The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.

Unlike books currently on the market, this book attempts to satisfy two goals: combine circuits and electronics into a single, unified treatment, and establish a strong connection with the contemporary world of digital systems. It will introduce a new way of looking not only at the treatment of circuits, but also at the treatment of introductory coursework in engineering in general.
Using the concept of ''abstraction, '' the book attempts to form a bridge between the world of physics and the world of large computer systems. In particular, it attempts to unify electrical engineering and computer science as the art of creating and exploiting successive abstractions to manage the complexity of building useful electrical systems. Computer systems are simply one type of electrical systems.
+Balances circuits theory with practical digital electronics applications.
+Illustrates concepts with real devices.
+Supports the popular circuits and electronics course on the MIT OpenCourse Ware from which professionals worldwide study this new approach.
+Written by two educators well known for their innovative teaching and research and their collaboration with industry.
+Focuses on contemporary MOS technology.

The second edition of "A Course in Real Analysis" provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent at balancing theory and applications with a wealth of examples and exercises. The authors take a progressive approach of skill building to help students learn to absorb the abstract. Real world applications, probability theory, harmonic analysis, and dynamical systems theory are included, offering considerable flexibility in the choice of material to cover in the classroom. The accessible exposition not only helps students master real analysis, but also makes the book useful as a reference.
* New chapter on Hausdorff Measure and Fractals
* Key concepts and learning objectives give studentsa deeper understanding of the material to enhance learning
* More than 200 examples (not including parts) are used to illustrate definitions and results
* Over 1300 exercises (not including parts) are provided to promote understanding
* Each chapter begins with a brief biography of a famous mathematician"

Now inits 7th edition, "Mathematical Methods for Physicists" continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining thekey features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus will help students succeed throughout their academic careers and well into their professions. Some notable enhancements include more refined and focused content in important topics, improved organization, updated notations, extensive explanations and intuitive exercise sets, a wider range of problem solutions, improvement in the placement, and a wider range of difficulty of exercises.
Revised and updated version of the leading text in mathematical physicsFocuses on problem-solving skills and active learning, offering numerous chapter problemsClearly identified definitions, theorems, and proofs promote clarity and understanding

New to this edition: Improved modular chaptersNew up-to-date examplesMore intuitive explanations"

This series is designed to meet the needs of students and lecturers of the National Certificate Vocational. Features for the student include: Easy-to-understand language; Real-life examples; A key word feature for important subject terms; A dictionary feature for difficult words; A reflect-on-how-you-learn feature to explore personal learning styles; Workplace-oriented activities; and Chapter summaries that are useful for exam revision.

"Engineering Materials 2" is one of the leading self-contained texts for more advanced students of materials science and mechanical engineering. The book provides a concise introduction to the microstructures and processing of materials and shows how these are related to the properties required in engineering design. As with previous editions, each chapter is designed to provide the content of one 50-minute lecture. The fourth edition has been updated to include new case studies, more worked examples, links to relevant websites and video clips. Other changes include an increased emphasis on the relationship between structure, processing and properties, and integration of the popular tutorial on phase diagrams into the main text.

"Engineering Materials 2, Fourth Edition" is perfect as a stand-alone text for an advanced course in engineering materials or a second text with its companion "Engineering Materials 1: An Introduction to Properties, Applications, and Design, Fourth Edition" in a two-semester course or sequence.
Many new or revised applications-based case studies and examplesTreatment of phase diagrams integrated within the main textIncreased emphasis on the relationship between structure, processing and properties, in both conventional and innovative materialsFrequent worked examples - to consolidate, develop, and challengeMany new photographs and links to Google Earth, websites, and video clipsAccompanying companion site with access to instructors resources, including a suite of interactive materials science tutorials, a solutions manual, and an image bank of figures from the book"

Gindis introduces AutoCAD with step-by-step instructions, stripping away complexities to begin working in AutoCAD immediately. All concepts are explained first in theory, and then shown in practice, helping the reader understand "what "it is they are doing and why before they do it.

The book contains supporting graphics (screen shots) and a summary with a self-test section at the end of each chapter. Also included are drawing examples and exercises, and two running projects that the reader works on as they progresses through the chaptersExplains the why and how of AutoCAD commands: all concepts are explained first in theory andthencovered in step-by-step detailExtensive use of screen shots, chapter summaries, and aself-test section at the end of each chapter Includesdrawing examples and exercises, and two running projects that the reader works on as he/she progresses through the chaptersEach chapter features a "Spotlight On..." section, highlighting theuse of AutoCAD in various industries Fully updated for AutoCAD 2010 release, including introduction of the ribbon menu structurein chapter 1Strips away complexities, both real and perceived, and reduces AutoCAD to easy-to-understand basic concepts; using the author's extensive multi-industry knowledge of what is widely used in practice, the material is presented by immediately immersing the reader in practical, critically essential knowledge
Strips away complexities, both real and perceived, and reduces AutoCAD to easy-to-understand basic concepts; using the author's extensive multi-industry knowledge of what is widely used in practice, the material is presented by immediately immersing the reader in practical, critically essential knowledgeExplains the why and how of AutoCAD commands: all concepts are explained first in theory andthencovered in step-by-step detailExtensive use of screen shots, chapter summaries, and aself-test section at the end of each chapter Includesdrawing examples and exercises, and two running projects that the reader works on as he/she progresses through the chaptersEach chapter features a "Spotlight On..." section, highlighting theuse of AutoCAD in various industries Fully updated for AutoCAD 2010 release, including introduction of the ribbon menu structurein chapter 1"

"A Concrete Approach to Abstract Algebra"begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students.The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus. The final four chapters presentthe more theoretical material needed for graduate study.

Ancillary list: * Online ISM- http: //textbooks.elsevier.com/web/manuals.aspx?isbn=9780123749413 * Online SSM- http: //www.elsevierdirect.com/product.jsp?isbn=9780123749413 * Ebook- http: //www.elsevierdirect.com/product.jsp?isbn=9780123749413
Presents a more natural 'rings first' approachto effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebraBridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices

"

Materials are the stuff of design. From the very beginning of human history, materials have been taken from the natural world and shaped, modified, and adapted for everything from primitive tools to modern electronics. This renowned book by noted materials engineering author Mike Ashby and Industrial designer, Kara Johnson, explores the role of materials and materials processing in product design, with a particular emphasis on creating both desired aesthetics and functionality. The new edition will feature even more of the highly useful 'materials profiles', that give critical design, processing, performance and applications criteria for each material in question. The reader will find information ranging from the generic and commercial names of each material, its physical and mechanical properties, its chemical properties, its common uses, how it is typically made and processed, and even its average price. And with improved photographs and drawings, the reader will be taken even more closely to the way real design is done by real designers, selecting the optimum materials for a successful product. This is the best guide ever published on the on the role of materials, past and present, in product development, by noted materials authority Mike Ashby and professional designer Kara Johnson - now with even better photos and drawings on the Design Process. It includes a significant new section on the use of re-cycled materials in products, and the importance of sustainable design for manufactured goods and services. There are enhanced materials profiles, with addition of new materials types like nanomaterials, advanced plastics and bio-based materials.

The Finite Element Method (FEM) has become an indispensable technology for the modelling and simulation of engineering systems. Written for engineers and students alike, the aim of the book is to provide the necessary theories and techniques of the FEM for readers to be able to use a commercial FEM package to solve primarily linear problems in mechanical and civil engineering with the main focus on structural mechanics and heat transfer.
Fundamental theories are introduced in a straightforward way, and state-of-the-art techniques for designing and analyzing engineering systems, including microstructural systems are explained in detail. Case studies are used to demonstrate these theories, methods, techniques and practical applications, and numerous diagrams and tables are used throughout.
The case studies and examples use the commercial software package ABAQUS, but the techniques explained are equally applicable for readers using other applications including NASTRAN, ANSYS, MARC, etc.
Full sets of PowerPoint slides developed by the authors for their course on FEM are available as a free download from a companion website.
* A practical and accessible guide to this complex, yet important subject
* Covers modeling techniques that predict how components will operate and tolerate loads, stresses and strains in reality
* Full set of PowerPoint presentation slides which illustrate and support the book are available on a companion website.

Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.

The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers.

The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functions
of the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions.

In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible.

The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.

This is a student solutions manual for Elementary Number Theory with Applications 1st edition by Thomas Koshy (2002). Note that the textbook itself is not included in this purchase. From the back cover of the textbook: Modern technology has brought a new dimension to the power of number theory: constant practical use. Once considered the purest of pure mathematics, number theory has become an essential tool in the rapid development of technology in a number of areas, including art, coding theory, cryptology, and computer science. The range of fascinating applications confirms the boundlessness of human ingenuity and creativity. Elementary Number Theory captures the author's fascination for the subject: its beauty, elegance, and historical development, and the opportunities number theory provides for experimentation, exploration, and, of course, its marvelous applications.

/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight into the underlying stability and accuracy properties of computational algorithms for PDEs was deepened by building upon recent progress in mathematical analysis and in the theory of PDEs. To embark on a comprehensive review of the field of numerical analysis of partial differential equations within a single volume of this journal would have been an impossible task. Indeed, the 16 contributions included here, by some of the foremost world authorities in the subject, represent only a small sample of the major developments. We hope that these articles will, nevertheless, provide the reader with a stimulating glimpse into this diverse, exciting and important field. The opening paper by Thomee reviews the history of numerical analysis of PDEs, starting with the 1928 paper by Courant, Friedrichs and Lewy on the solution of problems of mathematical physics by means of finite differences. This excellent survey takes the reader through the development of finite differences for elliptic problems from the 1930s, and the intense study of finite differences for general initial value problems during the 1950s and 1960s. The formulation of the concept of stability is explored in the Lax equivalence theorem and the Kreiss matrix lemmas. Reference is made to the introduction of the finite element method by structural engineers, and a description is given of the subsequent development and mathematical analysis of the finite element method with piecewise polynomial approximating functions. The penultimate section of Thomee's survey deals with `other classes of approximation methods', and this covers methods such as collocation methods, spectral methods, finite volume methods and boundary integral methods. The final section is devoted to numerical linear algebra for elliptic problems. The next three papers, by Bialecki and Fairweather, Hesthaven and Gottlieb and Dahmen, describe, respectively, spline collocation methods, spectral methods and wavelet methods. The work by Bialecki and Fairweather is a comprehensive overview of orthogonal spline collocation from its first appearance to the latest mathematical developments and applications. The emphasis throughout is on problems in two space dimensions. The paper by Hesthaven and Gottlieb presents a review of Fourier and Chebyshev pseudospectral methods for the solution of hyperbolic PDEs. Particular emphasis is placed on the treatment of boundaries, stability of time discretisations, treatment of non-smooth solutions and multidomain techniques. The paper gives a clear view of the advances that have been made over the last decade in solving hyperbolic problems by means of spectral methods, but it shows that many critical issues remain open. The paper by Dahmen reviews the recent rapid growth in the use of wavelet methods for PDEs. The author focuses on the use of adaptivity, where significant successes have recently been achieved. He describes the potential weaknesses of wavelet methods as well as the perceived strengths, thus giving a balanced view that should encourage the study of wavelet methods. Aspects of finite element methods and adaptivity are dealt with in the three papers by Cockburn, Rannacher and Suri. The paper by Cockburn is concerned with the development and analysis of discontinuous Galerkin (DG) finite element methods for hyperbolic problems. It reviews the key properties of DG methods for nonlinear hyperbolic conservation laws from a novel viewpoint that stems from the observation that hyperbolic conservation laws are normally arrived at via model reduction, by elimination of dissipation terms. Rannacher's paper is a first-rate survey of duality-based a posteriori error estimation and mesh adaptivity for Galerkin finite element approximations of PDEs. The approach is illustrated for simple examples of linear and nonlinear PDEs, including also an optimal control problem. Several open questions are identified such as the efficient determination of the dual solution, especially in the presence of oscillatory solutions. The paper by Suri is a lucid overview of the relative merits of the hp and p versions of the finite element method over the h version. The work is presented in a non-technical manner by focusing on a class of problems concerned with linear elasticity posed on thin domains. This type of problem is of considerable practical interest and it generates a number of significant theoretical problems. Iterative methods and multigrid techniques are reviewed in a paper by Silvester, Elman, Kay and Wathen, and in three papers by Stuben, Wesseling and Oosterlee and Xu. The paper by Silvester et al. outlines a new class of robust and efficient methods for solving linear algebraic systems that arise in the linearisation and operator splitting of the Navier-Stokes equations. A general preconditioning strategy is described that uses a multigrid V-cycle for the scalar convection-diffusion operator and a multigrid V-cycle for a pressure Poisson operator. This two-stage approach gives rise to a solver that is robust with respect to time-step-variation and for which the convergence rate is independent of the grid. The paper by Stuben gives a detailed overview of algebraic multigrid. This is a hierarchical and matrix-based approach to the solution of large, sparse, unstructured linear systems of equations. It may be applied to yield efficient solvers for elliptic PDEs discretised on unstructured grids. The author shows why this is likely to be an active and exciting area of research for several years in the new millennium. The paper by Wesseling and Oosterlee reviews geometric multigrid methods, with emphasis on applications in computational fluid dynamics (CFD). The paper is not an introduction to multigrid: it is more appropriately described as a refresher paper for practitioners who have some basic knowledge of multigrid methods and CFD. The authors point out that textbook multigrid efficiency cannot yet be achieved for all CFD problems and that the demands of engineering applications are focusing research in interesting new directions. Semi-coarsening, adaptivity and generalisation to unstructured grids are becoming more important. The paper by Xu presents an overview of methods for solving linear algebraic systems based on subspace corrections. The method is motivated by a discussion of the local behaviour of high-frequency components in the solution of an elliptic problem. Of novel interest is the demonstration that the method of subspace corrections is closely related to von Neumann's method of alternating projections. This raises the question as to whether certain error estimates for alternating directions that are available in the literature may be used to derive convergence estimates for multigrid and/or domain decomposition methods. Moving finite element methods and moving mesh methods are presented, respectively, in the papers by Baines and Huang and Russell. The paper by Baines reviews recent advances in Galerkin and least-squares methods for solving first- and second-order PDEs with moving nodes in multidimensions. The methods use unstructured meshes and they minimise the norm of the residual of the PDE over both the computed solution and the nodal positions. The relationship between the moving finite element method and L2 least-squares methods is discussed. The paper also describes moving finite volume and discrete l2 least-squares methods. Huang and Russell review a class of moving mesh algorithms based upon a moving mesh partial differential equation (MMPDE). The authors are leading players in this research area, and the paper is largely a review of their own work in developing viable MMPDEs and efficient solution strategies. The remaining three papers in this special issue are by Budd and Piggott, Ewing and Wang and van der Houwen and Sommeijer. The paper by Budd and Piggott on geometric integration is a survey of adaptive methods and scaling invariance for discretisations of ordinary and partial differential equations. The authors have succeeded in presenting a readable account of material that combines abstract concepts and practical scientific computing. Geometric integration is a new and rapidly growing area which deals with the derivation of numerical methods for differential equations that incorporate qualitative information in their structure. Qualitative features that may be present in PDEs might include symmetries, asymptotics, invariants or orderings and the objective is to take these properties into account in deriving discretisations. The paper by Ewing and Wang gives a brief summary of numerical methods for advection-dominated PDEs. Models arising in porous medium fluid flow are presented to motivate the study of the advection-dominated flows. The numerical methods reviewed are applicable not only to porous medium flow problems but second-order PDEs with dominant hyperbolic behaviour in general. The paper by van der Houwen and Sommeijer deals with approximate factorisation for time-dependent PDEs. The paper begins with some historical notes and it proceeds to present various approximate factorisation techniques. The objective is to show that the linear system arising from linearisation and discretisation of the PDE may be solved more efficiently if the coefficient matrix is replaced by an approximate factorisation based on splitting. The paper presents a number of new stability results obtained by the group at CWI Amsterdam for the resulting time integration methods.

Linear Algebra: An Introduction Using MAPLE is a text for a first undergraduate course in linear algebra. All students majoring in mathematics, computer science, engineering, physics, chemistry, economics, statistics, actuarial mathematics and other such fields of study will benefit from this text. The presentation is matrix-based and covers the standard topics for a first course recommended by the Linear Algebra Curriculum Study Group. The aim of the book is to make linear algebra accessible to all college majors through a focused presentation of the material, enriched by interactive learning and teaching with MAPLE. Development of analytical and computational skills is emphasized throughout Worked examples provide step-by-step methods for solving basic problems using Maple The subject's rich pertinence to problem solving across disciplines is illustrated with applications in engineering, the natural sciences, computer animation, and statistics

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This volume contains contributions in the area of differential equations and integral equations. Many numerical methods have arisen in response to the need to solve "real-life" problems in applied mathematics, in particular problems that do not have a closed-form solution. Contributions on both initial-value problems and boundary-value problems in ordinary differential equations appear in this volume. Numerical methods for initial-value problems in ordinary differential equations fall naturally into two classes: those which use one starting value at each step (one-step methods) and those which are based on several values of the solution (multistep methods).
John Butcher has supplied an expert's perspective of the development of numerical methods for ordinary differential equations in the 20th century.
Rob Corless and Lawrence Shampine talk about established technology, namely software for initial-value problems using Runge-Kutta and Rosenbrock methods, with interpolants to fill in the solution between mesh-points, but the 'slant' is new - based on the question, "How should such software integrate into the current generation of Problem Solving Environments?"
Natalia Borovykh and Marc Spijker study the problem of establishing upper bounds for the norm of the nth power of square matrices.
The dynamical system viewpoint has been of great benefit to ODE theory and numerical methods. Related is the study of chaotic behaviour.
Willy Govaerts discusses the numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamicalsystems.
Arieh Iserles and Antonella Zanna survey the construction of Runge-Kutta methods which preserve algebraic invariant functions.
Valeria Antohe and Ian Gladwell present numerical experiments on solving a Hamiltonian system of Henon and Heiles with a symplectic and a nonsymplectic method with a variety of precisions and initial conditions.
Stiff differential equations first became recognized as special during the 1950s. In 1963 two seminal publications laid to the foundations for later development: Dahlquist's paper on A-stable multistep methods and Butcher's first paper on implicit Runge-Kutta methods.
Ernst Hairer and Gerhard Wanner deliver a survey which retraces the discovery of the order stars as well as the principal achievements obtained by that theory.
Guido Vanden Berghe, Hans De Meyer, Marnix Van Daele and Tanja Van Hecke construct exponentially fitted Runge-Kutta methods with s stages.
Differential-algebraic equations arise in control, in modelling of mechanical systems and in many other fields.
Jeff Cash describes a fairly recent class of formulae for the numerical solution of initial-value problems for stiff and differential-algebraic systems.
Shengtai Li and Linda Petzold describe methods and software for sensitivity analysis of solutions of DAE initial-value problems.
Again in the area of differential-algebraic systems, Neil Biehn, John Betts, Stephen Campbell and William Huffman present current work on mesh adaptation for DAE two-point boundary-value problems.
Contrasting approaches to the question of how good an approximation is as a solution of a given equation involve (i) attempting to estimate the actual error (i.e., thedifference between the true and the approximate solutions) and (ii) attempting to estimate the defect - the amount by which the approximation fails to satisfy the given equation and any side-conditions.
The paper by Wayne Enright on defect control relates to carefully analyzed techniques that have been proposed both for ordinary differential equations and for delay differential equations in which an attempt is made to control an estimate of the size of the defect.
Many phenomena incorporate noise, and the numerical solution of stochastic differential equations has developed as a relatively new item of study in the area.
Keven Burrage, Pamela Burrage and Taketomo Mitsui review the way numerical methods for solving stochastic differential equations (SDE's) are constructed.
One of the more recent areas to attract scrutiny has been the area of differential equations with after-effect (retarded, delay, or neutral delay differential equations) and in this volume we include a number of papers on evolutionary problems in this area.
The paper of Genna Bocharov and Fathalla Rihan conveys the importance in mathematical biology of models using retarded differential equations.
The contribution by Christopher Baker is intended to convey much of the background necessary for the application of numerical methods and includes some original results on stability and on the solution of approximating equations.
Alfredo Bellen, Nicola Guglielmi and Marino Zennaro contribute to the analysis of stability of numerical solutions of nonlinear neutral differential equations.
Koen Engelborghs, Tatyana Luzyanina, Dirk Roose, Neville Ford and Volker Wulf consider the numerics ofbifurcation in delay differential equations.
Evelyn Buckwar contributes a paper indicating the construction and analysis of a numerical strategy for stochastic delay differential equations (SDDEs).
This volume contains contributions on both Volterra and Fredholm-type integral equations.
Christopher Baker responded to a late challenge to craft a review of the theory of the basic numerics of Volterra integral and integro-differential equations.
Simon Shaw and John Whiteman discuss Galerkin methods for a type of Volterra integral equation that arises in modelling viscoelasticity.
A subclass of boundary-value problems for ordinary differential equation comprises eigenvalue problems such as Sturm-Liouville problems (SLP) and Schrodinger equations.
Liviu Ixaru describes the advances made over the last three decades in the field of piecewise perturbation methods for the numerical solution of Sturm-Liouville problems in general and systems of Schrodinger equations in particular.
Alan Andrew surveys the asymptotic correction method for regular Sturm-Liouville problems.
Leon Greenberg and Marco Marletta survey methods for higher-order Sturm-Liouville problems.
R. Moore in the 1960s first showed the feasibility of validated solutions of differential equations, that is, of computing guaranteed enclosures of solutions.
Boundary integral equations. Numerical solution of integral equations associated with boundary-value problems has experienced continuing interest.
Peter Junghanns and Bernd Silbermann present a selection of modern results concerning the numerical analysis of one-dimensional Cauchy singular integral equations, in particular the stability of operator sequences associated with different projection methods.
Johannes Elschner and Ivan Graham summarize the most important results achieved in the last years about the numerical solution of one-dimensional integral equations of Mellin type of means of projection methods and, in particular, by collocation methods.
A survey of results on quadrature methods for solving boundary integral equations is presented by Andreas Rathsfeld.
Wolfgang Hackbusch and Boris Khoromski present a novel approach for a very efficient treatment of integral operators.
Ernst Stephan examines multilevel methods for the h-, p- and hp- versions of the boundary element method, including pre-conditioning techniques.
George Hsiao, Olaf Steinbach and Wolfgang Wendland analyze various boundary element methods employed in local discretization schemes.

Computable Calculus treats the fundamental topic of calculus in a novel way that is more in tune with today's computer age. Comprising 11 chapters and an accompanying CD-ROM, the book presents mathematical analysis that has been created to deal with constructively defined concepts. The book's "show your work" approach makes it easier to understand the pitfalls of various computations and, more importantly, how to avoid these pitfalls.
The accompanying CD-ROM has self-contained programs that interact with the text, providing for easy grasp of the new concepts and enabling readers to write their own demonstration programs.
Contains software on CD ROM:
The accompanying software demonstrates, through simulation and exercises, how each concept of calculus can be associated with a program for the 'ideal computer'
Using this software readers will be able to write their own demonstration programs

/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price

In one of the papers in this collection, the remark that "nothing at all takes place in the universe in which some rule of maximum of minimum does not appear" is attributed to no less an authority than Euler. Simplifying the syntax a little, we might paraphrase this as "Everything is an optimization problem." While this might be something of an overstatement, the element of exaggeration is certainly reduced if we consider the extended form: "Everything is an optimization problem or a system of equations." This observation, even if only partly true, stands as a fitting testimonial to the importance of the work covered by this volume.
Since the 1960s, much effort has gone into the development and application of numerical algorithms for solving problems in the two areas of optimization and systems of equations. As a result, many different ideas have been proposed for dealing efficiently with (for example) severe nonlinearities and/or very large numbers of variables. Libraries of powerful software now embody the most successful of these ideas, and one objective of this volume is to assist potential users in choosing appropriate software for the problems they need to solve. More generally, however, these collected review articles are intended to provide both researchers and practitioners with snapshots of the 'state-of-the-art' with regard to algorithms for particular classes of problem. These snapshots are meant to have the virtues of immediacy through the inclusion of very recent ideas, but they also have sufficient depth of field to show how ideas have developed and how today's research questions have grown out of previous solution attempts.
The most efficient methods for "local optimization, " both unconstrained and constrained, are still derived from the classical Newton approach.
As well as dealing in depth with the various classical, or neo-classical, approaches, the selection of papers on optimization in this volume ensures that newer ideas are also well represented.
Solving nonlinear algebraic systems of equations is closely related to optimization. The two are not completely equivalent, however, and usually something is lost in the translation.
Algorithms for nonlinear equations can be roughly classified as "locally convergent" or "globally convergent." The characterization is not perfect.
Locally convergent algorithms include Newton's method, modern quasi-Newton variants of Newton's method, and trust region methods. All of these approaches are well represented in this volume.

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This volume is dedicated to two closely related subjects: interpolation and extrapolation. The papers can be divided into three categories: historical papers, survey papers and papers presenting new developments.
Interpolation is an old subject since, as noticed in the paper by M. Gasca and T. Sauer, the term was coined by John Wallis in 1655. Interpolation was the first technique for obtaining an approximation of a function. Polynomial interpolation was then used in quadrature methods and methods for the numerical solution of ordinary differential equations.
Extrapolation is based on interpolation. In fact, extrapolation consists of interpolation at a point outside the interval containing the interpolation points. Usually, this point is either zero or infinity. Extrapolation is used in numerical analysis to improve the accuracy of a process depending of a parameter or to accelerate the convergence of a sequence. The most well-known extrapolation processes are certainly Romberg's method for improving the convergence of the trapezoidal rule for the computation of a definite integral and Aiken's &Dgr;2 process which can be found in any textbook of numerical analysis.
Obviously, all aspects of interpolation and extrapolation have not been treated in this volume. However, many important topics have been covered.

The TI-85 is the latest and most powerful graphing calculator produced by Texas Instruments. This book describes the use of the TI-85 in courses in precalculus, calculus, linear algebra, differential equations, business mathematics, probability, statistics and advanced engineering mathematics. The book features in-depth coverage of the calculator's use in specific course areas by distinguished experts in each field.

1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles.

Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Godel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.

These edited volumes present new statistical methods in a way that bridges the gap between theoretical and applied statistics. The volumes cover general problems and issues and more specific topics concerning the structuring of change, the analysis of time series, and the analysis of categorical longitudinal data. The book targets students of development and change in a variety of fields - psychology, sociology, anthropology, education, medicine, psychiatry, economics, behavioural sciences, developmental psychology, ecology, plant physiology, and biometry - with basic training in statistics and computing.

Introduction to Lie Groups and Lie Algebra, 51

This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry.

- A collection of articles of highest scientific standard.
- An excellent introduction and overview of recent topics from multivariate approximation.
- A valuable source of references for specialists in the field.
- A representation of the state-of-the-art in selected areas of multivariate approximation.
- A rigorous mathematical introduction to special topics of interdisciplinary research.

This book contains several introductory texts concerning the main directions in the theory
of evolutionary partial differential equations. The main objective is to present clear, rigorous,
and in depth surveys on the most important aspects of the present theory. The table of
contents includes:
W.Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimates
A.Bressan: The front tracking method for systems of conservation laws
E.DiBenedetto, J.M.Urbano, V.Vespri: Current issues on singular and degenerate evolution equations;
L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systems
A.Lunardi: Nonlinear parabolic equations and systems
D.Serre: L1-stability of nonlinear waves in scalar conservation laws
B.Perthame: Kinetic formulations of parabolic and hyperbolic PDE s: from theory to numerics