Geometry of Complex Numbers

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Author: Hans Schwerdtfeger

Publisher: Courier Corporation

ISBN: 0486135861

Category: Mathematics

Page: 224

View: 6021

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A

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Author: Barry Simon

Publisher: American Mathematical Soc.

ISBN: 1470411008

Category: Mathematical analysis

Page: 641

View: 7317

A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.

Distribution Theory and Transform Analysis

An Introduction to Generalized Functions, with Applications

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Author: A.H. Zemanian

Publisher: Courier Corporation

ISBN: 0486151948

Category: Mathematics

Page: 400

View: 7080

Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.

How to Solve Applied Mathematics Problems

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Author: B. L. Moiseiwitsch

Publisher: Courier Corporation

ISBN: 0486285227

Category: Mathematics

Page: 336

View: 2522

This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.

Mathematics for Quantum Chemistry

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Author: Jay Martin Anderson

Publisher: Courier Corporation

ISBN: 0486151484

Category: Science

Page: 160

View: 8507

Introduction to problems of molecular structure and motion covers calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics. Answers to problems. 1966 edition.

Advanced Calculus of Several Variables

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Author: Charles Henry Edwards

Publisher: Courier Corporation

ISBN: 9780486683362

Category: Mathematics

Page: 457

View: 4860

Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.

An Introduction to Lebesgue Integration and Fourier Series

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Author: Howard J. Wilcox,David L. Myers

Publisher: Courier Corporation

ISBN: 9780486682938

Category: Mathematics

Page: 159

View: 5384

This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Geometry: A Comprehensive Course

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Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

View: 3018

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Is Oedipus Online?

Siting Freud after Freud

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Author: Jerry Aline Flieger

Publisher: MIT Press

ISBN: 9780262265348

Category: Psychology

Page: 346

View: 3498

Psychoanalysis as a navigation device for the cultural maze of the twenty-first century. "Can Freud be 'updated' in the twenty-first century, or is he a venerated but outmoded genius?" asks Jerry Aline Flieger. In Is Oedipus Online? Flieger stages an encounter between psychoanalysis and the new century, testing the viability of Freud's theories in light of the emergent realities of our time. Responding to prominent critics of psychoanalysis and approaching our current preoccupations from a Freudian angle, she presents a reading of Freudian theory that coincides with and even clarifies new concepts in science and culture. Fractals, emergence, topological modeling, and other nonlinearities, for example, can be understood in light of both Freud's idea of the symptom as a nodal point and Lacan's concept of networks (rather than sequential cause and effect) that link psychic realities. At the same time, Flieger suggests how emerging paradigms in science and culture may elucidate Freud's cultural theory. Like Slavoj Zizek, editor of the Short Circuits series, Flieger shifts effortlessly from field to field, discussing psychoanalysis, millennial culture, nonlinear science, and the landscape of cyberspace. In the first half of the book, "Re-siting Oedipus," she draws on the work of Lyotard, Zizek, Deleuze, Virilio, Baudrillard, Haraway and others, to refute the assumption of Freud's outdatedness in the new century. Then, in "Freud Sitings in Millennial Theory," she recasts oedipal theory, siting/sighting/citing Freud in a twenty-first-century context. Thinking of Oedipus—decipherer of enigmas, wanderer—as a navigator or search engine allows us to see psychoanalysis as a navigation device for the cultural maze of the "bimillennial" era, and Oedipus himself as a circuit of intersubjective processes by which we become human. For humanity—still needed in the "posthuman" century—is at the core of Freud's theory: "Reading Freud today," Flieger writes, "reminds us of the complications of the Sphinx's riddle, the enigma that Oedipus only thought he solved: the question of what it is to be human. Psychoanalysis continues to pose that question at the crossroads between instincts and their vicissitudes."

Introduction to the Geometry of Complex Numbers

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Author: Roland Deaux

Publisher: Courier Corporation

ISBN: 0486158047

Category: Mathematics

Page: 208

View: 8704

Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.

Theory of Linear Operators in Hilbert Space

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Author: Naum Ilʹich Akhiezer,Izrailʹ Markovich Glazman

Publisher: Courier Corporation

ISBN: 9780486677484

Category: Mathematics

Page: 218

View: 4239

This classic textbook introduces linear operators in Hilbert Space, and presents the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. Invaluable for every mathematician and physicist. 1961, 1963 edition.

The Thirteen Books of the Elements

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Author: Euclid

Publisher: N.A

ISBN: 9780486600888

Category: Mathematics

Page: 443

View: 3367

Volume 1 of 3-volume set containing complete English text of all 13 books of the Elements plus critical apparatus analyzing each definition, postulate, and proposition in great detail. Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; commentators; refutations, supports, extrapolations, reinterpretations and historical notes. Vol. 1 includes Introduction, Books 1-2: Triangles, rectangles.

Almost All about Waves

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Author: John R. Pierce

Publisher: N.A

ISBN: N.A

Category: Science

Page: 213

View: 9625

This text considers waves the great unifying concept of physics, employing minimal mathematics to explore behavior common to earthquake waves, ocean waves, sound waves, and mechanical waves. 1974 edition.

The Theory of Remainders

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Author: Andrea Rothbart

Publisher: Courier Dover Publications

ISBN: N.A

Category: Mathematics

Page: 178

View: 9646

An imaginative introduction to number theory, this unique approach employs a pair of fictional characters, Ant and Gnam. Ant leads Gnam through a variety of theories, and together, they put the theories into action—applying linear diophantine equations to football scoring, using a black-magic device to simplify problems in modular structures, and developing intriguing modifications to the rules of chess. Appropriate for anyone familiar with algebra at the high-school level, The Theory of Remainders offers a captivating introduction to both number theory and abstract algebra. Both elementary and challenging, it provides a view of mathematics as a conceptual net and illustrates the differences between conceptual and paraconceptual claims—an excellent start to expanding students' perspectives on mathematics. Exercises throughout the book form an integral part of the text, extending students' experience with the concepts under discussion and presenting opportunities to observe patterns. In addition to the exercises, a series of optional problems allows more advanced readers to further develop the concepts.

Integral Equations

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Author: Benjamin Lawrence Moiseiwitsch

Publisher: Courier Corporation

ISBN: 9780486441627

Category: Mathematics

Page: 166

View: 7795

Geared toward upper-level undergraduate students, this text begins with a straightforward account, accompanied by simple examples of a variety of integral equations and the methods of their solution. The treatment becomes gradually more abstract, with discussions of Hilbert space and linear operators, the resolvent, Fredholm theory, and more. 1977 edition.

Experiencing Geometry

In Euclidean, Spherical, and Hyperbolic Spaces

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Author: David Wilson Henderson,Daina Taimin̦a

Publisher: Pearson College Division

ISBN: N.A

Category: Mathematics

Page: 352

View: 3461

For undergraduate-level courses in Geometry. Henderson invites students to explore the basic ideas of geometry beyond the formulation of proofs. The text conveys a distinctive approach, stimulating students to develop a broader, deeper understanding of mathematics through active participation including discovery, discussion, and writing about fundamental ideas. It provides a series of interesting, challenging problems, then encourages students to gather their reasonings and understandings of each problem and discuss their findings in an open forum.

Cable Structures

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Author: H. Max Irvine

Publisher: N.A

ISBN: N.A

Category: Technology & Engineering

Page: 259

View: 4925

A reprint of the MIT Press edition of 1981, this is a graduate-level study for practicing engineers, researchers and teachers. Annotation copyrighted by Book News, Inc., Portland, OR

Introduction to Vector and Tensor Analysis

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Author: Robert C. Wrede

Publisher: Dover Publications

ISBN: N.A

Category: Mathematics

Page: 418

View: 9538

This broad introduction to vector and tensor analysis is designed for the advanced undergraduate or graduate student in mathematics, physics, and engineering as well as for the practicing engineer or physicist who needs a theoretical understanding of these essential mathematical tools. In recent years, the vector approach has found its way even into writings on aspects of biology, economics, and other sciences. The many and various topics covered include: the algebra of vectors — linear dependence and independence, transformation equations, the inner product, the cross product, and the algebra of matrixes; the differentiation of vectors — geometry of space curves, kinematics, moving frames of reference, Newtonian orbits and special relativity theory; partial differentiation of vectors — geometry of space curves, kinematics, moving frames of reference, Newtonian orbits and special relativity theory; partial differentiation and associated concepts — surface representations, bases in general coordinate systems, and maxima and minima of functions of two variables; the integration of vectors — line integrals, surface integrals, surface tensors and volume integrals; tensor algebra and analysis — fundamental notions of n-space, transformations and tensors, Riemannian geometry, tensor processes of differentiation, geodesics, the curvature tensor and its algebraic properties, and general relativity theory. Throughout, Professor Wrede stresses the interrelationships between algebra and geometry, and moves frequently from one to the other. As he points out, vector and tensor analysis provides a kind of bridge between elementary aspects of linear algebra, geometry and analysis. He uses the classical notation for vector analysis, but introduces a more appropriate new notation for tensors, which he correlates with the common vector notation. He stresses proofs and concludes each section with a set of problems designed to help the student get a solid grasp of the ideas, and explore them more thoroughly on his own. His approach features a combination of important historical material with up-to-date developments in both fields. The knowledge of vector and tensor analysis gained in this way is excellent preparation for further studies in differential geometry, applied mathematics, and theoretical physics.

Directions

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Academic libraries

Page: N.A

View: 8573