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Computer Science 2006 - Scientific Computing and Applications
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Guillermo Sapiro
This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. It brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. The volume provides information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.
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Herbert Edelsbrunner
This book combines mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation) in order to solve the conceptual and technical problems in the combining of elements of combinatorial and numerical algorithms. The book develops methods from areas that are amenable to combination and explains recent breakthrough solutions to meshing that fit into this category. It should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, are useful, and interesting.
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Brian R. Hunt, Ronald L. Lipsman, Jonathan M. Rosenberg
Here is a short, focused introduction to MATLAB, a comprehensive software system for mathematics and technical computing that should be useful to both beginning and experienced users. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB's programming features, graphical capabilities, and desktop interface. It also includes an introduction to SIMULINK, a companion to MATLAB for system simulation. Written for MATLAB 6, this book can also be used with earlier (and later) versions of MATLAB. Chapters contain worked-out examples of applications of MATLAB to interesting problems in mathematics, engineering, economics, and physics. In addition, it contains explicit instructions for using MATLAB's Microsoft Word interface to produce polished, integrated, interactive documents for reports, presentations, or on-line publishing. This book explains everything you need to know to begin using MATLAB. Intermediate and advanced users will find useful information here, especially if they are making the switch to MATLAB 6 from an earlier version.
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George Em Karniadakis, Robert M. Kirby II
This book provides a seamless approach to numerical algorithms, modern programming techniques and parallel computing. These concepts and tools are usually taught serially across different courses and different textbooks, thus observing the connection between them. The necessity of integrating these subjects usually comes after such courses are concluded (e.g., during a first job or a thesis project), thus forcing the student to synthesize what is perceived to be three independent subfields into one in order to produce a solution. The book includes both basic and advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Advanced topics include wavelets, high-order methods, non-symmetric systems and parallelization of sparse systems. A CD-ROM accompanies the text.
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Ed Akin
Writing technical applications in a modern object-oriented approach, using Fortran 90 or 95, can be problematic. This book teaches how to employ the principles of object-oriented programming to produce clear, highly efficient executable codes (rather than focusing on the traditional procedural abilities of Fortran). This text is an excellent harbinger to all the features of the finalized, fully object-oriented Fortran 200X. In addition to covering the OOP methodologies, the basic foundation of the language and solid programming skills are reviewed, making the book valuable also as a good migration tool for experienced Fortran programmers that want to smoothly pick up the OOP paradigm. The author highlights common themes by using comparisons with Matlab® and C++ and uses numerous cross-referenced examples to convey all concepts quickly and clearly. Complete code for the examples is included on the accompanying CD.
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L. F. Shampine, I. Gladwell, S. Thompson
This book is a text for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics. Prerequisites are a first course in the theory of ODEs and a survey course in numerical analysis, in addition to specific programming experience, preferably in MATLAB, and knowledge of elementary matrix theory. Professionals will also find that this useful concise reference contains reviews of technical issues and realistic and detailed examples. The programs for the examples are supplied on the accompanying web site and can serve as templates for solving other problems.
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Bill Casselman
This practical introduction to the techniques needed to produce high-quality mathematical illustrations is suitable for anyone with basic knowledge of coordinate geometry. Bill Casselman combines a completely self-contained step-by-step introduction to the graphics programming language PostScript with an analysis of the requirements of good mathematical illustrations. The many small simple graphics projects can also be used in courses in geometry, graphics, or general mathematics. Code for many of the illustrations is included, and can be downloaded from the book's web site: www.math.ubc.ca/~cass/graphics/manualMathematicians; scientists, engineers, and even graphic designers seeking help in creating technical illustrations need look no further.
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Neil Gershenfeld
This book first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); numerical methods (finite differences for ODE's and PDE's, finite elements, cellular automata); model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation); as well as the special role of time in modeling (filtering and state estimation, hidden Markov processes, linear and nonlinear time series). Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications.
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J. M. Thijssen
Computional physics involves the use of computer calculations and simulations to solve physical problems. This book describes computational methods used in theoretical physics with emphasis on condensed matter applications. Coverage begins with an overview of the wide variety of topics and algorithmic approaches studied in this book. The next chapters concentrate on electronic structure calculations, presenting the Hartree-Fock and Density Functional formalisms, and band structure methods. Later chapters discuss molecular dynamics simulations and Monte Carlo methods in classical and quantum physics, with applications to condensed matter and particle field theories. Each chapter details the necessary fundamentals, describes the formation of a sample program, and includes problems that address related analytical and numerical issues. Useful appendices on numerical methods and random number generators are also included. This volume bridges the gap between undergraduate physics and computational research. It is an ideal textbook for graduate students as well as a valuable reference for researchers.
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Martin D. Buhmann
It is necessary to estimate parameters by approximation and interpolation in many areas-from computer graphics to inverse methods to signal processing. Radial basis functions are modern, powerful tools which are being used more widely as the limitations of other methods become apparent. Martin Buhmann provides a complete analysis of radial basic functions from the theoretical and practical implementation viewpoints. He also includes a comprehensive bibliography.
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Herbert Edelsbrunner
This book combines mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation) in order to solve the conceptual and technical problems in the combining of elements of combinatorial and numerical algorithms. The book develops methods from areas that are amenable to combination and explains recent breakthrough solutions to meshing that fit into this category. It should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, are useful, and interesting.
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Sriram Pemmaraju, Steven Skiena
With examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided--theorem/proof, programming exercises, and experimental explorations--ensuring great flexibility in teaching and learning the material. The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica.
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Henk A. van der Vorst
Based on extensive research by Henk van der Vorst, this book presents an overview of a number of Krylov projection methods for the solution of linear systems of equations. Van der Vorst demonstrates how these methods can be derived from basic iteration formulas and how they are related. Focusing on the ideas behind the methods rather than a complete presentation of the theory, the volume includes a substantial amount of references for further reading as well as exercises to help students initially encountering the material.
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Romualdo Pastor-Satorras, Alessandro Vespignani
Viewed in this analysis from a statistical physics perspective, the Internet is perceived as a developing system that evolves through the addition and removal of nodes and links. This perspective permits the authors to outline the dynamical theory that can appropriately describe the Internet's macroscopic evolution. The presence of such a theoretical framework will provide a revolutionary way of enhancing the reader's understanding of the Internet's varied network processes.
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David Yevick
C++ is rapidly becoming the programming language of choice for science and engineering applications because of its rich object-oriented features. Intended for beginning and intermediate programmers, this book surveys the application of C++ to technical problems. Modern object-oriented software engineering tools are employed to simplify the presentation and all aspects of modern C++ programming practices of relevance to scientific programming are surveyed.
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William Shaw
This volume exploits MATHEMATICA® for its power to illustrate, calculate or function as an investigative tool. The CD contains the entire manuscript in MATHEMATICA® enabling readers to use or modify any of the code featured in the book. The book can be used as a textbook for several different courses in complex analysis for mathematicians, physicists, or engineers.
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Afra J. Zomorodian
Written by a computer scientist for computer scientists, this book teaches topology from a computational point of view, and shows how to solve real problems that have topological aspects involving computers. Such problems arise in many areas, such as computer graphics, robotics, structural biology, and chemistry. The author starts from the basics of topology, assuming no prior exposure to the subject, and moves rapidly up to recent advances in the area, including topological persistence and hierarchical Morse complexes. Algorithms and data structures are presented when appropriate.
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Ke Chen
Preconditioning techniques have emerged as an essential part of successful and efficient iterative solutions of matrices. Ke Chen's book offers a comprehensive introduction to these methods. A vast range of explicit and implicit sparse preconditioners are covered, including the conjugate gradient, multi-level and fast multi-pole methods, matrix and operator splitting, fast Fourier and wavelet transforms, incomplete LU and domain decomposition, Schur complements and approximate inverses. In addition, aspects of parallel realization using the MPI are discussed. Very much a users-guide, the book provides insight to the use of these techniques in areas such as acoustic wave scattering, image restoration and bifurcation problems in electrical power stations. Supporting MATLAB files are available from the Web to support and develop readers' understanding, and provide stimulus for further study. Pitched at graduate level, the book is intended to serve as a useful guide and reference for students, computational practitioners, engineers and researchers alike.
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P. C. Gregory
Researchers in many branches of science are increasingly coming into contact with Bayesian statistics or Bayesian probability theory. This book provides a clear exposition of the underlying concepts with large numbers of worked examples and problem sets. It also discusses numerical techniques for implementing the Bayesian calculations, including Markov Chain Monte-Carlo integration and linear and nonlinear least-squares analysis seen from a Bayesian perspective.
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Paul R. Wellin, Richard J. Gaylord, Samuel N. Kamin
An Introduction to Programming with Mathematica® is designed to introduce the Mathematica programming language to a wide audience. Since the last edition of this book was published, significant changes have occurred in Mathematica and its use worldwide. Keeping pace with these changes, this substantially larger, updated version includes new and revised chapters on numerics, procedural, rule-based, and front-end programming, and gives significant coverage to the latest features up to, and including, Mathematica 5.1. Mathematica notebooks, available from www.cambridge.org/0521846781, contain examples, programs, and solutions to exercises in the book. Additionally, material to supplement later versions of the software will be made available. This is the ideal text for all scientific students, researchers, and programmers wishing to deepen their understanding of Mathematica, or even those keen to program using an interactive language that contains programming paradigms from all major programming languages: procedural, functional, recursive, rule-based, and object-oriented.
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Juergen Bokowski
Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The combination of concrete applications and computation, the profusion of illustrations, many in color, and the large number of examples and exercises make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.
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