Mathematics

Its Content, Methods and Meaning

Author: A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev

Publisher: Courier Corporation

ISBN: 0486157873

Category: Mathematics

Page: 1120

View: 7604

Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.
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Advanced Cataloguing Practice: Based On Anglo-American Cataloguing Rules 2Nd Ed.

Author: Krishan Kumar,B.S. Garg

Publisher: Har-Anand Publications

ISBN: 9788124109960

Category:

Page: 264

View: 5333

The book describes rules for cataloguing of printed monograph and serials; and also contains catalogue entries for 44 complex documents (printed monographs and serials) along with the one simple document (to illustrate different kinds of entries), prepared according to Anglo-American Cataloguing Rules (2nd editio) (1978) (AACR2) and Library of Congress Subject Headings (20th edition) (1997) (LCSH2O).
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Introduction to Partial Differential Equations and Hilbert Space Methods

Author: Karl E. Gustafson

Publisher: Courier Corporation

ISBN: 0486140873

Category: Mathematics

Page: 480

View: 2443

Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
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Mathematics for Economics and Finance

Methods and Modelling

Author: Martin Anthony,Norman Biggs

Publisher: Cambridge University Press

ISBN: 9780521559133

Category: Business & Economics

Page: 394

View: 7645

Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth.
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What is Mathematics?

An Elementary Approach to Ideas and Methods

Author: Richard Courant,Herbert Robbins,Ian Stewart

Publisher: Oxford University Press, USA

ISBN: 9780195105193

Category: Mathematics

Page: 566

View: 7417

A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.
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New Technical Books

Author: New York Public Library

Publisher: N.A

ISBN: N.A

Category: Engineering

Page: N.A

View: 7187

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Mathematics of the 19th Century

Mathematical Logic, Algebra, Number Theory, Probability Theory

Author: Andreĭ Nikolaevich Kolmogorov,Adolʹf Pavlovich I͡Ushkevich

Publisher: Springer Science & Business Media

ISBN: 9783764364410

Category: Mathematics

Page: 308

View: 690

New Edition - New in Paperback - This is the second revised edition of the first volume of the outstanding collection of historical studies of mathematics in the nineteenth century compiled in three volumes by A. N. Kolmogorov and A. P. Yushkevich. This second edition was carefully revised by Abe Shenitzer, York University, Ontario, Canada. The historical period covered in this book extends from the early nineteenth century up to the end of the 1930s, as neither 1801 nor 1900 are, in themselves, turning points in the history of mathematics, although each date is notable fo a remarkable event: the first for the publication of Gauss' "Disquisitiones arithmeticae," the second for Hilbert's "Mathematical Problems." Beginning in the second quarter of the nineteenth century mathematics underwent a revolution as crucial and profound in its consequences for the general world outlook as the mathematical revolution in the beginning of the modern era. The main changes included a new statement of the problem of the existence of mathematical objects, particulary in the calculus, and soon thereafter the formation of non-standard structures in geometry, arithmetic and algebra. The primary objective of the work has been to treat the evolution of mathematics in the nineteenth century as a whole; the discussion is concentrated on the essential concepts, methods, and algorithms.
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A Unified Approach to the Finite Element Method and Error Analysis Procedures

Author: Julian A. T. Dow

Publisher: Elsevier

ISBN: 9780080543420

Category: Technology & Engineering

Page: 533

View: 6696

A Unified Approach to the Finite Element Method and Error Analysis Procedures provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results. Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers. New, simpler element formulation techniques, model-independent results, and error measures New polynomial-based methods for identifying critical points New procedures for evaluating sheer/strain accuracy Accessible to undergraduates, insightful to researchers, and useful to practitioners Taylor series (polynomial) based Intuitive elemental and point-wise error measures Essential background information provided in 12 appendices
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Fractional Calculus

An Introduction for Physicists

Author: Richard Herrmann

Publisher: World Scientific

ISBN: 9814551090

Category: Science

Page: 500

View: 4440

The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area. The contents are devoted to the application of fractional calculus to physical problems. The fractional concept is applied to subjects in classical mechanics, group theory, quantum mechanics, nuclear physics, hadron spectroscopy and quantum field theory and it will surprise the reader with new intriguing insights. This new, extended edition now also covers additional chapters about image processing, folded potentials in cluster physics, infrared spectroscopy and local aspects of fractional calculus. A new feature is exercises with elaborated solutions, which significantly supports a deeper understanding of general aspects of the theory. As a result, this book should also be useful as a supporting medium for teachers and courses devoted to this subject. Contents:IntroductionFunctionsThe Fractional DerivativeFriction ForcesFractional CalculusThe Fractional Harmonic OscillatorWave Equations and ParityNonlocality and Memory EffectsFractional Calculus in Multidimensional Space — 2D-Image ProcessingFractional Calculus in Multidimensional Space — 3D-Folded Potentials in Cluster PhysicsQuantum MechanicsThe Fractional Schrödinger Equation with the Infinite Well Potential — Numerical Results using the Riesz DerivativeUniqueness of a Fractional Derivative — the Riesz and Regularized Liouville Derivative as ExamplesFractional Spin — A Property of Particles Described with the Fractional Schrödinger EquationFactorizationSymmetriesThe Fractional Symmetric Rigid Rotorq-Deformed Lie Algebras and Fractional CalculusInfrared Spectroscopy of Diatomic Molecules Fractional Spectroscopy of HadronsMagic Numbers in Atomic NucleiMagic Numbers in Metal ClustersFractors — Fractional Tensor CalculusFractional FieldsGauge Invariance in Fractional Field TheoriesOn the Origin of SpaceOutlook Readership: Students and researchers in physics. Keywords:Mathematical Physics;Fractional Calculus;Long-Memory Kernels;Non-Local Field Theories;Fractional Quantum MechanicsKey Features:This was the first book on the market covering the full area of a physical application of fractional calculusThe book provides a skillful insight into a vividly growing research area and guides the reader from his first steps on an introductory level up to the current state of the art of a physical interpretation and application in different fieldsThis book enables the reader to participate and contribute to the development of this exciting research area by applying these methods in his own research area tooReviews:Reviews of the First Edition: “Fractional Calculus is an affordable and valuable introduction to the field that will appeal to physicists interested in scientific what-ifs.” Physics Today “… the first three chapters actually appear very helpful at the graduate level. Each chapter has a careful precis at the start. There a many analyses illustrating outcomes of fractional analyses… If this [fractional calculus] is the field of your research then this book is essential with numerous references… ” Contemporary Physics “The book has the property that derived results are directly compared with experimental findings. As a consequence, the reader is guided and encouraged to apply the fractional calculus approach in her/his research area. The reviewer strongly recommends this book for beginners as well as specialists in the fields of physics, mathematics and complex adaptive systems.” Zentralblatt MATH “A very welcome new feature in the second edition is the inclusion of exercises at the end of every chapter, with detailed solutions in the back of the book. This book is specifically aimed at physicists, although many of my colleagues outside physics have also found it useful. This is particularly true of graduate students and beginning researchers, or those new to the subject of fractional calculus.” Mark Meerschaert Dept of Statistics and Probability, Michigan State University
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Mathematics and Its History

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 144196052X

Category: Mathematics

Page: 662

View: 7079

From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.
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Educational Research and Innovation Teachers as Designers of Learning Environments The Importance of Innovative Pedagogies

The Importance of Innovative Pedagogies

Author: Paniagua Alejandro,Istance David

Publisher: OECD Publishing

ISBN: 9264085378

Category:

Page: 204

View: 1717

Pedagogy is at the heart of teaching and learning. Preparing young people to become lifelong learners with a deep knowledge of subject matter and a broad set of social skills requires a better understanding of how pedagogy influences learning. Focusing on pedagogies shifts the perception of ...
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Differential Geometry

Author: Erwin Kreyszig

Publisher: Courier Corporation

ISBN: 0486318621

Category: Mathematics

Page: 384

View: 5836

An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.
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Mathematical Methods for the Physical Sciences

An Informal Treatment for Students of Physics and Engineering

Author: K. F. Riley

Publisher: Cambridge University Press

ISBN: 9780521098397

Category: Mathematics

Page: 533

View: 3380

Designed for first and second year undergraduates at universities and polytechnics, as well as technical college students.
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Numerical Methods for Ordinary Differential Equations

Author: J. C. Butcher

Publisher: John Wiley & Sons

ISBN: 9780470753750

Category: Mathematics

Page: 482

View: 4464

In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book include Introductory work on differential and difference equations. A comprehensive introduction to the theory and practice of solving ordinary differential equations numerically. A detailed analysis of Runge-Kutta methods and of linear multistep methods. A complete study of general linear methods from both theoretical and practical points of view. The latest results on practical general linear methods and their implementation. A balance between informal discussion and rigorous mathematical style. Examples and exercises integrated into each chapter enhancing the suitability of the book as a course text or a self-study treatise. Written in a lucid style by one of the worlds leading authorities on numerical methods for ordinary differential equations and drawing upon his vast experience, this new edition provides an accessible and self-contained introduction, ideal for researchers and students following courses on numerical methods, engineering and other sciences.
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Great Currents of Mathematical Thought

Marthematics in the Arts and Sciences

Author: François Le Lionnais

Publisher: Courier Corporation

ISBN: 9780486495798

Category: Mathematics

Page: 266

View: 9494

50 essays by eminent scholars include meditations on "Structures," Disciplines," "Space," "Function," "Group," "Probability," and "The Mathematical Epic" (Volume I) and on "Mathematics and the Human Intellect," "Mathematics and Technology," and "Mathematics and Civilization" (Volume II). 1962 edition.
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Differential and Integral Calculus

Author: Richard Courant

Publisher: John Wiley & Sons

ISBN: 9780471608424

Category: Mathematics

Page: 640

View: 4357

Now available in a low-priced paperback edition! Written by one of the foremost mathematicians of the 20th century, this text remains the only modern treatment to successfully integrate principles of analysis into first-year calculus. Further, Courant's treatment introduces the differential and integral calculus simultaneously, emphasizing the central point of the calculus, namely, the connection between definite integral, indefinite integral, and derivative. Exposition exhibits the close connection between analysis and its applications, making this text appropriate for students of mathematics, or of science and engineering. Courant makes the subject easier to grasp by giving proofs step-by-step, and by developing the intuition that gave rise to the calculus and guides its use today.
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Number Theory and Its History

Author: Oystein Ore

Publisher: Courier Corporation

ISBN: 9780486656205

Category: Mathematics

Page: 370

View: 5197

Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
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Schaum's Outline of Mathematical Methods for Business and Economics

Author: Edward Dowling

Publisher: McGraw Hill Professional

ISBN: 0071702466

Category: Education

Page: 408

View: 9050

Confused by the math of business and economics? Problem solved. Schaum's Outline of Mathematical Methods for Business and Economics reviews the mathematical tools, topics, and techniques essential for success in business and economics today. The theory and solved problem format of each chapter provides concise explanations illustrated by examples, plus numerous problems with fully worked-out solutions. And you don't have to know advanced math beyond what you learned high school. The pedagogy enables you to progress at your own pace and adapt the book to your own needs.
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Was ist Mathematik?

Author: Richard Courant,Herbert Robbins

Publisher: Springer-Verlag

ISBN: 3662000539

Category: Mathematics

Page: N.A

View: 4393

47 brauchen nur den Nenner n so groß zu wählen, daß das Intervall [0, IJn] kleiner wird als das fragliche Intervall [A, B], dann muß mindestens einer der Brüche m/n innerhalb des Intervalls liegen. Also kann es kein noch so kleines Intervall auf der Achse geben, das von rationalen Punkten frei wäre. Es folgt weiterhin, daß es in jedem Intervall unendlich viele rationale Punkte geben muß; denn wenn es nur eine endliche Anzahl gäbe, so könnte das Intervall zwischen zwei beliebigen benachbarten Punkten keine rationalen Punkte enthalten, was, wie wir eben sahen, unmöglich ist. § 2. Inkommensurable Strecken, irrationale Zahlen und der Grenzwertbegriff 1. Einleitung Vergleicht man zwei Strecken a und b hinsichtlich ihrer Größe, so kann es vor kommen, daß a in b genau r-mal enthalten ist, wobei r eine ganze Zahl darstellt. In diesem Fall können wir das Maß der Strecke b durch das von a ausdrücken, indem wir sagen, daß die Länge von b das r-fache der Länge von a ist.
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