Fundamental ideas of analysis

Author: Michael C. Reed

Publisher: John Wiley & Sons Inc

ISBN: 9780471159964

Category: Mathematics

Page: 413

View: 7017

The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.

The Four Fundamental Concepts of Psycho-Analysis

Author: Jacques Lacan

Publisher: Routledge

ISBN: 0429906595

Category: Psychology

Page: 302

View: 4846

Dr Lacan's writings, and especially the seminars for which he has become famous, have provoked intense controversies in French analytic circles, requiring as they do a radical reappraisal of the legacy bequeathed by Freud. This volume is based on a year's seminar, which is of particular importance because he was addressing a larger, less specialist audience than ever before, amongst whom he could not assume familiarity with his work. For his listeners then, and for his readers now, he wanted "to introduce a certain coherence into the major concepts on which psycho-analysis is based", namely the unconscious, repetition, the transference and the drive.In re-defining these four concepts he explores the question that, as he puts it, moves from "Is psycho-analysis a science?" to "What is a science that includes psycho-analysis?" Dr Lacan argues in particular that there is a structural affinity between psycho-analysis, construed as the science of the unconscious, and language - the science of linguistics being one of the significant discoveries of our time. He also discusses the relation of psycho-analysis to religion, and reveals his particular stance on a wide range of topics, such as sexuality and death, love and libido, alienation, interpretation, repression and desire.This book constitutes the essence of Dr Lacan's sensibility. There is no clearer statement of the ideas and issues which have aroused such passionate reactions in France, and which can now gain the hearing they deserve in the English-speaking world.

Mathematical Analysis

Linear and Metric Structures and Continuity

Author: Mariano Giaquinta,Giuseppe Modica

Publisher: Springer Science & Business Media

ISBN: 0817643753

Category: Mathematics

Page: 466

View: 2356

Examines linear structures, the topology of metric spaces, and continuity in infinite dimensions, with detailed coverage at the graduate level Includes applications to geometry and differential equations, numerous beautiful illustrations, examples, exercises, historical notes, and comprehensive index May be used in graduate seminars and courses or as a reference text by mathematicians, physicists, and engineers

Transformation - A Fundamental Idea of Mathematics Education

Author: Sebastian Rezat,Mathias Hattermann,Andrea Peter-Koop

Publisher: Springer Science & Business Media

ISBN: 1461434890

Category: Education

Page: 409

View: 1607

The diversity of research domains and theories in the field of mathematics education has been a permanent subject of discussions from the origins of the discipline up to the present. On the one hand the diversity is regarded as a resource for rich scientific development on the other hand it gives rise to the often repeated criticism of the discipline’s lack of focus and identity. As one way of focusing on core issues of the discipline the book seeks to open up a discussion about fundamental ideas in the field of mathematics education that permeate different research domains and perspectives. The book addresses transformation as one fundamental idea in mathematics education and examines it from different perspectives. Transformations are related to knowledge, related to signs and representations of mathematics, related to concepts and ideas, and related to instruments for the learning of mathematics. The book seeks to answer the following questions: What do we know about transformations in the different domains? What kinds of transformations are crucial? How is transformation in each case conceptualized?

Applied Analysis

Mathematical Methods in Natural Science

Author: Takashi Suzuki,Takasi Senba

Publisher: World Scientific Publishing Company

ISBN: 1911299549

Category: Mathematics

Page: 532

View: 2943

This book provides a general introduction to applied analysis; vector analysis with physical motivation, calculus of variation, Fourier analysis, eigenfunction expansion, distribution, and so forth, including a catalogue of mathematical theories, such as basic analysis, topological spaces, complex function theory, real analysis, and abstract analysis. This book also uses fundamental ideas of applied mathematics to discuss recent developments in nonlinear science, such as mathematical modeling of reinforced random motion of particles, semiconductor device equation in applied physics, and chemotaxis in biology. Several tools in linear PDE theory, such as fundamental solutions, Perron's method, layer potentials, and iteration scheme, are described, as well as systematic descriptions on the recent study of the blowup of the solution. Contents: Field FormationGeometric ObjectsCalculus of VariationsInfinite-Dimensional AnalysisScatteringRandom Motion of ParticlesLinear PDENonlinear PDE Readership: Mathematics undergraduates.

Real Analysis

Author: Patrick Fitzpatrick

Publisher: Brooks/Cole Publishing Company


Category: Mathematics

Page: 228

View: 318

Real Analysis is a shorter version of the author's Advanced Calculus text, and contains just the first nine chapters from the longer text. It provides a rigorous treatment of the fundamental concepts of mathematical analysis for functions of a single variable in a clear, direct way. The author wants students to leave the course with an appreciation of the subject's coherence and significance, and an understanding of the ideas that underlie mathematical analysis.

Numerical Analysis

Author: John Todd

Publisher: Academic Press

ISBN: 1483268918

Category: Mathematics

Page: 254

View: 9924

Basic Numerical Mathematics, Volume 1: Numerical Analysis focuses on numerical analysis, with emphasis on the ideas of "controlled computational experiments" and "bad examples". The concepts of convergence and continuity are discussed, along with the rate of convergence, acceleration, and asymptotic series. The more traditional topics of interpolation, quadrature, and differential equations are also explored. Comprised of 10 chapters, this volume begins with an analysis of the algorithms of Gauss, Borchardt, and Carlson in relation to the rate of convergence. The reader is then introduced to orders of magnitude and rates of convergence; recurrence relations for powers; and the solution of equations. Subsequent chapters deal with uniform convergence and approximation; the acceleration processes of Aitken and Euler; asymptotic series; interpolation; and quadrature. The final chapter is devoted to linear difference equations with constant coefficients, along with differentiation and differential equations. This book will be of interest to mathematicians and students of mathematics.

Fundamental Concepts in Modern Analysis

Author: Vagn Lundsgaard Hansen

Publisher: World Scientific

ISBN: 9789810238940

Category: Science

Page: 236

View: 5696

Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces. In this book, mathematically inclined engineering students are offered an opportunity to go into some depth with fundamental notions from mathematical analysis that are not only important from a mathematical point of view but also occur frequently in the more theoretical parts of the engineering sciences. The book should also appeal to university students in mathematics and in the physical sciences.

Essential Results of Functional Analysis

Author: Robert J. Zimmer

Publisher: University of Chicago Press

ISBN: 9780226983387

Category: Mathematics

Page: 157

View: 9944

Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach. Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter. For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.

Grundlagen der Photonik

Author: Bahaa E. A. Saleh,Malvin Carl Teich

Publisher: John Wiley & Sons

ISBN: 9783527406777

Category: Optoelectronics

Page: 1406

View: 7735

Schon die erste Auflage des englischen Lehrbuchs 'Fundamentals of Photonics' zeichnete sich durch seine ausgewogene Mischung von Theorie und Praxis aus, und deckte in detaillierter Darstellung die grundlegenden Theorien des Lichts ab. Es umfasste sowohl die Themen Strahlenoptik, Wellenoptik, elektromagnetische Optik, Photonenoptik, sowie die Wechselwirkung von Licht und Materie, als auch die Theorie der optischen Eigenschaften von Halbleitern. Die Photonik-Technologie hat eine rasante Entwicklung genommen seit der Publikation der ersten Ausgabe von 'Fundamentals of Photonics' vor 15 Jahren. Die nun vorliegende Zweite Auflage des Marksteins auf dem Gebiet der Photonik trägt mit zwei neuen und zusätzlichen Kapiteln den neuesten technologischen Fortschritten Rechnung: Photonische Kristalle sowie Ultrakurzpuls-Optik. Zudem wurden alle Kapitel gründlich überarbeitet und viele Abschnitte hinzugefügt, so z.B. über Laguerre-Gauss Strahlen, die Sellmeier-Gleichung, Photonenkristall-Wellenleiter, photonische Kristallfasern, Mikrosphären-Resonatoren, Optische Kohärenz Tomographie, Bahndrehimpuls des Photons, Bohrsche Theorie, Raman-Verstärker, rauscharme Avalanche-Photodioden, Abstimmkurven und Dispersions-Management.

Social Network Analysis

A Handbook

Author: John Scott

Publisher: SAGE

ISBN: 9780761963394

Category: Social Science

Page: 208

View: 7034

The revised and updated edition of this bestselling text provides an accessible introduction to the theory and practice of network analysis in the social sciences. It gives a clear and authoritative guide to the general framework of network analysis, explaining the basic concepts, technical measures and reviewing the available computer programs. The book outlines both the theoretical basis of network analysis and the key techniques for using it as a research tool. Building upon definitions of points, lines and paths, John Scott demonstrates their use in clarifying such measures as density, fragmentation and centralization. He identifies the various cliques, components and circles into which networks are formed, and outlines

Scenes from the History of Real Functions

Author: F.A. Medvedev

Publisher: Birkhäuser

ISBN: 3034886608

Category: Science

Page: 265

View: 1910

To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt.

Direct Methods for Limit and Shakedown Analysis of Structures

Advanced Computational Algorithms and Material Modelling

Author: Paolo Fuschi,Aurora Angela Pisano,Dieter Weichert

Publisher: Springer

ISBN: 3319129287

Category: Technology & Engineering

Page: 313

View: 8513

Articles in this book examine various materials and how to determine directly the limit state of a structure, in the sense of limit analysis and shakedown analysis. Apart from classical applications in mechanical and civil engineering contexts, the book reports on the emerging field of material design beyond the elastic limit, which has further industrial design and technological applications. Readers will discover that “Direct Methods” and the techniques presented here can in fact be used to numerically estimate the strength of structured materials such as composites or nano-materials, which represent fruitful fields of future applications. Leading researchers outline the latest computational tools and optimization techniques and explore the possibility of obtaining information on the limit state of a structure whose post-elastic loading path and constitutive behavior are not well defined or well known. Readers will discover how Direct Methods allow rapid and direct access to requested information in mathematically constructive manners without cumbersome step-by-step computation. Both researchers already interested or involved in the field and practical engineers who want to have a panorama of modern methods for structural safety assessment will find this book valuable. It provides the reader with the latest developments and a significant amount of references on the topic.

Introduction to Real Analysis, 4th Edition

Author: Robert G. Bartle,Donald R. Sherbert

Publisher: Wiley Global Education

ISBN: 1118135865

Category: Mathematics

Page: 402

View: 2470

This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations, and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with additional examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: Introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.

Das Kapital im 21. Jahrhundert

Author: Thomas Piketty

Publisher: C.H.Beck

ISBN: 3406671322

Category: Business & Economics

Page: 816

View: 7684

Wie entstehen die Akkumulation und die Distribution von Kapital? Welche Dynamiken sind dafür maßgeblich? Fragen der langfristigen Evolution von Ungleichheit, der Konzentration von Wohlstand in wenigen Händen und nach den Chancen für ökonomisches Wachstum bilden den Kern der Politischen Ökonomie. Aber befriedigende Antworten darauf gab es bislang kaum, weil aussagekräftige Daten und eine überzeugende Theorie fehlten. In Das Kapital im 21. Jahrhundert analysiert Thomas Piketty ein beeindruckendes Datenmaterial aus 20 Ländern, zurückgehend bis ins 18. Jahrhundert, um auf dieser Basis die entscheidenden ökonomischen und sozialen Abläufe freizulegen. Seine Ergebnisse stellen die Debatte auf eine neue Grundlage und definieren zugleich die Agenda für das künftige Nachdenken über Wohlstand und Ungleichheit. Piketty zeigt uns, dass das ökonomische Wachstum in der Moderne und die Verbreitung des Wissens es uns ermöglicht haben, den Ungleichheiten in jenem apokalyptischen Ausmaß zu entgehen, das Karl Marx prophezeit hatte. Aber wir haben die Strukturen von Kapital und Ungleichheit andererseits nicht so tiefgreifend modifiziert, wie es in den prosperierenden Jahrzehnten nach dem Zweiten Weltkrieg den Anschein hatte. Der wichtigste Treiber der Ungleichheit – nämlich die Tendenz von Kapitalgewinnen, die Wachstumsrate zu übertreffen – droht heute extreme Ungleichheiten hervorzubringen, die am Ende auch den sozialen Frieden gefährden und unsere demokratischen Werte in Frage stellen. Doch ökonomische Trends sind keine Gottesurteile. Politisches Handeln hat gefährliche Ungleichheiten in der Vergangenheit korrigiert, so Piketty, und kann das auch wieder tun.