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Complex Variables and Applications,
by James Ward Brown
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Complex Variables and the Laplace Transform for Engineers,
"An excellent text; the best I have found on the subject." — J. B. Sevart, Department of Mechanical Engineering, University of Wichita "An extremely useful textbook for both formal classes and for self-study." — Society for Industrial and Applied Mathematics Engineers often do not have time to take a course in complex variable theory as undergraduates, yet is is one of the most important and useful branches of mathematics, with many applications in engineering. This text is designed to remedy that need by supplying graduate engineering students (especially electrical engineering) with a course in the basic theory of complex variables, which in turn is essential to the understanding of transform theory. Presupposing a good knowledge of calculus, the book deals lucidly and rigorously with important mathematical concepts, striking an ideal balance between purely mathematical treatments that are too general for the engineer, and books of applied engineering which may fail to stress significant mathematical ideas. The text is divided into two basic parts: The first part (Chapters 1–7) is devoted to the theory of complex variables and begins with an outline of the structure of system analysis and an explanation of basic mathematical and engineering terms. Chapter 2 treats the foundation of the theory of a complex variable, centered around the Cauchy-Riemann equations. The next three chapters — conformal mapping, complex integration, and infinite series — lead up to a particularly important chapter on multivalued functions, explaining the concepts of stability, branch points, and riemann surfaces. Numerous diagrams illustrate the physical applications of the mathematical concepts involved. The second part (Chapters 8–16) covers Fourier and Laplace transform theory and some of its applications in engineering, beginning with a chapter on real integrals. Three important chapters follow on the Fourier integral, the Laplace integral (one-sided and two-sided) and convolution integrals. After a chapter on additional properties of the Laplace integral, the book ends with four chapters (13–16) on the application of transform theory to the solution of ordinary linear integrodifferential equations with constant coefficients, impulse functions, periodic functions, and the increasingly important Z transform. Dr. LePage's book is unique in its coverage of an unusually broad range of topics difficult to find in a single volume, while at the same time stressing fundamental concepts, careful attention to details and correct use of terminology. An extensive selection of interesting and valuable problems follows each chapter, and an excellent bibliography recommends further reading. Ideal for home study or as the nucleus of a graduate course, this useful, practical, and popular (8 printings in its hardcover edition) text offers students, engineers, and researchers a careful, thorough grounding in the math essential to many areas of engineering. "An outstanding job." — American Mathematical Monthly
by Wilbur R. LePage
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Introductory Complex Analysis,
A shorter version of A. I. Markushevich's masterly three-volume Theory of Functions of a Complex Variable, this edition is appropriate for advanced undergraduate and graduate courses in complex analysis. Numerous worked-out examples and more than 300 problems, some with hints and answers, make it suitable for independent study. 1967 edition.
by Richard A. Silverman
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Complex Variables for Scientists and Engineers,Second Edition
This outstanding text for undergraduate students of science and engineering requires only a standard course in elementary calculus. Designed to provide a thorough understanding of fundamental concepts and create the basis for higher-level courses, the treatment features numerous examples and extensive exercise sections of varying difficulty, plus answers to selected exercises. The two-part approach begins with the development of the primary concept of analytic function, advancing to the Cauchy integral theory, the series development of analytic functions through evaluation of integrals by residues, and some elementary applications of harmonic functions. The second part introduces some of the deeper aspects of complex function theory: mapping properties of analytic functions, applications to various vector field problems with boundary conditions, and a collection of further theoretical results. 1990 edition.
by John D. Paliouras
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Complex Variables,Introduction and Applications
Complex variables provide powerful methods for attacking problems that can be very difficult to solve in any other way, and it is the aim of this book to provide a thorough grounding in these methods and their application. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, and numerical methods. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann–Hilbert problems. The authors provide an extensive array of applications, illustrative examples and homework exercises. This 2003 edition was improved throughout and is ideal for use in undergraduate and introductory graduate level courses in complex variables.
by Mark J. Ablowitz
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Complex Variables,
The text covers a broad spectrum between basic and advanced complex variables on the one hand and between theoretical and applied or computational material on the other hand. With careful selection of the emphasis put on the various sections, examples, and exercises, the book can be used in a one- or two-semester course for undergraduate mathematics majors, a one-semester course for engineering or physics majors, or a one-semester course for first-year mathematics graduate students. It has been tested in all three settings at the University of Utah. The exposition is clear, concise, and lively. There is a clean and modern approach to Cauchy's theorems and Taylor series expansions, with rigorous proofs but no long and tedious arguments. This is followed by the rich harvest of easy consequences of the existence of power series expansions. Through the central portion of the text, there is a careful and extensive treatment of residue theory and its application to computation of integrals, conformal mapping and its applications to applied problems, analytic continuation, and the proofs of the Picard theorems. Chapter 8 covers material on infinite products and zeroes of entire functions. This leads to the final chapter which is devoted to the Riemann zeta function, the Riemann Hypothesis, and a proof of the Prime Number Theorem.
by Joseph L. Taylor
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COMPLEX VARIABLES,THEORY AND APPLICATIONS
The second edition of this comprehensive and accessible text continues to offer students a challenging and enjoyable study of complex variables that is infused with perfect balanced coverage of mathematical theory and applied topics. The author explains fundamental concepts and techniques with precision and introduces the students to complex variable theory through conceptual develop-ment of analysis that enables them to develop a thorough understanding of the topics discussed. Geometric interpretation of the results, wherever necessary, has been inducted for making the analysis more accessible. The level of the text assumes that the reader is acquainted with elementary real analysis. Beginning with the revision of the algebra of complex variables, the book moves on to deal with analytic functions, elementary functions, complex integration, sequences, series and infinite products, series expansions, singularities and residues. The application-oriented chapters on sums and integrals, conformal mappings, Laplace transform, and some special topics, provide a practical-use perspective. Enriched with many numerical examples and exercises designed to test the student's comprehension of the topics covered, this book is written for a one-semester course in complex variables for students in the science and engineering disciplines.
by H. S. KASANA
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Complex Analysis and Applications, Second Edition,
Complex Analysis and Applications, Second Edition explains complex analysis for students of applied mathematics and engineering. Restructured and completely revised, this textbook first develops the theory of complex analysis, and then examines its geometrical interpretation and application to Dirichlet and Neumann boundary value problems. A discussion of complex analysis now forms the first three chapters of the book, with a description of conformal mapping and its application to boundary value problems for the two-dimensional Laplace equation forming the final two chapters. This new structure enables students to study theory and applications separately, as needed. In order to maintain brevity and clarity, the text limits the application of complex analysis to two-dimensional boundary value problems related to temperature distribution, fluid flow, and electrostatics. In each case, in order to show the relevance of complex analysis, each application is preceded by mathematical background that demonstrates how a real valued potential function and its related complex potential can be derived from the mathematics that describes the physical situation.
by Alan Jeffrey
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Complex Variables,Principles and Problem Sessions
This textbook introduces the theory of complex variables at undergraduate level. A good collection of problems is provided in the second part of the book. The book is written in a user-friendly style that presents important fundamentals a beginner needs to master the technical details of the subject. The organization of problems into focused sets is an important feature of the book and the teachers may adopt this book for a course on complex variables and for mining problems.
by A. K. Kapoor
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Complex Variables,Harmonic and Analytic Functions
Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power series; singular points and Laurent series; and much more. Numerous problems and solutions. 1972 edition.
by Francis J. Flanigan
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Computational Fluid Mechanics and Heat Transfer, Third Edition,
Thoroughly updated to include the latest developments in the field, this classic text on finite-difference and finite-volume computational methods maintains the fundamental concepts covered in the first edition. As an introductory text for advanced undergraduates and first-year graduate students, Computational Fluid Mechanics and Heat Transfer, Third Edition provides the background necessary for solving complex problems in fluid mechanics and heat transfer. Divided into two parts, the book first lays the groundwork for the essential concepts preceding the fluids equations in the second part. It includes expanded coverage of turbulence and large-eddy simulation (LES) and additional material included on detached-eddy simulation (DES) and direct numerical simulation (DNS). Designed as a valuable resource for practitioners and students, new homework problems have been added to further enhance the student’s understanding of the fundamentals and applications.
by Richard H. Pletcher
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A Concise Handbook of Mathematics, Physics, and Engineering Sciences,
A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students find difficult to understand. The first part of the book contains chapters on arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, functions of complex variables, integral transforms, ordinary and partial differential equations, special functions, and probability theory. The second part discusses molecular physics and thermodynamics, electricity and magnetism, oscillations and waves, optics, special relativity, quantum mechanics, atomic and nuclear physics, and elementary particles. The third part covers dimensional analysis and similarity, mechanics of point masses and rigid bodies, strength of materials, hydrodynamics, mass and heat transfer, electrical engineering, and methods for constructing empirical and engineering formulas. The main text offers a concise, coherent survey of the most important definitions, formulas, equations, methods, theorems, and laws. Numerous examples throughout and references at the end of each chapter provide readers with a better understanding of the topics and methods. Additional issues of interest can be found in the remarks. For ease of reading, the supplement at the back of the book provides several long mathematical tables, including indefinite and definite integrals, direct and inverse integral transforms, and exact solutions of differential equations.
by Andrei D. Polyanin
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Differential Equations with Applications,
Coherent, balanced introductory text focuses on initial- and boundary-value problems, general properties of linear equations, and the differences between linear and nonlinear systems. Includes large number of illustrative examples worked out in detail and extensive sets of problems. Answers or hints to most problems appear at end.
by Paul D. Ritger
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Complex Analysis with Applications to Flows and Fields,
Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. The book explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics, steady heat conduction, and other problems. It provides the mathematical results to sufficiently justify the solution of these problems, eliminating the need to consult external references. The book is conveniently divided into four parts. In each part, the mathematical theory appears in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. Each chapter begins with an introduction or summary and concludes with related topics. The last chapter in each section offers a collection of many detailed examples. This self-contained book gives the necessary mathematical background and physical principles to build models for technological and scientific purposes. It shows how to formulate problems, justify the solutions, and interpret the results.
by Luis Manuel Braga da Costa Campos
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Fundamentals Of Complex Analysis: Theory And Applications,
The book divided in ten chapters deals with: " Algebra of complex numbers and its various geometrical properties, properties of polar form of complex numbers and regions in the complex plane. " Limit, continuity, differentiability. " Different kinds of complex valued functions. " Different types of transformations. " Conformal mappings of different functions. " Properties of bilinear and special bilinear transformation. " Line integrals, their properties and different theorems. " Sequences and series, Power series, Zero s of functions, residues and residue theorem, meromorphic functions, different kinds of singularities. " Evaluation of real integrals. " Analytic continuation, construction of harmonic functions, infinite product, their properties and Gamma function. " Schwarz-Christoffel transformations, mapping by multi valued functions, entire functions. " Jenson s theorem and Poisson-Jenson theorem. The book is designed as a textbook for UG and PG students of science as well as engineering
by K K Dube
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