Numerical Approximation Methods

This textbook teaches engineering students how to write computer programs (scripts) on the MATLAB platform that solves engineering type problems. By combining a textbook on MATLAB with basic numerical

Based on course notes from over twenty years of teaching engineering and physical sciences at Michigan Technological University, Tomas Co's engineering mathematics textbook is rich with examples, applications and exercises. Professor Co uses analytical approaches to solve smaller problems to provide mathematical insight and understanding, and numerical methods for large and complex problems. The book emphasises applying matrices with strong attention to matrix structure and computational issues such as sparsity and efficiency. Chapters on vector calculus and integral theorems are used to build coordinate-free physical models with special emphasis on orthogonal co-ordinates. Chapters on ODEs and PDEs cover both analytical and numerical approaches. Topics on analytical solutions include similarity transform methods, direct formulas for series solutions, bifurcation analysis, Lagrange–Charpit formulas, shocks/rarefaction and others. Topics on numerical methods include stability analysis,

"Preface This book has been written using notes developed for the course Numerical Methods for Chemical Engineers at Tulane University. The author has written two previous textbooks; one on FORTRAN pr

"The advantage of using the MATLAB software program over other packages is that it contains built-in functions that numerically solve systems of linear equations, systems of ordinary differential equa

The book describes and discusses the numerical methods which are successfully being used for analysing ecological data, using a clear and comprehensive approach. These methods are derived from the fie

Over the last 15 years, the application of innovative steel concepts in the automotive industry has increased steadily. Numerical simulation technology of hot forming of high-strength steel allows eng

Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, a

Rocks and soils can behave as discontinuous materials, both physically and mechanically, and for such discontinuous nature and behaviour there remain challenges in numerical modelling methods and tech

Revised and?updated, this second edition of Walter Gautschi's successful Numerical Analysis?explores?computational methods?for problems arising in the areas of classical analysis, approximation theory

Our presentation of some fundamental domains of celestial mechanics requires no special preliminary knowledge; however, the chosen mathe- matical method is new in so far as the pure two-body motion is

This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011). The cours

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques use

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, creating an exciting interplay between the subjects. This is the first and only book to prove i

This textbook teaches students to create computer codes used to engineer antennas, microwave circuits, and other critical technologies for wireless communications and other applications of electromagn

The new Ninth Edition of Burden and Faires provides a foundation in modern numerical-approximation techniques, explaining how, why, and when the techniques can be expected to work. A wealth of exampl

The first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial c

The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in the

Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to suppo

Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical l

This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-w

High resolution upwind and centered methods are a mature generation of computational techniques. They are applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dyna

Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.

Mathematical Finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Model

"Domain decomposition methods are divide and conquer methods for the parallel and computational solution of partial differential equations of elliptic or parabolic type. They include iterative algorit

Before a student or research scientist can master the idea of computer modeling, the basics of classical numerical methods must be learned. Zalizniak (Krasnoyarsk State U., Russia) reviews the various

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."—Zentrablatt Math ". . .

Mathematical physics equations, like some other problems, often require solving boundary value problems for partial differential equations. Attaining approximate solutions requires developing and exam

A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of financeThe use of mathematical models and numerical techniques is a practice employed by a growi

An elementary first course for students in mathematics and engineeringPractical in approach: examples of code are provided for students to debug, and tasks – with full solutions – are provided at the

Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to suppo

Stochastic approximation is a relatively new technique for studying the properties of an experimental situation; it has important applications in fields such as medicine and engineering. The subject can be treated either largely as a branch of pure mathematics, or else from an empirical and practical angle. In this book, Dr Wasan gives a rigorous mathematical treatment of the subject, drawing together the scattered results of a number of authors. He discusses the conditions under which the method gives a valid approximation to the required solution; methods for optimal choice of parameters to hasten convergence; the comparison of the method with other techniques. The discussion and proofs of theorems are given in enough detail to make them easy to follow, while a number of interesting examples show how the techniques may be applied in many fields.

The author develops the effective-mass theory of excitons in low-dimensional semiconductors and describes numerical methods for calculating the optical absorption including Coulomb interaction, geomet

A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence a

* Good reference text; clusters well with other Birkhauser integral equations & integral methods books (Estrada and Kanwal, Kythe/Puri, Constanda, et al). * Includes many practical applications/te

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweavin

Written from the perspective of a physicist rather than a mathematician, this book/CD-ROM text for advanced undergraduate and graduate students in the physical and engineering sciences focuses on mode

Numerical weather prediction is a problem of mathematical physics. The complex flows in the atmosphere and oceans are believed to be accurately modelled by the Navier-Stokes equations of fluid mechanics together with classical thermodynamics. However, due to the enormous complexity of these equations, meteorologists and oceanographers have constructed approximate models of the dominant, large-scale flows that control the evolution of weather systems and that describe, for example, the dynamics of cyclones and ocean eddies. The simplifications often result in models that are amenable to solution both analytically and numerically. The lectures in these volumes examine and explain why such simplifications to Newton's second law produce accurate, useful models and, just as the meteorologist seeks patterns in the weather, mathematicians seek structure in the governing equations, such as groups of transformations, Hamiltonian structure and stability. This 2002 book and its companion show how

This fresh and original text on quantum mechanics focuses on: the development of numerical methods for obtaining specific results; the presentation of group theory and the systematic use of operators;