Search results for: introduction-to-perturbation-methods-20-texts-in-applied-mathematics

Introduction to Perturbation Methods

Author : Mark H. Holmes
File Size : 56.68 MB
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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. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.

Introduction to Perturbation Methods

Author : Mark H. Holmes
File Size : 39.4 MB
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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. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.

Introduction to the Foundations of Applied Mathematics

Author : Mark H. Holmes
File Size : 82.51 MB
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The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change. What does not change as quickly is the approach used to derive the relevant mathematical models, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application. This does not mean applications are not considered, they are, and connections with experiment are a staple of this book. The book, as well as the individual chapters, is written in such a way that the material becomes more sophisticated as you progress. This provides some flexibility in how the book is used, allowing consideration for the breadth and depth of the material covered. Moreover, there are a wide spectrum of exercises and detailed illustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful. The material, and topics, have been updated to include recent developments in mathematical modeling. The exercises have also been expanded to include these changes, as well as enhance those from the first edition. Review of first edition: "The goal of this book is to introduce the mathematical tools needed for analyzing and deriving mathematical models. ... Holmes is able to integrate the theory with application in a very nice way providing an excellent book on applied mathematics. ... One of the best features of the book is the abundant number of exercises found at the end of each chapter. ... I think this is a great book, and I recommend it for scholarly purposes by students, teachers, and researchers." Joe Latulippe, The Mathematical Association of America, December, 2009

Analyzing Multiscale Phenomena Using Singular Perturbation Methods

Author : Jane Cronin
File Size : 83.50 MB
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To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.

Methods and Applications of Singular Perturbations

Author : Ferdinand Verhulst
File Size : 59.95 MB
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Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Equadiff 99

Author : Bernold Fiedler
File Size : 41.70 MB
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This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences. Contents: Volume 1: Celestial MechanicsHomoclinic TangenciesSingular PerturbationsStochastic SystemsSymmetryTopological Methods and Conley IndexDelay EquationsGeometric DynamicsHyperbolic Conservation LawsHyperbolic Wave EquationsHysteresisLarge DomainsLattice Dynamical SystemsMicrostructureNonlinear Functional AnalysisVariational MethodsViscosity SolutionsGlobal Attractors and LimitsNonautonomous AttractorsOrder-Preserving Dynamical SystemsQualitative Theory of Parabolic EquationsStability of Fronts and Pulses Volume 2: Computer Algebra ToolsControl and OptimizationDynamics and AlgorithmsExponentially Small PhenomenaGeometric IntegratorsNumerical Ergodic TheoryNumerics of DynamicsChemistryChemotaxis, Cross-Diffusion, and Blow-UpIndustrial ApplicationsMechanicsModels in Biology, Medicine, and PhysiologyMolecular ModellingPatternsSemiconductorsSteady Water WavesUnsteady Hydrodynamic WavesDelay EquationsNumericsOrdinary Differential EquationsPartial Differential Equations Keywords:Dynamical Systems;Infinite Dimensions;Global Attractors;Stability;Computational Aspects;Celestial Mechanics;Homoclinic Tangencies;Singular Perturbations;Stochastic Systems;Conley Index;Delay Equations;Hyperbolic Wave Equations;Viscosity Solutions;Control and Optimization;Geometric Integrators;Numerical Ergodic Theory;Molecular Modelling;Patterns;Steady Water Waves

International Conference on Differential Equations Berlin Germany 1 7 August 1999

Author : Bernold Fiedler
File Size : 57.59 MB
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This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences

Ordinary Differential Equations and Linear Algebra A Systems Approach

Author : Todd Kapitula
File Size : 74.17 MB
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Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system.÷Ordinary Differential Equations and Linear Algebra: A Systems Approach÷systematically develops the linear algebra needed to solve systems of ODEs and includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters). It emphasizes mathematical modeling and contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modeling of a system, the solution of the model, and the resulting physical description.÷

Theory of Differential Equations in Engineering and Mechanics

Author : Kam Tim Chau
File Size : 78.22 MB
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This gives comprehensive coverage of the essential differential equations students they are likely to encounter in solving engineering and mechanics problems across the field -- alongside a more advance volume on applications. This first volume covers a very broad range of theories related to solving differential equations, mathematical preliminaries, ODE (n-th order and system of 1st order ODE in matrix form), PDE (1st order, 2nd, and higher order including wave, diffusion, potential, biharmonic equations and more). Plus more advanced topics such as Green’s function method, integral and integro-differential equations, asymptotic expansion and perturbation, calculus of variations, variational and related methods, finite difference and numerical methods. All readers who are concerned with and interested in engineering mechanics problems, climate change, and nanotechnology will find topics covered in these books providing valuable information and mathematics background for their multi-disciplinary research and education.

Asymptotics of Elliptic and Parabolic PDEs

Author : David Holcman
File Size : 69.45 MB
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This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.