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R 780.00
R 946.23
Vector Analysis
This book presents modern vector analysis and carefully describes the classical notation and understanding of the theory. It covers all of the classical vector analysis in Euclidean space, as well as on manifolds, and goes on to introduce de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality. The material is accessible to readers and students with only calculus and linear algebra as prerequisites. A large number of illustrations, exercises, and tests with answers make this book an invaluable self-study source.
R 2,265.85
Vector Analysis and Cartesian Tensors, Third edition
This is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at the back of the book.
R 5,332.68
Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding
Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.
R 4,030.64
R 2,133.57
R 1,248.41
Advances in Self-Organizing Maps and Learning Vector Quantization
The book collects the scientific contributions presented at the 10th Workshop on Self-Organizing Maps (WSOM 2014) held at the University of Applied Sciences Mittweida, Mittweida (Germany, Saxony), on July 2–4, 2014. Starting with the first WSOM-workshop 1997 in Helsinki this workshop focuses on newest results in the field of supervised and unsupervised vector quantization like self-organizing maps for data mining and data classification.This 10th WSOM brought together more than 50 researchers, experts and practitioners in the beautiful small town Mittweida in Saxony (Germany) nearby the mountains Erzgebirge to discuss new developments in the field of unsupervised self-organizing vector quantization systems and learning vector quantization approaches for classification. The book contains the accepted papers of the workshop after a careful review process as well as summaries of the invited talks. Among these book chapters there are excellent examples of the use of self-organizing maps in agriculture, computer science, data visualization, health systems, economics, engineering, social sciences, text and image analysis and time series analysis. Other chapters present the latest theoretical work on self-organizing maps as well as learning vector quantization methods, such as relating those methods to classical statistical decision methods.All the contribution demonstrate that vector quantization methods cover a large range of application areas including data visualization of high-dimensional complex data, advanced decision making and classification or data clustering and data compression.
R 10,687.96
Variable Ordering Structures in Vector Optimization
This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space. The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.
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R 1,050.05
Vector Calculus in Regional Development Analysis
Methods used for regional development analysis are employed mainly to make forecasts and comparisons. Forecasting models of various types (e.g. econometric models) are usually used for forecasting. Recently, vector-autoregressive models (VAR) have become popular. These models were proposed by Sims in 1980. On the contrary, taxonomic methods (that are in the center of attention as far as the present publication is concerned) are most often employed to make comparisons. Linear ordering methods, including standard methods, are the most popular among ta- nomic methods. They are based on different distance and similarity measures, which leads to the fact that they do not always provide reliable information. When, for example, one construes the standard for a base year and then compares it with data for other years, it may turn out that the measure determined will have worse values than the standard for a real object (region, micro region) although this object is better from the standard. Hence, one must look for new methods employed in regional development analysis or improve hitherto existing ones in such a way so that information obtained re?ects the reality to a larger extent. The main aim of the present publication is to work out methodological basis for regional development analysis based on vector calculus together with assumptions about computer system supporting the implementation of the method suggested.
R 4,096.85
R 365.00
Vector and Parallel Processing - VECPAR 2000
This book is the ?nal outcome of VECPAR 2000 – 4th International Meeting on Vector and Parallel Processing. VECPAR constitutes a series of conferences, which have been organized by the Faculty of Engineering of the University of Porto since 1993, with the main objective of disseminating new knowledge on parallel computing. Readership of This Book The book is aimed at an audience of researchers and graduate students in a broad range of scienti?c areas, including not only computer science, but also applied mathematics and numerical analysis, physics, and engineering. Book Plan From a total of 66 papers selected on the basis of extended abstracts for p- sentation at the conference, a subset of 34 papers were chosen during a second review process leading to their inclusion in the book, together with the invited talks. The book contains a total of 40 papers organized into 6 chapters, where each may appeal to people in di?erent but still related scienti?c areas. All ch- ters, with the exception of Chapter 6, are initiated by a short text, providing a quick overview of the organization and papers in the chapter. The 13 papers in Chapter 1 cover the aspects related to the use of multiple processors. Operating systems, languages and software tools for scheduling, and code transformation are the topics included in this chapter, initiated by the talk on computing over the Internet, entitled Grid Computing,byIan Foster.
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R 341.00
Vector Quantization and Signal Compression
Herb Caen, a popular columnist for the San Francisco Chronicle, recently quoted a Voice of America press release as saying that it was reorganizing in order to "eliminate duplication and redundancy. " This quote both states a goal of data compression and illustrates its common need: the removal of duplication (or redundancy) can provide a more efficient representation of data and the quoted phrase is itself a candidate for such surgery. Not only can the number of words in the quote be reduced without losing informa tion, but the statement would actually be enhanced by such compression since it will no longer exemplify the wrong that the policy is supposed to correct. Here compression can streamline the phrase and minimize the em barassment while improving the English style. Compression in general is intended to provide efficient representations of data while preserving the essential information contained in the data. This book is devoted to the theory and practice of signal compression, i. e. , data compression applied to signals such as speech, audio, images, and video signals (excluding other data types such as financial data or general purpose computer data). The emphasis is on the conversion of analog waveforms into efficient digital representations and on the compression of digital information into the fewest possible bits. Both operations should yield the highest possible reconstruction fidelity subject to constraints on the bit rate and implementation complexity.
R 3,111.38
Normal Forms and Bifurcation of Planar Vector Fields
This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary. The theory has developed rapidly over the past two decades. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: centre manifold theory and normal form theory, by which the dimension of equations may be reduced and the forms changed so that they are as simple as possible. Chapters 3–5 of the book study in considerable detail the bifurcation of those one- or two-dimensional equations with one, two or several parameters. This book is aimed at mathematicians and graduate students interested in dynamical systems, ordinary differential equations and/or bifurcation theory. The basic knowledge required by this book is advanced calculus, functional analysis and qualitative theory of ordinary differential equations.
R 7,382.79
Vector Calculus
Vector calculus is the fundamental language of mathematical physics. It pro vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.
R 1,392.00
R 1,301.00
Plant Virus, Vector
Stressing the key role vectors play spread of virus diseases, this volume represents the priorities in practical plant virus research and ways in which their control or management should be sought through an understanding of the practical and environmental aspects of the interactions of viruses with their vectors and their environment. It provides an in-depth understanding of the vectors, their biology, dispersal, movement and migration, contemporary canvases of epidemiology, and the management of virus diseases keeping in view the globalization of agriculture as also the viruses and their quarantine requirements.
R 12,359.15
Classical Vector Algebra
Every physicist, engineer, and certainly a mathematician, would undoubtedly agree that vector algebra is a part of basic mathematical instruments packed in their toolbox.Classical Vector Algebra should be viewed as a prerequisite, an introduction, for other mathematical courses dealing with vectors, following typical form and appropriate rigor of more advanced mathematics texts. Vector algebra discussed in this book briefly addresses vectors in general 3-dimensional Euclidian space, and then, in more detail, looks at vectors in Cartesian □□3 space. These vectors are easier to visualize and their operational techniques are relatively simple, but they are necessary for the study of Vector Analysis. In addition, this book could also serve as a good way to build up intuitive knowledge for more abstract structures of □□-dimensional vector spaces.Definitions, theorems, proofs, corollaries, examples, and so on are not useless formalism, even in an introductory treatise -- they are the way mathematical thinking has to be structured. In other words, "introduction" and "rigor" are not mutually exclusive. The material in this book is neither difficult nor easy. The text is a serious exposition of a part of mathematics students need to master in order to be proficient in their field. In addition to the detailed outline of the theory, the book contains literally hundreds of corresponding examples/exercises.
R 2,619.43
Rotation Sequences and the Theory of Vectors and Coordinates
This book applies rotation theory to problems involving vectors and coordinates, with an approach that combines easily visualised procedures with smart mathematics. It constructs rotation theory from the ground up, building from basic geometry through to the motion and attitude equations of rockets, and the tensor analysis of relativity. The author replaces complicated pictures of superimposed axes with a simple and intuitive procedure of rotating a model aircraft, to create rotation sequences that are easily turned into mathematics. He combines the best of the 'active' and 'passive' approaches to rotation into a single coherent theory, and discusses many potential traps for newcomers. This volume will be useful to astronomers and engineers sighting planets and satellites, computer scientists creating graphics for movies, and aerospace engineers designing aircraft; also to physicists and mathematicians who study its abstract aspects.
R 8,207.40
Advances in Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization
In this collection, the reader can find recent advancements in self-organizing maps (SOMs) and learning vector quantization (LVQ), including progressive ideas on exploiting features of parallel computing. The collection is balanced in presenting novel theoretical contributions with applied results in traditional fields of SOMs, such as visualization problems and data analysis. Besides, the collection further includes less traditional deployments in trajectory clustering and recent results on exploiting quantum computation. The presented book is worth interest to data analysis and machine learning researchers and practitioners, specifically those interested in being updated with current developments in unsupervised learning, data visualization, and self-organization.
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R 878.00
From Vectors to Tensors
This textbook deals with tensors that are treated as vectors. Coverage details such new tensor concepts as the rotation of tensors, the transposer tensor, the eigentensors, and the permutation tensor structure. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. A complementary computer package, written in Mathematica, is available through the Internet.
R 2,562.30
Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding
Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.
R 1,759.00
Vector and Parallel Processing - VECPAR'96
This book constitutes a carefully arranged selection of revised full papers chosen from the presentations given at the Second International Conference on Vector and Parallel Processing - Systems and Applications, VECPAR'96, held in Porto, Portugal, in September 1996.Besides 10 invited papers by internationally leading experts, 17 papers were accepted from the submitted conference papers for inclusion in this documentation following a second round of refereeing. A broad spectrum of topics and applications for which parallelism contributes to progress is covered, among them parallel linear algebra, computational fluid dynamics, data parallelism, implementational issues, optimization, finite element computations, simulation, and visualisation.
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R 1,445.15
V-Invex Functions and Vector Optimization
This volume summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past few decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990’s. The authors integrate related research into the book and demonstrate the wide context from which the area has grown and continues to grow.
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R 528.00
Vector Optimization with Infimum and Supremum
The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.
R 3,294.23
Vector Quantization and Signal Compression
Herb Caen, a popular columnist for the San Francisco Chronicle, recently quoted a Voice of America press release as saying that it was reorganizing in order to "eliminate duplication and redundancy. " This quote both states a goal of data compression and illustrates its common need: the removal of duplication (or redundancy) can provide a more efficient representation of data and the quoted phrase is itself a candidate for such surgery. Not only can the number of words in the quote be reduced without losing informa tion, but the statement would actually be enhanced by such compression since it will no longer exemplify the wrong that the policy is supposed to correct. Here compression can streamline the phrase and minimize the em barassment while improving the English style. Compression in general is intended to provide efficient representations of data while preserving the essential information contained in the data. This book is devoted to the theory and practice of signal compression, i. e. , data compression applied to signals such as speech, audio, images, and video signals (excluding other data types such as financial data or general purpose computer data). The emphasis is on the conversion of analog waveforms into efficient digital representations and on the compression of digital information into the fewest possible bits. Both operations should yield the highest possible reconstruction fidelity subject to constraints on the bit rate and implementation complexity.
R 2,842.88
Vector Variational Inequalities and Vector Equilibria
In the fifties and sixties, several real problems, old and new, especially in Physics, Mechanics, Fluidodynamics, Structural Engi- neering, have shown the need of new mathematical models for study- ing the equilibrium of a system. This has led to the formulation of Variational Inequalities (by G. Stampacchia), and to the develop- ment of Complementarity Systems (by W.S. Dorn, G.B. Dantzig, R.W. Cottle, O.L. Mangasarian et al.) with important applications in the elasto-plastic field (initiated by G. Maier). The great advan- tage of these models is that the equilibrium is not necessarily the extremum of functional, like energy, so that no such functional must be supposed to exist. In the same decades, in some fields like Control Theory, Net- works, Industrial Systems, Logistics, Management Science, there has been a strong request of mathmatical models for optimizing situa- tions where there are concurrent objectives, so that Vector Optimiza- tion (initiated by W. Pareto) has received new impetus. With regard to equilibrium problems, Vector Optimization has the above - mentioned drawback of being obliged to assume the exis- tence of a (vector) functional.Therefore, at the end of the seventies the study of Vector Variational Inequalities began with the scope of exploiting the advantages of both variational and vector models. This volume puts together most of the recent mathematical results in Vector Variational Inequalities with the purpose of contributing to further research.
R 6,040.82
Vector Mode in the Second-order Cosmological Perturbation Theory
This thesis sheds valuable new light on the second-order cosmological perturbation theory, extensively discussing it in the context of cosmic microwave background (CMB) fluctuations. It explores the observational consequences of the second-order vector mode, and addresses magnetic field generation and the weak lensing signatures, which are key phenomena of the vector mode. The author demonstrates that the second-order vector mode, which never appears at the linear-order level, naturally arises from the non-linear coupling of the first-order scalar modes. This leads to the remarkable statement that the vector-order mode clearly contributes to the generation of cosmological magnetic fields. Moreover, the weak lensing observations are shown to be accessible to the vector mode. On the basis of ongoing and forthcoming observations, the thesis concludes that the second-order vector mode is detectable.
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R 1,496.31
An Illustrative Guide to Multivariable and Vector Calculus
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion.Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques.An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
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R 946.23
