISBN | : 9780486659640 |
This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.
| Author | : Lester L. Helms |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 494 |
| Release | : 2014-04-10 |
| Genre | : Mathematics |
| ISBN | : 1447164229 |
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book will undoubtedly be useful to graduate students and researchers in mathematics, physics and engineering.
| Author | : David R. Adams |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 372 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3662032821 |
"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society
| Author | : Suzanne Lenhart |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 365 |
| Release | : 2023-05-22 |
| Genre | : Mathematics |
| ISBN | : 3110792788 |
This volume is dedicated to the legacy of David R. Adams (1941-2021) and discusses calculus of variations, functional - harmonic - potential analysis, partial differential equations, and their applications in modeling, mathematical physics, and differential - integral geometry.
| Author | : Arthur Godon Webster |
| Publisher | : Courier Dover Publications |
| Total Pages | : 465 |
| Release | : 2016-06-20 |
| Genre | : Mathematics |
| ISBN | : 0486805158 |
A classic treatise on partial differential equations, this comprehensive work by one of America's greatest early mathematical physicists covers the basic method, theory, and application of partial differential equations. In addition to its value as an introductory and supplementary text for students, this volume constitutes a fine reference for mathematicians, physicists, and research engineers. Detailed coverage includes Fourier series; integral and elliptic equations; spherical, cylindrical, and ellipsoidal harmonics; Cauchy's method; boundary problems; the Riemann-Volterra method; and many other basic topics. The self-contained treatment fully develops the theory and application of partial differential equations to virtually every relevant field: vibration, elasticity, potential theory, the theory of sound, wave propagation, heat conduction, and many more. A helpful Appendix provides background on Jacobians, double limits, uniform convergence, definite integrals, complex variables, and linear differential equations.
| Author | : Dorina Mitrea |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 475 |
| Release | : 2013-09-20 |
| Genre | : Mathematics |
| ISBN | : 1461482089 |
The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differential operators: the Laplace, heat, wave, Lam\'e and Schrodinger operators.
| Author | : James Kirkwood |
| Publisher | : Academic Press |
| Total Pages | : 431 |
| Release | : 2012-01-20 |
| Genre | : Mathematics |
| ISBN | : 0123869110 |
Suitable for advanced undergraduate and beginning graduate students taking a course on mathematical physics, this title presents some of the most important topics and methods of mathematical physics. It contains mathematical derivations and solutions - reinforcing the material through repetition of both the equations and the techniques.
| Author | : Walter A. Strauss |
| Publisher | : John Wiley & Sons |
| Total Pages | : 467 |
| Release | : 2007-12-21 |
| Genre | : Mathematics |
| ISBN | : 0470054565 |
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
| Author | : Dmitry Khavinson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 226 |
| Release | : 2018-07-09 |
| Genre | : Mathematics |
| ISBN | : 1470437805 |
Why do solutions of linear analytic PDE suddenly break down? What is the source of these mysterious singularities, and how do they propagate? Is there a mean value property for harmonic functions in ellipsoids similar to that for balls? Is there a reflection principle for harmonic functions in higher dimensions similar to the Schwarz reflection principle in the plane? How far outside of their natural domains can solutions of the Dirichlet problem be extended? Where do the continued solutions become singular and why? This book invites graduate students and young analysts to explore these and many other intriguing questions that lead to beautiful results illustrating a nice interplay between parts of modern analysis and themes in “physical” mathematics of the nineteenth century. To make the book accessible to a wide audience including students, the authors do not assume expertise in the theory of holomorphic PDE, and most of the book is accessible to anyone familiar with multivariable calculus and some basics in complex analysis and differential equations.
| Author | : David A. Kopriva |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 397 |
| Release | : 2009-05-27 |
| Genre | : Mathematics |
| ISBN | : 9048122619 |
This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.
