Chaos in Classical and Quantum Mechanics

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Author: Martin C. Gutzwiller

Publisher: Springer Science & Business Media

ISBN: 1461209838

Category: Mathematics

Page: 432

View: 8779

Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.

A Synopsis of Elementary Results in Pure and Applied Mathematics: Volume 1

Containing Propositions, Formulae, and Methods of Analysis, with Abridged Demonstrations

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Author: George Shoobridge Carr,G S Carr

Publisher: Cambridge University Press

ISBN: 1108050670

Category: Mathematics

Page: 298

View: 9067

When George Shoobridge Carr (1837-1914) wrote his Synopsis of Elementary Results he intended it as an aid to students preparing for degree-level examinations such as the Cambridge Mathematical Tripos, for which he provided private tuition. He would have been startled to see the two volumes, first published in 1880 and 1886 respectively, reissued more than a century later. Notably, in 1903 the work fell into the hands of the Indian prodigy Srinivasa Ramanujan (1887-1920) and greatly influenced his mathematical education. It is the interaction between a methodical teaching aid and the soaring spirit of a self-taught genius which gives this reissue its interest. Volume 1, presented here in its 1886 printing, contains sections on mathematical tables, algebra, the theory of equations, plane trigonometry, spherical trigonometry, elementary geometry and geometrical conics.

Foundations of Applied Mathematics, Volume I

Mathematical Analysis

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Author: Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans

Publisher: SIAM

ISBN: 1611974909

Category: Mathematics

Page: 689

View: 8821

This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell–Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?

Boundary Value Problems of Mathematical Physics

2-Volume Set

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Author: Ivar Stakgold

Publisher: SIAM

ISBN: 1611972388

Category:

Page: 748

View: 3557

For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Originally published in 1967, this graduate-level introduction is devoted to the mathematics needed for the modern approach to boundary value problems using Green's functions and using eigenvalue expansions. Now a part of SIAM's Classics series, these volumes contain a large number of concrete, interesting examples of boundary value problems for partial differential equations that cover a variety of applications that are still relevant today. For example, there is substantial treatment of the Helmholtz equation and scattering theory?subjects that play a central role in contemporary inverse problems in acoustics and electromagnetic theory.

Journal of Approximation Theory and Applied Mathematics - 2013 Vol. 1 and

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Author: Marco Schuchmann

Publisher: BoD – Books on Demand

ISBN: 3735791859

Category: Mathematics

Page: 108

View: 9761

Journal of Approximation Theory and Applied Mathematics (ISSN 2196-1581) is a journal which started in 2013. Themes of our journal are: Approximation theory (with a focus on wavelets) and applications in mathematics like numerical analysis, statistics or financial mathematics. Contents 2013 Vol. 1: An Approximation on a Compact Interval Calculated with a Wavelet Collocation Method can Lead to Much Better Results than other Methods, Parameter Identification with a Wavelet Collocation Method in a Partial Differential Equation, An Approach for a Parameter Estimation with a Wavelet Collocation Method, Notes on Nonparametric Regression with Wavelets, Extrapolation and Approximation with a Wavelet Collocation Method for ODEs 2013 Vol. 2: Solving ODEs and DAEs with a Wavelet Collocation Method with Examples from the Chemical Reaction Kinetics, Solving Integral Equations with a Wavelet Collocation Approach, Approximation of Non L2(R) Functions on a Compact Interval with a Wavelet Base, Comparing Approximations of a Wavelet Collocation Method of Various Wavelets

Foundations of Applied Mathematics

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Author: Michael D. Greenberg

Publisher: Courier Corporation

ISBN: 0486492796

Category: Mathematics

Page: 636

View: 1618

"A longtime classic text in applied mathematics, this volume also serves as a reference for undergraduate and graduate students of engineering. Topics include real variable theory, complex variables, linear analysis, partial and ordinary differential equations, and other subjects. Answers to selected exercises are provided, along with Fourier and Laplace transformation tables and useful formulas. 1978 edition"--

Practical Bifurcation and Stability Analysis

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Author: Rüdiger U. Seydel

Publisher: Springer Science & Business Media

ISBN: 1441917403

Category: Mathematics

Page: 477

View: 6411

Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.

Mathematical Biology II

Spatial Models and Biomedical Applications

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Author: James D. Murray

Publisher: Springer Science & Business Media

ISBN: 0387952284

Category: Mathematics

Page: 814

View: 9494

This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences. It has been extensively updated and extended to cover much of the growth of mathematical biology. From the reviews: ""This book, a classical text in mathematical biology, cleverly combines mathematical tools with subject area sciences."--SHORT BOOK REVIEWS

Foundations of Applied Mathematics, Volume I

Mathematical Analysis

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Author: Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans

Publisher: SIAM

ISBN: 1611974895

Category: Mathematics

Page: 689

View: 6818

This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell–Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?

Applied Mathematics for Engineers and Physicists

Third Edition

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Author: Louis A. Pipes,Lawrence R. Harvill

Publisher: Courier Corporation

ISBN: 0486794997

Category: Mathematics

Page: 1040

View: 5749

Suitable for advanced courses in applied mathematics, this text covers analysis of lumped parameter systems, distributed parameter systems, and important areas of applied mathematics. Answers to selected problems. 1970 edition.

Applied Mathematics Reviews

(Volume 1)

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Author: George A Anastassiou

Publisher: World Scientific

ISBN: 9814492884

Category: Mathematics

Page: 624

View: 2906

Applied mathematics connects the mathematical theory to the reality by solving real world problems and shows the power of the science of mathematics, greatly improving our lives. Therefore it plays a very active and central role in the scientific world. This volume contains 14 high quality survey articles — incorporating original results and describing the main research activities of contemporary applied mathematics — written by top people in the field. The articles have been written in review style, so that the researcher can have a quick and thorough view of what is happening in the main subfields of applied mathematics. Contents:Two Contemporary Computational Concepts in Numerical Analysis (I K Argyros)On the Simultaneous Approximation of Functions and Their Derivatives (T Kilgore)Copositive Polynomial Approximation Revisited (Y K Hu & X M Yu)Sampling Theory and Function Spaces (H-J Schmeisser & W Sickel)Evaluating Statistical Functionals by Means of Projections onto Convex Cones in Hilbert Spaces: Part I and II (T Rychlik)Extrapolation: From Calculation of π to Finite Element Method of Partial Differential Equations (X-P Shen)A Survey on Scaling Function Interpolation and Approximation (E-B Lin)and other papers Readership: Applied mathematicians, statisticians, economists and engineers. Keywords:Singular Integrals;Numerical Analysis;Convolution Operators;Approximation of Functions;Minimal Projection;Fuzzy Control;Sampling Theory;Stable Financial Modelling;Ill-Posed Problems;Finite Element Method

The Princeton Companion to Applied Mathematics

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Author: Nicholas J. Higham

Publisher: Princeton University Press

ISBN: 1400874475

Category: Mathematics

Page: 1016

View: 5299

This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Methods of Mathematical Physics

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Author: Richard Courant,D. Hilbert

Publisher: John Wiley & Sons

ISBN: 3527617221

Category: Science

Page: 575

View: 4577

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.

A Course of Higher Mathematics: Elementary calculus

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Author: Vladimir Ivanovich Smirnov

Publisher: Pergamon

ISBN: N.A

Category: Mathematical analysis

Page: 635

View: 8094

Determinants the solution of systems of equations; Linear transformation and quadratic forms; The basic theory of group and linear representations of groups.

A Synopsis of Elementary Results in Pure and Applied Mathematics: Volume 2

Containing Propositions, Formulae, and Methods of Analysis, with Abridged Demonstrations

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Author: George Shoobridge Carr

Publisher: Cambridge University Press

ISBN: 1108050689

Category: Mathematics

Page: 718

View: 772

When George Shoobridge Carr (1837-1914) wrote his Synopsis of Elementary Results he intended it as an aid to students preparing for degree-level examinations such as the Cambridge Mathematical Tripos, for which he provided private tuition. He would have been startled to see the two volumes, first published in 1880 and 1886 respectively, reissued more than a century later. Notably, in 1903 the work fell into the hands of the Indian prodigy Srinivasa Ramanujan (1887-1920) and greatly influenced his mathematical education. It is the interaction between a methodical teaching aid and the soaring spirit of a self-taught genius which gives this reissue its interest. Volume 2 contains sections on differential calculus, integral calculus, calculus of variations, differential equations, calculus of finite differences, plane coordinate geometry and solid coordinate geometry. Also included is a historically valuable index insofar as it provides references to 890 volumes of 32 periodicals dating back to 1800.

A Course of Mathematics for Engineers and Scientists

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Author: Brian H. Chirgwin,Charles Plumpton

Publisher: Elsevier

ISBN: 148318417X

Category: Mathematics

Page: 334

View: 9982

A Course of Mathematics for Engineers and Scientists, Volume 1 studies the various concepts in pure and applied mathematics, specifically the technique and applications of differentiation and integration of one variable, geometry of two dimensions, and complex numbers. The book is divided into seven chapters, wherein the first of which presents the introductory concepts, such as the functional notation and fundamental definitions; the roots of equations; and limits and continuity. The text then tackles the techniques and applications of differentiation and integration. Geometry of two dimensions and complex numbers are also encompassed in the book. The text will be very invaluable to students of pure and applied mathematics and engineering, as well as those mathematicians and engineers who need a refresher on the topic.

Introduction to Applied Mathematics

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Author: Gilbert Strang

Publisher: Wellesley-Cambridge Press

ISBN: 9780961408800

Category: Mathematics

Page: 760

View: 1441

Renowned applied mathematician Gilbert Strang teaches applied mathematics with the clear explanations, examples and insights of an experienced teacher. This book progresses steadily through a range of topics from symmetric linear systems to differential equations to least squares and Kalman filtering and optimization. It clearly demonstrates the power of matrix algebra in engineering problem solving. This is an ideal book (beloved by many readers) for a first course on applied mathematics and a reference for more advanced applied mathematicians. The only prerequisite is a basic course in linear algebra.

A Course of Higher Mathematics

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Author: V. I. Smirnov

Publisher: Elsevier

ISBN: 1483139379

Category: Mathematics

Page: 652

View: 825

International Series of Monographs in Pure and Applied Mathematics, Volume 62: A Course of Higher Mathematics, V: Integration and Functional Analysis focuses on the theory of functions. The book first discusses the Stieltjes integral. Concerns include sets and their powers, Darboux sums, improper Stieltjes integral, jump functions, Helly’s theorem, and selection principles. The text then takes a look at set functions and the Lebesgue integral. Operations on sets, measurable sets, properties of closed and open sets, criteria for measurability, and exterior measure and its properties are discussed. The text also examines set functions, absolute continuity, and generalization of the integral. Absolutely continuous set functions; absolutely continuous functions of several variables; supplementary propositions; and the properties of the Hellinger integral are presented. The text also focuses on metric and normed spaces. Separability, compactness, linear functionals, conjugate spaces, and operators in normed spaces are underscored. The book also discusses Hilbert space. Linear functionals, projections, axioms of the space, sequences of operators, and weak convergence are described. The text is a valuable source of information for students and mathematicians interested in studying the theory of functions.