Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

Author: Carl M. Bender,Steven A. Orszag

Publisher: Springer Science & Business Media

ISBN: 9780387989310

Category: Mathematics

Page: 593

View: 2927

This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form. The presentation provides insights that will be useful in approaching new problems.
Release

Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

Author: Carl M. Bender,Steven A. Orszag

Publisher: Springer Science & Business Media

ISBN: 1475730691

Category: Mathematics

Page: 593

View: 7074

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Release

Introduction to Perturbation Methods

Author: Mark H. Holmes

Publisher: Springer Science & Business Media

ISBN: 1461253470

Category: Mathematics

Page: 356

View: 549

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.
Release

Vibration and Coupling of Continuous Systems

Asymptotic Methods

Author: Jacqueline Sanchez Hubert

Publisher: Springer Science & Business Media

ISBN: 364273782X

Category: Science

Page: 421

View: 4447

Real problems concerning vibrations of elastic structures are among the most fascinating topics in mathematical and physical research as well as in applications in the engineering sciences. This book addresses the student familiar with the elementary mechanics of continua along with specialists. The authors start with an outline of the basic methods and lead the reader to research problems of current interest. An exposition of the method of spectra, asymptotic methods and perturbation is followed by applications to linear problems where elastic structures are coupled to fluids in bounded and unbounded domains, to radiation of immersed bodies, to local vibrations, to thermal effects and many more.
Release

Mathematical Methods of Classical Mechanics

Author: V.I. Arnol'd

Publisher: Springer Science & Business Media

ISBN: 1475720637

Category: Mathematics

Page: 520

View: 9484

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Release

Perturbation Methods for Engineers and Scientists

Author: Alan W. Bush

Publisher: CRC Press

ISBN: 9780849386145

Category: Mathematics

Page: 320

View: 5096

The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution, for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions.
Release

Methods and Applications of Singular Perturbations

Boundary Layers and Multiple Timescale Dynamics

Author: Ferdinand Verhulst

Publisher: Springer Science & Business Media

ISBN: 0387283137

Category: Mathematics

Page: 328

View: 871

Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Release

Numerical Partial Differential Equations

Conservation Laws and Elliptic Equations

Author: J.W. Thomas

Publisher: Springer Science & Business Media

ISBN: N.A

Category: Mathematics

Page: 556

View: 9918

Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation. Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text, allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient. This is the second volume of a two-part book.
Release

Singular Perturbation in the Physical Sciences

Author: John C. Neu

Publisher: American Mathematical Soc.

ISBN: 1470425556

Category: Asymptotic expansions

Page: 336

View: 7193

This book is the testimony of a physical scientist whose language is singular perturbation analysis. Classical mathematical notions, such as matched asymptotic expansions, projections of large dynamical systems onto small center manifolds, and modulation theory of oscillations based either on multiple scales or on averaging/transformation theory, are included. The narratives of these topics are carried by physical examples: Let's say that the moment when we "see" how a mathematical pattern fits a physical problem is like "hitting the ball." Yes, we want to hit the ball. But a powerful stroke includes the follow-through. One intention of this book is to discern in the structure and/or solutions of the equations their geometric and physical content. Through analysis, we come to sense directly the shape and feel of phenomena. The book is structured into a main text of fundamental ideas and a subtext of problems with detailed solutions. Roughly speaking, the former is the initial contact between mathematics and phenomena, and the latter emphasizes geometric and physical insight. It will be useful for mathematicians and physicists learning singular perturbation analysis of ODE and PDE boundary value problems as well as the full range of related examples and problems. Prerequisites are basic skills in analysis and a good junior/senior level undergraduate course of mathematical physics.
Release

The Optimal Homotopy Asymptotic Method

Engineering Applications

Author: Vasile Marinca,Nicolae Herisanu

Publisher: Springer

ISBN: 3319153749

Category: Technology & Engineering

Page: 465

View: 7798

This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Release

Advanced Mathematical Methods

Author: Adam Ostaszewski

Publisher: Cambridge University Press

ISBN: 9780521289641

Category: Mathematics

Page: 545

View: 3750

Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a cookbook approach, giving concrete and geometric explanations, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.
Release

Partial Differential Equations

Author: Harold Levine

Publisher: American Mathematical Soc.

ISBN: 9780821888100

Category:

Page: N.A

View: 3498

Release

Mathematical Methods in Science and Engineering

Author: Selçuk S. Bayin

Publisher: John Wiley & Sons

ISBN: 111942545X

Category: Education

Page: 864

View: 1352

A Practical, Interdisciplinary Guide to Advanced Mathematical Methods for Scientists and Engineers Mathematical Methods in Science and Engineering, Second Edition, provides students and scientists with a detailed mathematical reference for advanced analysis and computational methodologies. Making complex tools accessible, this invaluable resource is designed for both the classroom and the practitioners; the modular format allows flexibility of coverage, while the text itself is formatted to provide essential information without detailed study. Highly practical discussion focuses on the “how-to” aspect of each topic presented, yet provides enough theory to reinforce central processes and mechanisms. Recent growing interest in interdisciplinary studies has brought scientists together from physics, chemistry, biology, economy, and finance to expand advanced mathematical methods beyond theoretical physics. This book is written with this multi-disciplinary group in mind, emphasizing practical solutions for diverse applications and the development of a new interdisciplinary science. Revised and expanded for increased utility, this new Second Edition: Includes over 60 new sections and subsections more useful to a multidisciplinary audience Contains new examples, new figures, new problems, and more fluid arguments Presents a detailed discussion on the most frequently encountered special functions in science and engineering Provides a systematic treatment of special functions in terms of the Sturm-Liouville theory Approaches second-order differential equations of physics and engineering from the factorization perspective Includes extensive discussion of coordinate transformations and tensors, complex analysis, fractional calculus, integral transforms, Green's functions, path integrals, and more Extensively reworked to provide increased utility to a broader audience, this book provides a self-contained three-semester course for curriculum, self-study, or reference. As more scientific disciplines begin to lean more heavily on advanced mathematical analysis, this resource will prove to be an invaluable addition to any bookshelf.
Release

Mathematical Methods and Models in Composites

Author: Vladislav Mantič

Publisher: World Scientific

ISBN: 178326411X

Category: Technology & Engineering

Page: 520

View: 657

This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics covered include: scaling and homogenization procedures in composite structures, thin plate and wave solutions in anisotropic materials, laminated structures, instabilities, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing. The results presented are useful in the design, fabrication, testing, and industrial applications of composite components and structures. The book is written by well-known experts in different areas of applied mathematics, physics, and composite engineering and is an essential source of reference for graduate and doctoral students, as well as researchers. It is also suitable for non-experts in composites who wish to have an overview of both the mathematical methods and models used in this area and the related open problems requiring further research. Contents:Asymptotic Homogenization Method and Micromechanical Models for Composite Materials and Thin-Walled Composite Structures (Alexander L Kalamkarov)Scaling and Homogenization in Spatially Random Composites (Martin Ostoja-Starzewski and Shivakumar I Ranganathan)Stroh-Like Formalism for General Thin Laminated Plates and Its Applications (Chyanbin Hwu)Classical, Refined, Zig-Zag and Layer-Wise Models for Laminated Structures (Erasmo Carrera and Maria Cinefra)Bifurcation of Elastic Multilayers (Davide Bigoni, Massimiliano Gei and Sara Roccabianca)Propagation of Rayleigh Waves in Anisotropic Media and an Inverse Problem in the Characterization of Initial Stress (Kazumi Tanuma and Chi-Sing Man)Advanced Model Order Reduction for Simulating Composite-Forming Processes (Francisco Chinesta, Adrien Leygue and Arnaud Poitou)Modeling Fracture and Complex Crack Networks in Laminated Composites (Carlos G Dávila, Cheryl A Rose and Endel V Iarve)Delamination and Adhesive Contact Models and Their Mathematical Analysis and Numerical Treatment (Tomáš Roubíček, Martin Kružík and Jan Zeman)Crack Nucleation at Stress Concentration Points in Composite Materials — Application to Crack Deflection by an Interface (Dominique Leguillon and Eric Martin)Singular Elastic Solutions in Anisotropic Multimaterial Corners. Applications to Composites (Vladislav Mantič, Alberto Barroso and Federico París) Readership: Graduate students and researchers in composite engineering. Key Features:Competing titles are much more specialized - providing in-depth treatments but of only one area of research related to compositesContributing authors are worldwide prominent experts in the very different areas of applied mathematics, physics and engineering related to compositesEspecially suitable for young researchers showing a great variety of different approaches available today to model composites manufacturing, behavior and damage mechanisms. This unique volume allows them to find different approaches to related problems, to realize possible connections between them, and to finally take advantage of the already existing in-depth results related to composites in sometimes apparently very distant scientific fieldsKeywords:Composite Material;Laminate;Plate;Thin-Walled;Elastic Multilayer;Fiber-Reinforced;Homogenization;Anisotropic Material;Stroh Formalism;Nonlinear Elasticity;Wave;Inverse Problem;Fabrication;Manufacturing;Damage Mechanism;Crack;Delamination;Adhesive Contact;Fracture Criteria;Instability;Stress Singularity;X-FEM;SGBEM;Zig-Zag;Matched Asymptotic Expansion
Release

Applied Asymptotic Analysis

Author: Peter David Miller

Publisher: American Mathematical Soc.

ISBN: 0821840789

Category: Mathematics

Page: 467

View: 1507

"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects."--BOOK JACKET.
Release

Asymptotic Expansions of Integrals

Author: Norman Bleistein,Richard A. Handelsman

Publisher: Courier Corporation

ISBN: 0486650820

Category: Mathematics

Page: 425

View: 9468

Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.
Release

Mathematical Methods for Scientists and Engineers

Linear and Nonlinear Systems

Author: Peter B. Kahn

Publisher: Courier Corporation

ISBN: 0486435164

Category: Mathematics

Page: 469

View: 7034

Appropriate for advanced undergraduate and graduate students in a variety of scientific and engineering fields, this text introduces linear and nonlinear problems and their associated models. The first part covers linear systems, emphasizing perturbation or approximation techniques and asymptotic methods. The second part comprises nonlinear problems, including weakly nonlinear oscillatory systems and nonlinear difference equations. The two parts, both of which include exercises, merge smoothly, and many of the nonlinear techniques arise from the study of the linear systems. 1990 edition. 70 figures. 4 tables. Appendix. Index.
Release

A Guided Tour of Mathematical Methods for the Physical Sciences

Author: Roel Snieder,Kasper van Wijk,Matthew M. Haney

Publisher: Cambridge University Press

ISBN: 1107084962

Category: Mathematics

Page: 584

View: 385

This completely revised edition provides a tour of the mathematical knowledge and techniques needed by students across the physical sciences. There are new chapters on probability and statistics and on inverse problems. It serves as a stand-alone text or as a source of exercises and examples to complement other textbooks.
Release