Approximation And Computation In Science And Engineering

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume. It is addressed to graduate students, research mathematicians, physicists, and engineers. Individual contributions are devoted to topics of approximation theory, functional equations and inequalities, fixed point theory, numerical analysis, theory of wavelets, convex analysis, topology, operator theory, differential operators, fractional integral operators, integro-differential equations, ternary algebras, super and hyper relators, variational analysis, discrete mathematics, cryptography, and a variety of applications in interdisciplinary topics. Several of these domains have a strong connection with both theories and problems of linear and nonlinear optimization. The combination of results from various domains provides the reader with a solid, state-of-the-art interdisciplinary reference to theory and problems. Some of the works provide guidelines for further research and proposals for new directions and open problems with relevant discussions.

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 used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines; - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in the computational and applied sciences.

"This book was written to provide a text for graduate and undergraduate students who took our courses in numerical methods. It incorporates the essential elements of all the numerical methods currently used extensively in the solution of partial differential equations encountered regularly in science and engineering. Because our courses were typically populated by students from varied backgrounds and with diverse interests, we attempted to eliminate jargon or nomenclature that would render the work unintelligible to any student. Moreover, in response to student needs, we incorporated not only classical (and not so classical) finite-difference methods but also finite-element, collocation, and boundary-element procedures. After an introduction to the various numerical schemes, each equation type--parabolic, elliptic, and hyperbolic--is allocated a separate chapter. Within each of these chapters the material is presented by numerical method. Thus one can read the book either by equation-type or numerical approach."--Preface, page [v].

Numerical Methods and Methods of Approximation in Science and Engineering prepares students and other readers for advanced studies involving applied numerical and computational analysis. Focused on building a sound theoretical foundation, it uses a clear and simple approach backed by numerous worked examples to facilitate understanding of numerical methods and their application. Readers will learn to structure a sequence of operations into a program, using the programming language of their choice; this approach leads to a deeper understanding of the methods and their limitations. Features: Provides a strong theoretical foundation for learning and applying numerical methods Takes a generic approach to engineering analysis, rather than using a specific programming language Built around a consistent, understandable model for conducting engineering analysis Prepares students for advanced coursework, and use of tools such as FEA and CFD Presents numerous detailed examples and problems, and a Solutions Manual for instructors

This textbook provides an introduction to the growing interdisciplinary field of computational science. It combines a foundational development of numerical methods with a variety of illustrative applications spread across numerous areas of science and engineering. The intended audience is the undergraduate who has completed introductory coursework in mathematics and computer science. Students gain computational acuity by authoring their own numerical routines and by practicing with numerical methods as they solve computational models. This education encourages students to learn the importance of answering: How expensive is a calculation, how trustworthy is a calculation, and how might we model a problem to apply a desired numerical method? The text is written in two parts. Part I provides a succinct, one-term inauguration into the primary routines on which a further study of computational science rests. The material is organized so that the transition to computational science from coursework in calculus, differential equations, and linear algebra is natural. Beyond the mathematical and computational content of Part I, students gain proficiency with elemental programming constructs and visualization, which are presented in MATLAB syntax. The focus of Part II is modeling, wherein students build computational models, compute solutions, and report their findings. The models purposely intersect numerous areas of science and engineering to demonstrate the pervasive role played by computational science.

Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f

This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.

Scientific Computation has established itself as a stand-alone area of knowledge at the borderline between computer science and applied mathematics. Nonetheless, its interdisciplinary character cannot be denied: its methodologies are increasingly used in a wide variety of branches of science and engineering. A Gentle Introduction to Scientific Computing intends to serve a very broad audience of college students across a variety of disciplines. It aims to expose its readers to some of the basic tools and techniques used in computational science, with a view to helping them understand what happens "behind the scenes" when simple tools such as solving equations, plotting and interpolation are used. To make the book as practical as possible, the authors explore their subject both from a theoretical, mathematical perspective and from an implementation-driven, programming perspective. Features Middle-ground approach between theory and implementation. Suitable reading for a broad range of students in STEM disciplines. Could be used as the primary text for a first course in scientific computing. Introduces mathematics majors, without any prior computer science exposure, to numerical methods. All mathematical knowledge needed beyond Calculus (together with the most widely used Calculus notation and concepts) is introduced in the text to make it self-contained.