- Complex Analysis: Some References
- Complex analysis an introduction to the theory of analytic functions of one complex variable.
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- Math 6350: Functions of a Complex Variable 1
Abstract Accurate river bathymetry is required for applications including hydrodynamic flow modelling and understanding morphological processes. Bathymetric measurements are typically a set of depths at discrete points that must be reconstructed into a continuous surface.
Complex Analysis: Some References
A number of algorithms exist for this reconstruction, including spline-based techniques and kriging methods. A novel and efficient method is introduced to produce a co-ordinate system fitted to the river path suitable for bathy Zeros of the Selberg zeta function for symmetric infinite area hyperbolic surfaces. Published on Sep 7, in Geometriae Dedicata 0. Mark Pollicott 25 Estimated H-index: Estimated H-index: 2.
Complex analysis an introduction to the theory of analytic functions of one complex variable.
For definiteness, we consider the case of three funneled surfaces. We show that the zeta function is a complex almost periodic function which can be approximated by complex trigonometric polynomials on large domains in Theorem 4. As our main application, we provide an explanation of the striking empirical results of Zhiming Chen , Shiqi Zhou. We propose a direct imaging method based on the reverse time migration to reconstruct extended obstacles in the half space with finite aperture elastic scattering data at a fixed frequency.
We prove the resolution of the reconstruction method in terms of the aperture and the depth of the obstacle embedded in the half space. The resolution analysis is studied by virtue of the point spread function and implies that the imaginary part of the cross-correlation imaging function always peaks on the up Evaluation of Abramowitz functions in the right half of the complex plane. Published on Jun 28, in arXiv: Numerical Analysis.
On the skein module of the product of a surface and a circle. Patrick M. Gilmer 14 Estimated H-index: There are lots and lots of introductory complex analysis texts that lean toward the power series and integral side. Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis.
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Login Join Give Shops. Halmos - Lester R. Ford Awards Merten M. Lars Ahlfors. Secondly, some suggestions for further reading would be valuable.
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Review by: Pierre Lelong. Mathematical Reviews, MR 14,a. The book has a presentation designed for first year students of the theory of analytic functions of a complex variable. The contents are classical; however, the book contains some very remarkable paragraphs that can serve as an introduction to further study and concern the Dirichlet problem, subharmonic functions, Riemann surfaces, and some other points.
The talents of the author's style allows him to evoke very succinctly images that give the reader insight into and understanding of rigorous proofs; these qualities combine to make the book a very remarkable success in many ways.
Math 6350: Functions of a Complex Variable 1
Review by: William Munger Boothby. The Mathematics Teacher 47 2 , Here is a book which is surely destined to become a standard text for a first-year graduate course in the theory of functions of a complex variable. The subject is treated with clarity and elegance and well illustrated with numerous problems.
The emphasis throughout is on the geometric approach and power series are not introduced until the middle of the book. In addition to a thorough treatment of the standard material of such a course, some topics not usually found in books of this type are discussed, in particular a chapter on the Dirichlet Problem including a discussion of Perron's method. Review by: Pasquale Porcelli.
Mathematics Magazine 27 1 , This is an excellent book that reflects the author's broad experience as both a contributor and a teacher of complex variable theory. The principle asset of the book is the spirit of integrity set forth by the author in the preface and rigidly adhered to throughout the text. The reviewer's overall estimate of the book can be best expressed by saying that he hopes it will become the accepted text in each class where complex variable theory is studied and where a book is used to outline the course.
Review by: Pierce Waddell Ketchum. Monthly 60 10 , Professor Ahlfors has fulfilled expectations that he would produce a scholarly and novel treatment of analytic function theory. The only disappointment which the reviewer experiences is that the author stopped too soon. One could wish for a continued discussion of more material in the same vein. It has been generally recognized that expositions of analytic functions in English have failed to make sufficient use of relevant topological tools.
This is the more surprising in view of the great mutual influence that complex variable theory and topology have exerted upon each other.
In the present book Ahlfors remedies this deficiency by making systematic use of topological techniques, and he has also provided brief but reasonably adequate introductions to the topological ideas which he uses. At the same time he has retained the flavour of classical function theory; and he has avoided the assembly-line format wherein every paragraph is labelled Theorem, Definition, Corollary, Remark, and the like.
Review by: Swarupchand Mohanial Shah.
Monthly 75 8 , The first edition of this book appeared in The main changes in the second edition are the addition of a section on conformal mapping of polygons, a chapter on elliptic functions and a section on Picard's theorem on entire functions. The reviewer considers this book as one of the best on the subject. It is rigorous, readable and has a number of challenging exercises, some with hints. It is a suitable textbook for a two semester course on complex analysis for first-year graduate students. Mathematical Reviews , MR 32 This new edition offers some additions, made possible, says the author in his preface, by the higher level of students entering university; accordingly, while still very basic in its first part, the book has been extended on important topics topological notions, Riemann surfaces ; it gives the reader an overview of modern methods subharmonic functions, Dirichlet problem ; a chapter on elliptic functions has been added and allows the author, using the modular function, to give the theorem of Picard.
The work thus remains a remarkable introduction to a theory that retains an important place in basic teaching.