complex analysis and differential equations

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Complex Analysis And Differential Equations

Author : Luis Barreira
ISBN : 9781447140085
Genre : Mathematics
File Size : 80. 28 MB
Format : PDF
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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.

Partial Differential Equations And Complex Analysis

Author : Steven G. Krantz
ISBN : 0849371554
Genre : Mathematics
File Size : 67. 29 MB
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Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.

Applied Complex Analysis With Partial Differential Equations

Author : Nakhlé H. Asmar
ISBN : 0130892394
Genre : Mathematics
File Size : 81. 42 MB
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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.

Complex Analysis And Differential Equations

Author : Matts R. Essén
ISBN : 9155444954
Genre : Mathematics
File Size : 58. 9 MB
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A First Course In Partial Differential Equations With Complex Variables And Transform Methods

Author : Hans F. Weinberger
ISBN : 048668640X
Genre : Mathematics
File Size : 44. 43 MB
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Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Topics include one-dimensional wave equation, properties of elliptic and parabolic equations, separation of variables and Fourier series, nonhomogeneous problems, and analytic functions of a complex variable. Solutions. 1965 edition.

Partial Differential Equations In Several Complex Variables

Author : So-Chin Chen
ISBN : 0821829610
Genre : Mathematics
File Size : 78. 39 MB
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This book is intended both as an introductory text and as a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the fields of Cauchy-Riemann and tangential Cauchy-Riemann operators. This book gives an up-to-date account of the theories for these equations and their applications. The background material in several complex variables is developed in the first three chapters, leading to the Levi problem. The next three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the $\bar\partial$-Neumann problem, including $L^2$ existence theorems on pseudoconvex domains, $\frac 12$-subelliptic estimates for the $\bar\partial$-Neumann problems on strongly pseudoconvex domains, global regularity of $\bar\partial$ on more general pseudoconvex domains, boundary regularity of biholomorphic mappings, irregularity of the Bergman projection on worm domains. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations. Chapter 7 introduces the tangential Cauchy-Riemann complex and the Lewy equation. An extensive account of the $L^2$ theory for $\square_b$ and $\bar\partial_b$ is given in Chapters 8 and 9. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Holder and $L^p$ spaces. Embeddability of abstract $CR$ structures is discussed in detail in the last chapter. This self-contained book provides a much-needed introductory text to several complex variables and partial differential equations. It is also a rich source of information to experts.

Multidimensional Complex Analysis And Partial Differential Equations

Author : Francois Treves
ISBN : 9780821805091
Genre : Mathematics
File Size : 29. 55 MB
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This collection of papers by outstanding contributors in analysis, partial differential equations, and several complex variables is dedicated to Professor Francois Treves in honor of his 65th birthday. There are five important survey articles covering analytic singularities, holomorphically nondegenerate algebraic hypersurfaces, analyticity of CR mappings, removable singularities of vector fields, and local solvability for systems of vector fields. The other papers are original research contributions on topics such as Klein-Gordon and Dirac equations, Toeplitz operators, elliptic structures, complexification of Lie groups, pseudo-differential operators, nonlinear equations, CR and Mizohata structures, analytic hypoellipticity, overdetermined systems, and group invariant convex hypersurfaces.

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