Applications of Interval Computations (Applied Optimization)

Book Description

Applications of Interval Computations contains primarily survey articles of actual industrial applications of numerical analysis with automatic result verification and of interval representation of data. Underlying topics include branch and bound algorithms for global optimization, constraint propagation, solution sets of linear systems, hardware and software systems for interval computations, and fuzzy logic. Actual applications described in the book include economic input-output models, quality control in manufacturing design, a computer-assisted proof in quantum mechanics, medical expert systems, and others. A realistic view of interval computations is taken: the articles indicate when and how overestimation and other challenges can be overcome. An introductory chapter explains the content of the papers in terminology accessible to mathematically literate graduate students. The style of the individual, refereed contributions has been made uniform and understandable, and there is an extensive book-wide index. Audience: Valuable to students and researchers interested in automatic result verification.

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Numerical Algorithms with C
Giesela Engeln-Müllges , and Frank Uhlig
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Numerical Recipes in C Example Book: The Art of Scientific Computing

ASIN: 3540605304

Book Description

This book contains computer-ready algorithms for many standard methods of numerical mathematics, describes the principles of the various methods, and offers support in choosing the appropriate method for a given task. Topics given special emphasis include: converging methods for solving nonlinear equations, methods for solving systems of linear equations for many special matrix structures, and the Shepard method for multidimensional interpolation. The CD contains C-programs for almost all the algorithms given in the book and variants of the algorithms.

Nonsmooth/Nonconvex Mechanics: Modeling, Analysis and Numerical Methods (Nonconvex Optimization and Its Applications)

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Nonsmooth/Nonconvex Mechanics: Modeling, Analysis and Numerical Methods (Nonconvex Optimization and Its Applications)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792367863

Book Description

Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity.
The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems.
This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics.
Audience: Faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.

Applied Numerical Modelling for Engineers (Textbook in Electrical and Electronic Engineering, 6)

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An "Engineering" Text Without a Home

Applied Numerical Modelling for Engineers (Textbook in Electrical and Electronic Engineering, 6)
Donard de Cogan , and Anne de Cogan
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0198564384

Book Description

This is a broad ranging introductory text on applied numerical modelling and simulation. It covers many techniques and develops the relevant mathematics in parallel. The material is presented in the context of realistic practical examples. Many of the end-of-chapter exercises may be treated as open-ended projects which can be easily extended. The presentation makes the text easy to assimilate with a progression of concepts chapter by chpater. The more difficult material is assembled towards the end of the book. Each chapter has a list of references to accessible texts as well as journal publications which should provide pointers for research projects. The provision of software code in a range of languages should help the user to make rapid use of the material. This textbook will broaden the understanding of engineers and others using models leading to better and more productive modelling.

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An "Engineering" Text Without a Home.......2001-05-21

This could be a very useful book if it:

1. Had answers to at least selected problems (its usefulness as an independent text is rather curtailed by a junior engineer's ability to check his understanding)

2. More attention to actual engineering details (e.g. p31 bottom states,"There is little point to having a mathematical simulation that is accurate to 100 decimal places if the best display or plotting equipment is only accurate to +- 1%.") First, the rounding should be done at the END of the simulation not IN it if the limitation is in the display; second, 100 decimal places versus +- 1% is a careless confusion of units, not to mention the ambiguity of 1% in a display (to what scale or register length?).

I suppose it might be used as a text for an undergraduate or graduate course somewhere, but more likely it would be purchased by an engineer or scientist interested in modeling, and here the lack of answers is a real deficiency.

The demands of the book are small for a senior level electrical engineering course, and not severe for someone with a decent grounding in discrete and continuous mathematics including orthogonal transforms, linear algebra, calculus of several variables, and an introductory probability course.

Book Description

This book gives an overview of statistical turbulence-modelling with applications to oceanography and limnology. It discusses how these models can be derived from the Navier-Stokes equations, step by step simplifications result in models applicable to numerical simulations for realistic solutions. Results from one-dimensional simulations are shown for various oceanic and limnic water column studies. The integration of these turbulence models in three-dimensioanl models is discussed and some selected results are shown. The two-equation turbulence models prove to be a good compromise between accuracy and economy are published as a FORTRAN source code on the internet in the framework of the General Ocean Turbulence Model (GOTM) - see URL: http.//www.gotm.net. This web site also provides forcing and validation data for several idealized scenarios. The book and the home page enables graduate students and researchers to understand the theory and provides tools for the models.

Geometric Dynamics (MATHEMATICS AND ITS APPLICATIONS Volume 513) (Mathematics and Its Applications)

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Geometric Dynamics (MATHEMATICS AND ITS APPLICATIONS Volume 513) (Mathematics and Its Applications)
C. Udriste
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792364015

Book Description

The theme of this book is the philosophy that any particle flow generates a particle dynamics, in a suitable geometrical framework. It introduces the reader in a gradual and accessible manner to this subject, covering topics that include: geometrical and physical vector fields; field lines; flows; stability of equilibrium points; potential systems and catastrophe geometry; field hypersurfaces; bifurcations; distribution orthogonal to a vector field; extrema with nonholonomic constraints; thermodynamic systems; energies; geometric dynamics induced by a vector field; magnetic fields around piecewise rectilinear electric circuits; geometric magnetic dynamics; and granular materials and their mechanical behavior. Primary audience: First-year graduate students in mathematics, mechanics, physics, engineering, biology, chemistry, economics. Part of the book can be used for undergraduate students. Secondary audience: The book is addressed also to professors and researchers whose work involves mathematics, mechanics, physics, engineering, biology, chemistry, and economics.

Mathematical Models in Applied Mechanics (Oxford Texts in Applied and Engineering Mathematics)

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Mathematical Models in Applied Mechanics (Oxford Texts in Applied and Engineering Mathematics)
A. B. Tayler
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Paperback

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ASIN: 0198515596

Book Description

This textbook demonstrates the power of mathematics in solving practical, scientific, and technical problems through mathematical modelling techniques. It has been designed specifically for final year undergraduate and graduate students, and springs from the author's extensive teaching experience. The text is combined with twenty-one carefully ordered problems taken from real situations, and students are encouraged to develop the skill of constructing their own models of new situations.

Mathematical Models of Fluiddynamics: Modelling, Theory, Basic Numerical Facts - An Introduction

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Mathematical Models of Fluiddynamics: Modelling, Theory, Basic Numerical Facts - An Introduction
Rainer Ansorge
Manufacturer: Wiley-VCH
ProductGroup: Book
Binding: Hardcover

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ASIN: 3527403973

Book Description

This introduction to the field contains a careful selection of topics and examples without sacrificing scientific strictness. The author guides readers through mathematical modelling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behaviour of the dynamics of physical flow. Both students and experts intending to control or predict the behavior of fluid flows by theoretical and computational fluid dynamics will benefit from the combination of all relevant aspects in one handy volume.

The book consists of three main parts:

The design of mathematical models of physical fluid flow;
A theoretical treatment of the equations representing the model, as Navier-Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as well as quantitative insights into the processes of flow events;
The construction and effective use of numerical procedures in order to find quantitative descriptions of concrete physical or technical fluid flow situations.

Book Description

This book provides a concise presentation of the majortechniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems. These systems model many important phenomena in the sciences and engineering. In addition to the usual perturbation procedures, the book gives the details of when and how to correctly apply the method of harmonic balance for both first-order and higher-order calculations. This procedure is rarely given or discussed fully in standard textbooks. The basic philosophy of the book stresses how to initiate and complete the calculation of approximate solutions. This is done by a clear presentation of necessary background materials and by the working out of many examples.

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Practical Asymptotics

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792369203

Book Description

Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their accuracy. It exploits the full potential of the dimensionless representation of these models by considering the special nature of the characteristic dimensionless quantities. It can be argued that these dimensionless quantities mostly assume extreme values, particularly for practical parameter settings. Thus, otherwise complicated models can be rendered far less complex and the numerical effort to solve them is greatly reduced.
In this book the effectiveness of Practical Asymptotics is demonstrated by fifteen papers devoted to widely differing fields of applied science, such as glass-bottle production, semiconductors, surface-tension-driven flows, microwaving joining, heat generation in foodstuff production, chemical-clock reactions, low-Mach-number flows, to name a few.
A strong plea is made for making asymptotics teaching an integral part of any numerics curriculum. Not only will asymptotics reduce the computational effort, it also provides a fuller understanding of the underlying problems.

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