Complex Variables II Essentials

Author: Alan D. Solomon
Publisher: Research & Education Assoc.
ISBN: 9780738672175
Format: PDF, Docs
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Includes elementary mappings and mobius transformation, mappings by general functions, conformal mappings and harmonic functions, applying complex functions to applied mathematics, analytic continuation, and analytic function properties.

Complex Variables I Essentials

Author: Alan D. Solomon
Publisher: Research & Education Assoc.
ISBN: 9780738672434
Format: PDF
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Includes functions of a complex variable, elementary complex functions, integrals of complex functions in the complex plane, sequences and series, and poles and residues.

Essential Mathematics for the Physical Sciences Volume 1

Author: Brett Borden
Publisher: Morgan & Claypool Publishers
ISBN: 1681744856
Format: PDF, Mobi
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Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus asound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations (PDEs) and the special functions introduced. Solving PDEs can't be done, however, outside of the context in which they apply to physical systems. The solutions to PDEs must conform to boundary conditions, a set of additional constraints in space or time to be satisfied at the boundaries of the system, that small part of the universe under study. The first volume is devoted to homogeneous boundary-value problems (BVPs), homogeneous implying a system lacking a forcing function, or source function. The second volume takes up (in addition to other topics) inhomogeneous problems where, in addition to the intrinsic PDE governing a physical field, source functions are an essential part of the system. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well. It is based on the assumption that it follows a math review course, and was designed to coincide with the second quarter of student study, which is dominated by BVPs but also requires an understanding of special functions and Fourier analysis.

Theory of Functions of a Complex Variable

Author: A. I. Markushevich
Publisher: American Mathematical Soc.
ISBN: 082183780X
Format: PDF, Docs
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Theorems are presented in a logical way and are carefully proved, making this a most useful book for students. --Choice This magnificent textbook, translated from the Russian, was first published in 1965-1967. The book covers all aspects of the theory of functions of one complex variable. The chosen proofs give the student the best `feel' for the subject. The watchwords are clarity and straightforwardness. The author was a leading Soviet function-theorist: It is seldom that an expert of his stature puts himself so wholly at the service of the student. This book includes over 150 illustrations and 700 exercises.

Theory of Functions of a Complex Variable

Author: C. Caratheodory
Publisher: American Mathematical Soc.
ISBN: 0821828312
Format: PDF, ePub, Docs
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This book is a translation by F. Steinhardt of the last of Caratheodory's celebrated text books, Funktiontheorie, Volume 1.

A Course in Mathematical Analysis Volume 1 Foundations and Elementary Real Analysis

Author: D. J. H. Garling
Publisher: Cambridge University Press
ISBN: 1107311381
Format: PDF, Mobi
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The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration.

Classical Complex Analysis

Author: I-Hsiung Lin
Publisher: World Scientific
ISBN: 981426122X
Format: PDF, Kindle
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Classical Complex Analysis provides an introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. This volume begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described In detail, and various applications of residues are Included; analytic continuation is also introduced. --Book Jacket.