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Author: B Dahlberg Publisher: ISBN: 9781461228998 Category : Languages : en Pages : 240
Book Description
In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new directions for future progress - this volume contains articles from participants of the workshop.
Author: B Dahlberg Publisher: ISBN: 9781461228998 Category : Languages : en Pages : 240
Book Description
In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new directions for future progress - this volume contains articles from participants of the workshop.
Author: B. Dahlberg Publisher: Springer Science & Business Media ISBN: 1461228980 Category : Mathematics Languages : en Pages : 227
Book Description
In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new directions for future progress - this volume contains articles from participants of the workshop.
Author: Michael Shearer Publisher: Princeton University Press ISBN: 0691161291 Category : Mathematics Languages : en Pages : 286
Book Description
An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors
Author: Mark A. Pinsky Publisher: American Mathematical Soc. ISBN: 0821868896 Category : Mathematics Languages : en Pages : 545
Book Description
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Author: Boško S. Jovanović Publisher: Springer Science & Business Media ISBN: 1447154606 Category : Mathematics Languages : en Pages : 416
Book Description
This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.
Author: Piero Bassanini Publisher: Springer Science & Business Media ISBN: 1489918752 Category : Mathematics Languages : en Pages : 446
Book Description
This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years. Our goal in writing it has been to introduce the subject with precise and rigorous analysis on the one hand, and interesting and significant applications on the other. The starting level of the book is at the first-year graduate level in a U.S. university. Previous experience with partial differential equations is not required, but the use of classical analysis to find solutions of specific problems is not emphasized. From that perspective our treatment is decidedly theoretical. We have avoided abstraction and full generality in many situations, however. Our plan has been to introduce fundamental ideas in relatively simple situations and to show their impact on relevant applications. The student is then, we feel, well prepared to fight through more specialized treatises. There are parts of the exposition that require Lebesgue integration, distributions and Fourier transforms, and Sobolev spaces. We have included a long appendix, Chapter 8, giving precise statements of all results used. This may be thought of as an introduction to these topics. The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.
Author: Peter Charles Greiner Publisher: American Mathematical Soc. ISBN: 0821806874 Category : Mathematics Languages : en Pages : 327
Book Description
Presents lectures given at the 1995 Annual Seminar of the Canadian Mathematical Society on Partial Differential Equations and Their Applications held at the University of Toronto in June 1995. This volume includes contributions on a variety of topics related to PDE, such as spectral asymptotics, harmonic analysis, and applications to geometry.
Author: B. N. Chetverushkin Publisher: Springer ISBN: 3319783254 Category : Technology & Engineering Languages : en Pages : 452
Book Description
This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose outstanding achievements are recognised in this volume. It contains 20 contributions from leading scientists in applied mathematics dealing with partial differential equations and their applications to engineering, ab-initio chemistry and life sciences. It includes the mathematical and numerical contributions to PDE for applications presented at the ECCOMAS thematic conference "Contributions to PDE for Applications" held at Laboratoire Jacques Louis Lions in Paris, France, August 31- September 1, 2015, and at the Department of Mathematics, University of Houston, Texas, USA, February 26-27, 2016. This event brought together specialists from universities and research institutions who are developing or applying numerical PDE or ODE methods with an emphasis on industrial and societal applications. This volume is of interest to researchers and practitioners as well as advanced students or engineers in applied and computational mathematics. All contributions are written at an advanced scientific level with no effort made by the editors to make this volume self-contained. It is assumed that the reader is a specialist already who knows the basis of this field of research and has the capability of understanding and appreciating the latest developments in this field.
Author: Walter A. Strauss Publisher: John Wiley & Sons ISBN: 0470054565 Category : Mathematics Languages : en Pages : 467
Book Description
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: B Dahlberg
Author: B Dahlberg
Author: B. Dahlberg
Author: Michael Shearer
Author: Mark A. Pinsky
Author: Boško S. Jovanović
Author: Robert C. McOwen
Author: Piero Bassanini
Author: Peter Charles Greiner
Author: B. N. Chetverushkin
Author: Walter A. Strauss