Author : François Treves
Publisher : Academic Press
Page : 493 pages
File Size : 17,19 MB
Release : 1975-08-08
Category : Mathematics
ISBN : 0080880258
Basic Linear Partial Differential Equations
Author : Tyn Myint-U
Publisher : Springer Science & Business Media
Page : 790 pages
File Size : 42,55 MB
Release : 2007-04-05
Category : Mathematics
ISBN : 0817645608
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.
Author : J. Chazarain
Publisher : Elsevier
Page : 575 pages
File Size : 34,85 MB
Release : 2011-08-18
Category : Computers
ISBN : 0080875351
Introduction to the Theory of Linear Partial Differential Equations
Author : David. Bleecker
Publisher : CRC Press
Page : 974 pages
File Size : 36,44 MB
Release : 2018-01-18
Category : Mathematics
ISBN : 1351086987
Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.
Author : Francois Treves
Publisher : Courier Corporation
Page : 498 pages
File Size : 33,13 MB
Release : 2006-11-17
Category : Mathematics
ISBN : 0486453464
Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories. The four-part treatment covers the basic examples of linear partial differential equations and their fundamental solutions; the Cauchy problem; boundary value problems; and mixed problems and evolution equations. Nearly 400 exercises appear throughout the text, several containing detailed information that enables readers to reconstruct the proofs.
Author : Stig Larsson
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 33,94 MB
Release : 2008-12-05
Category : Mathematics
ISBN : 3540887059
The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
Author : Michael E. Taylor
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 21,14 MB
Release : 2010-10-29
Category : Mathematics
ISBN : 144197055X
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
Author : Grigoriĭ Ilʹich Eskin
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 35,65 MB
Release : 2011
Category : Mathematics
ISBN : 0821852841
This is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory.
Author : Andrei D. Polyanin
Publisher : CRC Press
Page : 800 pages
File Size : 46,66 MB
Release : 2001-11-28
Category : Mathematics
ISBN : 1420035320
Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. Parabolic, hyperbolic, and elliptic equations with
Author : Marcus Pivato
Publisher : Cambridge University Press
Page : 631 pages
File Size : 12,81 MB
Release : 2010-01-07
Category : Mathematics
ISBN : 0521199700
This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.
