This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.

* Exciting exposition integrates history, philosophy, and mathematics * Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development * Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation

With the advent of a host of new materials ranging from shape memory alloys to biomaterials to multiphase alloys, acquiring the capacity to model inelastic behavior and to choose the right model in a commercial analysis software has become a pressing need for practicing engineers. Even with the traditional materials, there is a continued emphasis on optimizing and extending their full range of capability in the applications. This textbook builds upon the existing knowledge of elasticity and thermodynamics, and allows the reader to gain confidence in extending one's skills in understanding and analyzing problems in inelasticity. By reading this textbook and working through the assigned exercises, the reader will gain a level of comfort and competence in developing and using inelasticity models. Thus, the book serves as a valuable book for practicing engineers and senior-level undergraduate/graduate-level students in the mechanical, civil, aeronautical, metallurgical and other disciplines.The book is written in three parts. Part 1 is primarily focused on lumped parameter models and simple structural elements such as trusses and beams. This is suitable for an advanced undergraduate class with just a strength of materials background. Part II is focused on small deformation multi-dimensional inelasticity and is suitable for a beginning graduate class. Sufficient material is included on how to numerically implement an inelastic model and solve either using a simple stress function type of approach or using commercial software. Case studies are included as examples. There is also an extensive discussion of thermodynamics in the context of small deformations. Part III focuses on more advanced situations such as finite deformation inelasticity, thermodynamical ideas and crystal plasticity. More advanced case studies are included in this part.• This textbook takes a new, task- or scenario-based approach to teaching and learning inelasticity. The book is written in an active learning style that appeals to engineers and students who wish to design or analyze structures and components that are subject to inelasticity.• The book incorporates thermodynamical considerations into the modeling right from an early stage. Extensive discussions are provided throughout the book on the thermodynamical underpinnings of the models.• This textbook is the first to make extensive use of MATLAB to implement many inelasticity models. It includes the use of concepts such as Airy stress functions to solve plane problems for inelastic materials. The MATLAB codes are listed in the appendix for one to modify with their own models and requirements.• Step-by-step procedures for formulations and calculations are provided for the reader to readily adapt to the inelastic problems that he or she attempts to solve.• A large number of problems, exercises and projects for one to teach or learn from are included. These can be assigned as homework, in-class exercises or projects.• The book is written in a modular fashion, which provides adequate flexibility for adaptation in classes that cater to different audiences such as senior-level students, graduate students, research scholars, and practicing engineers.

Mathematics of Computing -- Numerical Analysis.

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Contents: 1. Power reactors.--2. Research and test reactors.--3. Fuels and materials facilities.--4. Environmental and siting.--5. Materials and plant protection.--6. Products.--7. Transportation.--8. Occupational health.--9. Antitrust reviews.--10. General.

Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.

Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations.Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, and the lifting scheme for wavelet transform computation. The text serves as a supplement to existing books on structured linear algebra problems, rational approximation and orthogonal polynomials.Features of this book:• provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials• requires an elementary knowledge of calculus and linear algebra yet introduces advanced topics.The book will be of interest to applied mathematicians and engineers and to students and researchers.