C++ and Object-Oriented Numeric Computing

C++ and Object-Oriented Numeric Computing

This new text/reference presents an accessible, concise, but rather complete, introduction to the C++ programming language with special emphasis on object-oriented numeric computation for scientific and engineering program development. The description of the language is in compliance with ISO/ANSI standards and is platform independent for maximum versatility. Requiring only basic calculus and linear algebra as prerequisites, the book introduces concepts, techniques, and standard libraries of C++ in a manner that is easy to understand and uses such familiar examples as vectors, matrices, integrals, and complex numbers. It also contains an introduction to C++ programs for applications with many numberic methods that are fundamental to science and engineering computing: polynomial evaluation and interpolation; numeric integration; methods for solving nonlinear equations; systems of linear equations in full, band, and sparse matrix storage formats; and ordinary and partial differential equations. Numerous techniques and examples are provided on how to reduce (C and Fortran) run-time overhead and improve program efficiency. Topics and features: *concise coverage of C++ programming concepts with object-oriented emphasis*numerous examples, coding tools, sample programs and exercises for reinforcement and self-study purposes*develops and uses basic and advanced features, as well as standard libraries of C++*covers many fundamental numeric methods for scientific and engineering computing applications*downloadable user-defined numeric linear algebra library available from author web site With an accessible style, intuitive topic development, and numerous examples, the book is an excellent resource and guide to the power, versatility and efficiency of C++ programming for numeric computing applications. Advanced students, practitioners and professionals in computer science, engineering and scientific computing in general will find the book a practical guide and resource for their work and applications program development.

C++ and Object-Oriented Numeric Computing

Maple By Example

Maple By Example

Maple by Example, Third Edition, is a reference/text with CD for beginning and experienced students, professional engineers, and other Maple users. This new edition has been updated to be compatible with the most recent release of the Maple software. Coverage includes built-in Maple commands used in courses and practices that involve calculus, linear algebra, business mathematics, ordinary and partial differential equations, numerical methods, graphics and more. The CD-ROM provides updated Maple input and all text from the book.

Maple By Example

Introductory Real Analysis

Introductory Real Analysis

Self-contained and comprehensive, this elementary introduction to real and functional analysis is readily accessible to those with background in advanced calculus. It covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, and much more. 350 problems. 1970 edition.

Introductory Real Analysis

A Problem Text in Advanced Calculus

A Problem Text in Advanced Calculus

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A Problem Text in Advanced Calculus

Non-fickian Solute Transport in Porous Media

Non-fickian Solute Transport in Porous Media

The advection-dispersion equation that is used to model the solute transport in a porous medium is based on the premise that the fluctuating components of the flow velocity, hence the fluxes, due to a porous matrix can be assumed to obey a relationship similar to Fick s law. This introduces phenomenological coefficients which are dependent on the scale of the experiments. This book presents an approach, based on sound theories of stochastic calculus and differential equations, which removes this basic premise. This leads to a multiscale theory with scale independent coefficients. This book illustrates this outcome with available data at different scales, from experimental laboratory scales to regional scales.

Non-fickian Solute Transport in Porous Media

Many-Body Boson Systems

Many-Body Boson Systems

Many-body Boson Systems: Half a Century Later offers a modern way of dealing with the problems of equilibrium states of Bose systems. Starting with the variation principle of statistical mechanics and the energy-entropy balance principle as equilibrium criteria, results for general boson systems and models are explicitly derived using simple functional analytic calculus. Bridging the gap between ideas of general theoretical physics and the phenomenological research in the field of Bose systems, this book provides an insight into the fascinating quantum world of bosons. Key topics include the occurrence of BEC and its intimate structural relation with the phenomena of spontaneous symmetry breaking and off-diagonal long range order; the condensate equation; the issue concerning the choice of boundary conditions; solvable versus non-solvable boson models; the set of quasi-free boson states; the role of dissipative perturbations; and the surprising but general relation between general quantum fluctuations and boson systems. Only some knowledge of quantum mechanics and undergraduate algebra and analysis is assumed. This textbook brings students and researchers smoothly from general concepts to vivid applications.

Many-Body Boson Systems

Introduction to Stochastic Calculus for Finance

Introduction to Stochastic Calculus for Finance

The large number of already available textbooks on stochastic calculus with specific applications to finance requires a justification for another contribution to this subject. The justifcation is mainly pedagogical. These lecture notes start with an elementary approach to stochastic calculus due to Fllmer, who showed that one can develop Ito’s calculus ‘pathwise’ as an exercise in real analysis. The text opens to students interested in finance a quick (but by no means ‘dirty’) road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model. The reader is supposed only to be familiar with elementary real analysis (e.g. Taylor’s Theorem) and basic probability theory. The text is also useful for mathematicians interested in the methods of modern mathematical finance without prior knowledge of advanced stochastic analysis.

Introduction to Stochastic Calculus for Finance

Introduction to Probability

Introduction to Probability

Introduction to Probability, Second Edition, is written for students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, and some of the social sciences with a background in a year-long elementary calculus, taking upper level or graduate level introduction to probability courses. Roussas utilizes his trademark clarity and economy of expression to elucidate important concepts of probability, while providing a plethora of useful examples and exercises of real world applications for students to consider.

Introduction to Probability

Mathematica in Action - Third edition

Mathematica in Action - Third edition

With the third edition of his popular Mathematica in Action, award-winning author Stan Wagon guides readers through the important changes that have been made to Mathematica 6.0. To utilize the more sophisticated graphics capabilities of 6.0, Wagon has significantly expanded the chapters on surfaces and the parametric plotting of surfaces. The chapter on differential equations now includes material from VisualDSolve , built into Mathematica 6.0. Like previous editions, this is not only an introduction to Mathematica 6.0, but also a tour of modern mathematics by one of the fields most gifted expositors. Wagon explores some of the most important areas of modern mathematics with new chapters on optimization, including algebraic and numerical optimization, and linear and integer programming. Connections are also made to computer science with new material on graphs and networks. Wagon is the author of nine books on mathematics, including A Course in Computational Number Theory , named one of the ten best math books of 2000 by the American Library Association. He has written extensively on the educational applications of Mathematica, inlcuding the books VisualDSolve: Visualizing Differential Equations with Mathematica, and Animating Calculus: Mathematica Notebooks for the Laboratory. From Reviews of the Second Edition: ‘The bottom line is that is an outstanding book containing many examples of real uses of Mathematica for the novice, intermediate, and expert user.’ Mark McClure, Mathematica in Education and Research Journal ‘In a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional graphics and high-precision integer arithmetic can contribute to our understanding and enjoyment of mathematics.’ Richard Walker, The Mathematical Gazette

Mathematica in Action - Third edition

The Development of Arabic Mathematics

The Development of Arabic Mathematics

An understanding of developments in Arabic mathematics between the IXth and XVth century is vital to a full appreciation of the history of classical mathematics. This book draws together more than ten studies to highlight one of the major developments in Arabic mathematical thinking, provoked by the double fecondation between arithmetic and the algebra of al-Khwarizmi, which led to the foundation of diverse chapters of mathematics: polynomial algebra, combinatorial analysis, algebraic geometry, algebraic theory of numbers, diophantine analysis and numerical calculus. Thanks to epistemological analysis, and the discovery of hitherto unknown material, the author has brought these chapters into the light, proposes another periodization for classical mathematics, and questions current ideology in writing its history.

The Development of Arabic Mathematics

Soft Computing Approach to Pattern Classification and Object Recognition

Soft Computing Approach to Pattern Classification and Object Recognition

Soft Computing Approach to Pattern Classification and Object Recognition establishes an innovative, unified approach to supervised pattern classification and model-based occluded object recognition. The book also surveys various soft computing tools, fuzzy relational calculus (FRC), genetic algorithm (GA) and multilayer perceptron (MLP) to provide a strong foundation for the reader. The supervised approach to pattern classification and model-based approach to occluded object recognition are treated in one framework , one based on either a conventional interpretation or a new interpretation of multidimensional fuzzy implication (MFI) and a novel notion of fuzzy pattern vector (FPV). By combining practice and theory, a completely independent design methodology was developed in conjunction with this supervised approach on a unified framework, and then tested thoroughly against both synthetic and real-life data. In the field of soft computing, such an application-oriented design study is unique in nature. The monograph essentially mimics the cognitive process of human decision making, and carries a message of perceptual integrity in representational diversity. Soft Computing Approach to Pattern Classification and Object Recognition is intended for researchers in the area of pattern classification and computer vision. Other academics and practitioners will also find the book valuable.

Soft Computing Approach to Pattern Classification and Object Recognition

Vector and Geometric Calculus

Vector and Geometric Calculus

This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. It is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one.

Vector and Geometric Calculus

Stochastic Models for Fractional Calculus

Stochastic Models for Fractional Calculus

This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. The reader will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. The book covers basic limit theorems for random variables and random vectors with heavy tails. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering.

Stochastic Models for Fractional Calculus

Linear and Geometric Algebra

Linear and Geometric Algebra

This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. Geometric algebra is an extension of linear algebra. It enhances the treatment of many linear algebra topics. And geometric algebra does much more. Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas. They provide a unified mathematical language for many areas of physics, computer science, and other fields. The book can be used for self study by those comfortable with the theorem/proof style of a mathematics text. This is a second printing, corrected and slightly revised. Visit the book’s web site for more information: http: //faculty.luther.edu/ macdonal/laga I commend Alan Macdonald for his excellent book! His exposition is clean and spare. He has done a fine job of engineering a gradual transition from standard views of linear algebra to the perspective of geometric algebra. The book is sufficiently conventional to be adopted as a textbook by an adventurous teacher without getting flack from colleagues. Yet it leads to gems of geometric algebra that are likely to delight thoughtful students and surprise even the most experienced instructors. — David Hestenes, Distinguished Research Professor, Arizona State University

Linear and Geometric Algebra

Mathematics

Mathematics

This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed explanations of the important mathematical procedures actually used by famous mathematicians, giving more mathematically talented students a greater opportunity to learn the history and philosophy by way of problem solving. Several important philosophical topics are pursued throughout the text, giving the student an opportunity to come to a full and consistent knowledge of their development. These topics include infinity, the nature of motion, and Platonism. This book offers, in fewer pages, a deep penetration into the key mathematical and philosophical aspects of the history of mathematics.

Mathematics

A First Course in Fourier Analysis

A First Course in Fourier Analysis

This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

A First Course in Fourier Analysis

Introduction to Stochastic Integration - Second Edition

Introduction to Stochastic Integration - Second Edition

A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability.

Introduction to Stochastic Integration - Second Edition

Partial Differential Equation Analysis in Biomedical Engineering

Partial Differential Equation Analysis in Biomedical Engineering

Aimed at graduates and researchers, and requiring only a basic knowledge of multi-variable calculus, this introduction to computer-based partial differential equation (PDE) modeling provides readers with the practical methods necessary to develop and use PDE mathematical models in biomedical engineering. Taking an applied approach, rather than using abstract mathematics, the reader is instructed through six biomedical example applications, each example characterized by step-by-step discussions of established numerical methods and implemented in reliable computer routines. Adopting this technique, the reader will understand how PDE models are formulated, implemented and tested. Supported by a set of rigorously tested general purpose PDE routines online, and with enhanced understanding through animations, this book will be ideal for anyone faced with interpreting large experimental data sets that need to be analyzed with PDE models in biomedical engineering.

Partial Differential Equation Analysis in Biomedical Engineering

An Expedition to Continuum Theory

An Expedition to Continuum Theory

This book introduces field theory as required in solid and fluid mechanics as well as in electromagnetism. It includes the necessary applied mathematical framework of tensor algebra and tensor calculus, using an inductive approach particularly suited to beginners. It is geared toward undergraduate classes in continuum theory for engineers in general, and more specifically to courses in continuum mechanics. Students will gain a sound basic understanding of the subject as well as the ability to solve engineering problems by applying the general laws of nature in terms of the balances for mass, momentum, and energy in combination with material-specific relations in terms of constitutive equations, thus learning how to use the theory in practice for themselves. This is facilitated by numerous examples and problems provided throughout the text.

An Expedition to Continuum Theory

A Distributed Pi-Calculus

A Distributed Pi-Calculus

Distributed systems are fast becoming the norm in computer science. Formal mathematical models and theories of distributed behavior are needed in order to understand them. This book proposes a distributed pi-calculus called Dpi, for describing the behavior of mobile agents in a distributed world. It is based on an existing formal language, the pi-calculus, to which it adds a network layer and a primitive migration construct. A mathematical theory of the behavior of these distributed systems is developed, in which the presence of types plays a major role. It is also shown how in principle this theory can be used to develop verification techniques for guaranteeing the behavior of distributed agents. The text is accessible to computer scientists with a minimal background in discrete mathematics. It contains an elementary account of the pi-calculus, and the associated theory of bisimulations. It also develops the type theory required by Dpi from first principles.

A Distributed Pi-Calculus