Fundamental ideas of analysis

Author: Michael C. Reed

Publisher: John Wiley & Sons Inc

ISBN: 9780471159964

Category: Mathematics

Page: 413

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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: 3634

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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.

Applied Analysis

Mathematical Methods in Natural Science

Author: Takasi Senba,Takashi Suzuki

Publisher: World Scientific

ISBN: 1848166524

Category: Mathematics

Page: 515

View: 4780

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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.

Real Analysis

Author: Patrick Fitzpatrick

Publisher: Brooks/Cole Publishing Company

ISBN: N.A

Category: Mathematics

Page: 228

View: 3373

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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.

Mathematical Analysis

Linear and Metric Structures and Continuity

Author: Mariano Giaquinta,Giuseppe Modica

Publisher: Springer Science & Business Media

ISBN: 0817645144

Category: Mathematics

Page: 466

View: 2579

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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: 7492

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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?

Numerical Analysis

Author: John Todd

Publisher: Academic Press

ISBN: 1483268918

Category: Mathematics

Page: 254

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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: 5432

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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.

Social Network Analysis

A Handbook

Author: John Scott

Publisher: SAGE

ISBN: 9780761963394

Category: Social Science

Page: 208

View: 3951

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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: Mathematics

Page: 265

View: 8704

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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: 7506

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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.

Homotopy Analysis Method in Nonlinear Differential Equations

Author: Shijun Liao

Publisher: Springer Science & Business Media

ISBN: 3642251323

Category: Mathematics

Page: 400

View: 346

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"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.

Representation Theory and Noncommutative Harmonic Analysis I

Fundamental Concepts. Representations of Virasoro and Affine Algebras

Author: Alexandre Kirillov

Publisher: Springer Science & Business Media

ISBN: 9783540186984

Category: Mathematics

Page: 236

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This two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody algebra. It presents a wealth of recent results on representations of infinite-dimensional groups.

Hillbilly-Elegie

Die Geschichte meiner Familie und einer Gesellschaft in der Krise

Author: J. D. Vance

Publisher: Ullstein Buchverlage

ISBN: 3843715777

Category: Biography & Autobiography

Page: 304

View: 9952

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Seine Großeltern versuchten, mit Fleiß und Mobilität der Armut zu entkommen und sich in der Mitte der Gesellschaft zu etablieren. Doch letztlich war alles vergeblich. J. D. Vance erzählt die Geschichte seiner Familie — eine Geschichte vom Scheitern und von der Resignation einer ganzen Bevölkerungsschicht. Armut und Chaos, Hilflosigkeit und Gewalt, Drogen und Alkohol: Genau in diesem Teufelskreis befinden sich viele weiße Arbeiterfamilien in den USA — entfremdet von der politischen Führung, abgehängt vom Rest der Gesellschaft, anfällig für populistische Parolen. Früher konnten sich die »Hillbillys«, die weißen Fabrikarbeiter, erhoffen, sich zu Wohlstand zu schuften. Doch spätestens gegen Ende des 20sten Jahrhunderts zog der Niedergang der alten Industrien ihre Familien in eine Abwärtsspirale, in der sie bis heute stecken. Vance gelingt es wie keinem anderen, diese ausweglose Situation und die Krise einer ganzen Gesellschaft eindrücklich zu schildern. Sein Buch bewegte Millionen von Lesern in den USA und erklärt nicht zuletzt den Wahltriumph eines Donald Trump.

Advanced Calculus

A Course in Mathematical Analysis

Author: Patrick Fitzpatrick

Publisher: Brooks/Cole

ISBN: 9780534926120

Category: Mathematics

Page: 508

View: 8618

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Advanced Calculus is designed for the two-semester course on functions of one and several variables. The text provides a rigorous treatment of the fundamental concepts of mathematical analysis, yet it does so 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.

Functions of a Complex Variable and Some of Their Applications

Author: B. A. Fuchs,B. V. Shabat

Publisher: Elsevier

ISBN: 1483155056

Category: Mathematics

Page: 458

View: 4548

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Functions of a Complex Variable and Some of Their Applications, Volume 1, discusses the fundamental ideas of the theory of functions of a complex variable. The book is the result of a complete rewriting and revision of a translation of the second (1957) Russian edition. Numerous changes and additions have been made, both in the text and in the solutions of the Exercises. The book begins with a review of arithmetical operations with complex numbers. Separate chapters discuss the fundamentals of complex analysis; the concept of conformal transformations; the most important of the elementary functions; and the complex potential for a plane vector field and the application of the simplest methods of function theory to the analysis of such a field. Subsequent chapters cover the fundamental apparatus of the theory of regular functions, i.e. basic integral theorems and expansions in series; the general concept of an analytic function; applications of the theory of residues; and polygonal domain mapping. This book is intended for undergraduate and postgraduate students of higher technical institutes and for engineers wishing to increase their knowledge of theory.

The Nature and Future of Philosophy

Author: Michael Dummett

Publisher: Columbia University Press

ISBN: 0231522185

Category: Philosophy

Page: 160

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Philosophy is a discipline that makes no observations, conducts no experiments, and needs no input from experience. It is an armchair subject, requiring only thought. Yet that thought can advance knowledge in unexpected directions, not only through the discovery of new facts but also through the enhancement of what we already know. Philosophy can clarify our vision of the world and provide exciting ways to interpret it. Of course, philosophy's unified purpose hasn't kept the discipline from splintering into warring camps. Departments all over the world are divided among analytical and continental schools, Heidegger, Hegel, and other major thinkers, challenging the growth of the discipline and obscuring its relevance and intent. Having spent decades teaching in American, Asian, African, and European universities, Michael Dummett has felt firsthand the fractured state of contemporary practice and the urgent need for reconciliation. Setting forth a proposal for renewal and reengagement, Dummett begins with the nature of philosophical inquiry as it has developed for centuries, especially its exceptional openness and perspective-which has, ironically, led to our present crisis. He discusses philosophy in relation to science, religion, morality, language, and meaning and recommends avenues for healing around a renewed investigation of mind, language, and thought. Employing his trademark frankness and accessibility, Dummett asks philosophers to resolve theoretical difference and reclaim the vital work of their practice.