Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

Books Journals

Thinking Computers and Virtual Persons

1st Edition
May 10, 2014
Eric Dietrich
English
eBook
9 7 8 1 4 8 3 2 1 7 6 5 9

Thinking Computers and Virtual Persons: Essays on the Intentionality of Machines explains how computations are meaningful and how computers can be cognitive agents like humans. This book focuses on the concept that cognition is computation. Organized into four parts encompassing 13 chapters, this book begins with an overview of the analogy between intentionality and phlogiston, the 17th-century principle of burning. This text then examines the objection to computationalism that it cannot prevent arbitrary attributions of content to the various data structures and representations involved in a computational process. Other chapters consider that the notion of original intentionality is incoherent. This book argues as well that the only way to build an intelligent machine is to build a neural network. The final chapter claims that an entire theoretical framework in cognitive psychology is incompatible with the view that human brains are computers of some sort. This book is a valuable resource for cognitive scientists.

Advanced Calculus of Several Variables

1st Edition
May 10, 2014
C. H. Edwards
English
eBook
9 7 8 1 4 8 3 2 6 8 0 5 7

Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence.

Programming in an Object-Oriented Environment

1st Edition
May 10, 2014
Raimund K. Ege
English
eBook
9 7 8 1 4 8 3 2 6 8 6 8 2

Programming in an Object-Oriented Environment provides an in-depth look at the concepts behind the technology of object-oriented programming. This book explains why object-oriented programming has the potential to vastly improve the productivity of programmers and how to apply this technology in a practical environment. Many programming examples are included, focusing on how different programming languages support the core of object-oriented concepts. C++ is used as the main sample language throughout this text. This monograph consists of two major parts. Part I provides an introduction to object-oriented concepts, their rationale and their implementation in programming languages. The object-oriented approach to programming in an object-oriented environment is discussed in Part II. This publication is intended for software professionals who are interested in learning the fundamental concepts of object-oriented programming and how to apply these concepts in a practical computer environment.

Structured Programming Using Turbo BASIC

1st Edition
May 10, 2014
Wade Ellis + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 1 0 4 1

Structured Programming Using Turbo BASIC explains programming methods using this language through mathematical or business examples and problems. The book approaches problem-solving using a top-down, structured programming method. This method consists of 1) breaking a problem into smaller, more manageable tasks, and 2) using the action block, the decision block, and the loop block—the three fundamental programming structures—to perform each task. The text describes the Turbo Basic environment on an IBM PC or compatible, the fundamental programming structures and concepts, the two data structures (arrays, files), graphics creation, as well as computer simulations. The book explains in detail variables, screen formatting, the decision block, the loop block, functions. The text also discusses parameter lists, and libraries The student learns to use the OPEN statement to associate a buffer with a file, or the CLOSE statement to end the file/buffer. The text explains the use of the Turbo BASIC random generator that produces unique sequences of random numbers. The book can be used in introductory lecture courses in business, computer science, or mathematics. It can be beneficial for students in an open-entry/open-exit computer laboratory courses or for self-study.

Inverse and Ill-Posed Problems

1st Edition
May 10, 2014
Heinz W. Engl + 1 more
English
eBook
9 7 8 1 4 8 3 2 7 2 6 5 8

Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June 1986. The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator equations of the first kind. Other papers deal with applications in tomography, inverse scattering, detection of radiation sources, optics, partial differential equations, and parameter estimation problems. One paper discusses three topics on ill-posed problems, namely, the imposition of specified types of discontinuities on solutions of ill-posed problems, the use of generalized cross validation as a data based termination rule for iterative methods, and also a parameter estimation problem in reservoir modeling. Another paper investigates a statistical method to determine the truncation level in Eigen function expansions and for Fredholm equations of the first kind where the data contains some errors. Another paper examines the use of singular function expansions in the inversion of severely ill-posed problems arising in confocal scanning microscopy, particle sizing, and velocimetry. The collection can benefit many mathematicians, students, and professor of calculus, statistics, and advanced mathematics.

Introductory Statistics for the Behavioral Sciences

1st Edition
May 10, 2014
Robert B. Ewen
English
eBook
9 7 8 1 4 8 3 2 5 8 2 7 0

Introductory Statistics for the Behavioral Sciences is a workbook on statistical procedures and formulas that are relevant to research and field work. The book explains frequency distributions, graphs, and measures of central tendency. The workbook uses as example hypothetical scores of a test given to students in four universities. The book then has sections on reminders and problems to guide the reader. Other topics the book discusses include measures of variability, transformed scores, probability, and general strategy of inferential statistics. Other subjects the book also covers include inferences about the mean of a single population and testing hypotheses about the differences between the means of two populations. The workbook also includes practice problems on linear correlation, prediction, and other correlational techniques such as the Spearmen rank-order correlation coefficient or the point biserial correlation coefficient. The book also includes review chapters on normal curves, standard error procedures, and inferential statistics. The workbook can be a great aid for students of behavioral and physical sciences where statistics is applied in research and analysis.

From Pixels to Animation

1st Edition
May 10, 2014
James Alan Farrell
English
eBook
9 7 8 1 4 8 3 2 6 5 6 8 1

From Pixels to Animation: An Introduction to Graphics Programming deals with the C programming language, particularly for the Borland C and Microsoft C languages. The book reviews the basics of graphics programming, including graphics hardware, graphs, charts, changing colors, 3D graphics, high level functions provided by Borland and Microsoft C. The text also explains low-level graphics, getting around the limitations of standard, graphics libraries, SVGA programming, and creating graphics functions. Advanced topics include linear transformations, ray tracing, and fractals. The book explains in detail the aspect ratio of pixels (length of the pixel dot divided by its width), pixel colors, line styles, and the functions to create the graphic. The text also describes the presentation of a three-dimensional object by using perspective, shading, and texturing. Between the operating system, which carries out the instruction of the program, and the hardware, which displays the output of the program, is the Basic Input/Output Services (BIOS). The BIOS is a set of routine instruction inside the different parts or hardware devices in the computer. The book explains programing animation effects by utilizing routines provided by Microsoft or Borland. The text also notes that a programmer can create good animation effects by directly addressing the graphics adapter, bypassing the BIOS or the high-level routines created by Microsoft or Borland. The book is suitable for beginning programmers, computer science, operators, animators, and artists involved with computer aided designs.

Numerical Methods for Initial Value Problems in Ordinary Differential Equations

1st Edition
May 10, 2014
Simeon Ola Fatunla
Werner Rheinboldt + 1 more
English
eBook
9 7 8 1 4 8 3 2 6 9 2 6 9

Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implic... singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.

Numerical and Computer Methods in Structural Mechanics

1st Edition
May 10, 2014
Steven J. Fenves + 2 more
English
eBook
9 7 8 1 4 8 3 2 7 2 5 4 2

Numerical and Computer Methods in Structural Mechanics is a compendium of papers that deals with the numerical methods in structural mechanics, computer techniques, and computer capabilities. Some papers discus the analytical basis of the computer technique most widely used in software, that is, the finite element method. This method includes the convergence (in terms of variation principles) isoparametrics, hybrid models, and incompatible displacement models. Other papers explain the storage or retrieval of data, as well as equation-solving algorithms. Other papers describe general-purpose structural mechanics programs, alternatives to, and extension of the usual finite element approaches. Another paper explores nonlinear, dynamic finite element problems, and a direct physical approach to determine finite difference models. Special papers explain structural mechanics used in computing, particularly, those related to integrated data bases, such as in the Structures Oriented Exchange System of the Office of Naval Research and the integrated design of tanker structures. Other papers describe software and hardware capabilities, for example, in ship design, fracture mechanics, biomechanics, and crash safety. The text is suitable for programmers, computer engineers, researchers, and scientists involved in materials and industrial design.

Associative Networks

1st Edition
May 10, 2014
Nicholas V. Findler
English
eBook
9 7 8 1 4 8 3 2 6 3 0 1 4

Associative Networks: Representation and Use of Knowledge by Computers is a collection of papers that deals with knowledge base of programs exhibiting some operational aspects of understanding. One paper reviews network formalism that utilizes unobstructed semantics, independent of the domain to which it is applied, that is also capable of handling significant epistemological relationships of concept structuring, attribute/value inheritance, multiple descriptions. Another paper explains network notations that encode taxonomic information; general statements involving quantification; information about processes and procedures; the delineation of local contexts, as well as the relationships between syntactic units and their interpretations. One paper shows that networks can be designed to be intuitively and formally interpretable. Network formalisms are computer-oriented logics which become distinctly significant when access paths from concepts to propositions are built into them. One feature of a topical network organization is its potential for learning. If one topic is too large, it could be broken down where groupings of propositions under the split topics are then based on "co-usage" statistics. As an example, one paper cites the University of Maryland artificial intelligence (AI) group which investigates the control and interaction of a meaning-based parser. The group also analyzes the inferences and predictions from a number of levels based on mundane inferences of actions and causes that can be used in AI. The collection can be useful for computer engineers, computer programmers, mathematicians, and researchers who are working on artificial intelligence.

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