Chaos in Classical and Quantum Mechanics

Author: Martin C. Gutzwiller

Publisher: Springer Science & Business Media

ISBN: 1461209838

Category: Mathematics

Page: 432

View: 9335

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

Author: George Shoobridge Carr,G S Carr

Publisher: Cambridge University Press

ISBN: 1108050670

Category: Mathematics

Page: 298

View: 2469

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.

Boundary Value Problems of Mathematical Physics

2-Volume Set

Author: Ivar Stakgold

Publisher: SIAM

ISBN: 1611972388

Category:

Page: 748

View: 4878

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.

Foundations of Applied Mathematics, Volume I

Mathematical Analysis

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

Publisher: SIAM

ISBN: 1611974909

Category: Mathematics

Page: 689

View: 3559

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?

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

Author: Marco Schuchmann

Publisher: BoD – Books on Demand

ISBN: 3735791859

Category: Mathematics

Page: 108

View: 490

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

Author: Michael D. Greenberg

Publisher: Courier Corporation

ISBN: 0486492796

Category: Mathematics

Page: 636

View: 1812

"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

Author: Rüdiger U. Seydel

Publisher: Springer Science & Business Media

ISBN: 1441917403

Category: Mathematics

Page: 477

View: 9128

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

Author: James D. Murray

Publisher: Springer Science & Business Media

ISBN: 3662085429

Category: Mathematics

Page: 770

View: 6357

Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.

Foundations of Applied Mathematics, Volume I

Mathematical Analysis

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

Publisher: SIAM

ISBN: 1611974895

Category: Mathematics

Page: 689

View: 8953

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

Author: Louis A. Pipes,Lawrence R. Harvill

Publisher: Courier Corporation

ISBN: 0486794997

Category: Mathematics

Page: 1040

View: 9578

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: Body and Soul

Calculus in Several Dimensions

Author: Kenneth Eriksson,Donald Estep,Claes Johnson

Publisher: Springer Science & Business Media

ISBN: 9783540008910

Category: Mathematics

Page: 426

View: 9517

Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.

Methods of Mathematical Physics, Volume 2

Differential Equations

Author: Richard Courant,D. Hilbert

Publisher: John Wiley & Sons

ISBN: 3527617248

Category: Science

Page: 852

View: 4313

Since the first volume of this work came out in Germany in 1937, this book, together with its first 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 final revision of 1961.

Applied Mathematics Reviews

(Volume 1)

Author: George A Anastassiou

Publisher: World Scientific

ISBN: 9814492884

Category: Mathematics

Page: 624

View: 2969

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

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

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

Author: George Shoobridge Carr

Publisher: Cambridge University Press

ISBN: 1108050689

Category: Mathematics

Page: 718

View: 1114

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.

The Princeton Companion to Applied Mathematics

Author: Nicholas J. Higham

Publisher: Princeton University Press

ISBN: 1400874475

Category: Mathematics

Page: 1016

View: 3683

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

Advanced Techniques in Applied Mathematics

Author: Shaun Bullett,Tom Fearn,Frank Smith

Publisher: World Scientific

ISBN: 1786340240

Category: Mathematics

Page: 204

View: 8879

This book is a guide to advanced techniques used widely in applied mathematical sciences research. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in techniques such as practical analytical methods, finite elements and symmetry methods for differential equations. Advanced Techniques in Applied Mathematics is the first volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas. Contents:Practical Analytical Methods for Partial Differential Equations (Helen J Wilson)Resonances in Wave Scattering (Dmitry V Savin)Modelling — What is it Good For? (Oliver S Kerr)Finite Elements (Matthias Maischak)Introduction to Random Matrix Theory (Igor E Smolyarenko)Symmetry Methods for Differential Equations (Peter A Clarkson) Readership: Researchers, graduate or PhD mathematical-science students who require a reference book that covers advanced techniques used in applied mathematics research.

A Course of Higher Mathematics

Author: V. I. Smirnov

Publisher: Elsevier

ISBN: 1483139379

Category: Mathematics

Page: 652

View: 2874

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.