Methods Of Complex Analysis In Partial Differential Equations With Applications
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| Author | : Nakhlé H. Asmar |
| Publisher | : |
| Total Pages | : 904 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Helmut Florian |
| Publisher | : World Scientific |
| Total Pages | : 473 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9812794557 |
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.
| Author | : E. C. Zachmanoglou |
| Publisher | : Courier Corporation |
| Total Pages | : 434 |
| Release | : 2012-04-20 |
| Genre | : Mathematics |
| ISBN | : 048613217X |
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.
| Author | : Luis Barreira |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 417 |
| Release | : 2012-04-23 |
| Genre | : Mathematics |
| ISBN | : 1447140087 |
This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty. Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.
| Author | : Haim Brezis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 600 |
| Release | : 2010-11-02 |
| Genre | : Mathematics |
| ISBN | : 0387709142 |
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
| Author | : Manfred Kracht |
| Publisher | : New York ; Toronto : Wiley |
| Total Pages | : 424 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Heinrich G. W. Begehr |
| Publisher | : World Scientific |
| Total Pages | : 288 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9789810215507 |
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.
| Author | : Ali Seif Mshimba |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 406 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : H. F. Weinberger |
| Publisher | : Courier Corporation |
| Total Pages | : 482 |
| Release | : 2012-04-20 |
| Genre | : Mathematics |
| ISBN | : 0486132048 |
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.
| Author | : Randall J. LeVeque |
| Publisher | : SIAM |
| Total Pages | : 356 |
| Release | : 2007-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898717839 |
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.
