Download or read book Applied Complex Analysis with Partial Differential Equations written by Nakhlé H. Asmar and published by . This book was released on 2002 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reader-friendly book presents traditional material using a modern approach that invites the use of technology. Abundant exercises, examples, and graphics make it a comprehensive and visually appealing resource. Chapter topics include complex numbers and functions, analytic functions, complex integration, complex series, residues: applications and theory, conformal mapping, partial differential equations: methods and applications, transform methods, and partial differential equations in polar and spherical coordinates. For engineers and physicists in need of a quick reference tool.
Download or read book Implementing Spectral Methods for Partial Differential Equations written by David A. Kopriva and published by Springer Science & Business Media. This book was released on 2009-05-27 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Complex Methods for Partial Differential Equations written by Heinrich Begehr and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to Partial Differential Equations. Since classical complex analysis of one and several variables has a long tra dition it is of high level. But most of its basic problems are solved nowadays so that within the last few decades it has lost more and more attention. The area of complex and functional analytic methods in partial differential equations, however, is still a growing and flourishing field, in particular as these methods are not only applied. Whithin the framework of holomorphic functions but are also combined with properties of generalized analytic functions. This can be seen by the many books which recently were published in this field and also by the proceedings in this ISAAC series and the ISAAC congresses and workshops.
Download or read book Complex Methods on Partial Differential Equations written by Claudio I. Withalm and published by Mathematical Research. This book was released on 1990-01-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex Analytic Methods for Partial Differential Equations written by Heinrich G. W. Begehr and published by World Scientific. This book was released on 1994 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations. Riemann and Riemann-Hilbert boundary value problems are discussed for analytic functions, for inhomogeneous Cauchy-Riemann systems as well as for generalized Beltrami systems. Related problems such as the Poincar problem, pseudoparabolic systems and complex elliptic second order equations are also considered. Estimates for solutions to linear equations existence and uniqueness results are thus available for related nonlinear problems; the method is explained by constructing entire solutions to nonlinear Beltrami equations. Often problems are discussed just for the unit disc but more general domains, even of multiply connectivity, are involved.
Download or read book Functional analytic and Complex Methods Their Interactions and Applications to Partial Differential Equations written by Helmut Florian and published by World Scientific. This book was released on 2001 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today''s rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell''s equations, crystal optics, dynamical problems for cusped bars, and conservation laws. Sample Chapter(s). Hyperbolic Equations, Waves and the Singularity Theory (858 KB). Contents: Boundary Value Problems and Initial Value Problems for Partial Differential Equations; Applications of Functional-Analytic and Complex Methods to Mathematical Physics; Partial Complex Differential Equations in the Plane; Complex Methods in Higher Dimensions. Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics.
Download or read book Methods of Complex Analysis in Partial Differential Equations with Applications written by Manfred Kracht and published by New York ; Toronto : Wiley. This book was released on 1988 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the development of complex function theoretic methods in partial differential equations and to the study of analytic behaviour of solutions. It presents basic facts of the subject and includes recent results, emphasizing the method of integral operators and the method of differential operators. The first chapter gives a motivation for and the underlying ideas of, the later chapters. Chapters 2 to 7 give a detailed exposition of the basic concepts and fundamental theorems, as well as their most recent development. Chapters 8 to 13 are concerned with the application of the theory to three important classes of differential equations of mathematical physics.
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Download or read book A First Course in Partial Differential Equations written by H. F. Weinberger and published by Courier Corporation. This book was released on 2012-04-20 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Methods for Constructing Exact Solutions of Partial Differential Equations written by Sergey V. Meleshko and published by Springer Science & Business Media. This book was released on 2006-06-18 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Download or read book Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations written by A S A Mshimba and published by World Scientific. This book was released on 1995-10-17 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings concentrate on recent results in the following fields of complex analysis: complex methods for solving boundary value problems with piecewise smooth boundary data, complex methods for linear and nonlinear differential equations and systems of second order, and applications of scales of Banach spaces to initial value problems.Some problems in higher dimensions (such as the unification of global and local existence theorems for holomorphic functions and an elementary approach to Clifford analysis) are also discussed.Particular emphasis is placed on Symbolic Computation in Complex Analysis and on the new approaches to teach mathematical analysis based on interactions between complex analysis and partial differential equations.
Download or read book Numerical Methods for Partial Differential Equations written by Sandip Mazumder and published by Academic Press. This book was released on 2015-12-01 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow. For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses. - Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry - Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes - Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives
Download or read book Complex Methods on Partial Differential Equations written by Claudio I. Withalm and published by De Gruyter Akademie Forschung. This book was released on 1989 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Partial Differential Equations with Applications written by E. C. Zachmanoglou and published by Courier Corporation. This book was released on 2012-04-20 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.
Download or read book Numerical Approximation of Partial Differential Equations written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).
Download or read book Partial Differential and Integral Equations written by Heinrich Begehr and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.
