**Author**: Ann Hirst

**Publisher:** Butterworth-Heinemann

**ISBN:** 0080572014

**Category:** Mathematics

**Page:** 144

**View:** 3584

Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics. The author has approached the subject from a geometrical standpoint and although applications to mechanics will be pointed out and techniques from linear algebra employed, it is the geometric view which is emphasised throughout. Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to more advanced theories. * Adopts a geometric approach * Develops gradually, building from basics to the concept of isometry and vector calculus * Assumes virtually no prior knowledge * Numerous worked examples, exercises and challenge questions

This book deals with vector algebra and analysis and with their application to three-dimensional geometry and the analysis of fields in three dimensions. While many treatments of the application of vectors have approached the fundamentals of the subject intuitively, assuming some prior knowledge of Euclidean and Cartesian geometry, Professor Chrisholm here bases the subject on the axioms of linear space algebra, which are fundamental to many branches of mathematics. While developing the properties of vectors from axioms, however, he continually emphasizes the geometrical interpretation of vector algebra in order to build up intuitive relations between the algebraic equations and geometrical concepts. Throughout, examples are used to illustrate the theory being developed; several sets of problems are incorporate in each chapter, and outline answers to many of these are given. Written primarily for undergraduate mathematicians in the early part of their courses, this lucidly written book will also appeal to mathematical physicists and to mathematically inclined engineers.

In many cases, the beginning engineering student is thrown into upper-level engineering courses without an adequate introduction to the basic material. This, at best, causes undue stress on the student as they feel unprepared when faced with unfamiliar material, and at worst, results in students dropping out of the program or changing majors when they discover that their chosen field of engineering is not what they thought it was. The purpose of this text is to introduce the student to a general cross-section of the field of electrical and computer engineering. The text is aimed at incoming freshmen, and as such, assumes that the reader has a limited to nonexistent background in electrical engineering and knowledge of no more than pre-calculus in the field of mathematics. By exposing students to these fields at an introductory level, early in their studies, they will have both a better idea of what to expect in later classes and a good foundation of knowledge upon which to build.

Intended for upper-level undergraduate and graduate courses in chemistry, physics, mathematics and engineering, this text is also suitable as a reference for advanced students in the physical sciences. Detailed problems and worked examples are included.

As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modeling and Computing with MATLAB examines a variety of applications and their modeling processes, showing you how to develop matrix models and solve algebraic systems. Emphasizing practical skills, it creates a bridge from problems with two and three variables to more realistic problems that have additional variables. Elements of Matrix Modeling and Computing with MATLAB focuses on seven basic applications: circuits, trusses, mixing tanks, heat conduction, data modeling, motion of a mass, and image filters. These applications are developed from very simple to more complex models. To explain the processes, the book explores numerous topics in linear algebra, including complex numbers and functions, matrices, algebraic systems, curve fitting, elements of linear differential equations, transform methods, and tools of computation. For example, the author uses linearly independent vectors and subspaces to explain over- and under-determined systems, eigenvalues and eigenvectors to solve initial value problems, and discrete Fourier transforms to perform image filtering in the frequency domain. Although the primary focus is to cultivate calculation skills by hand, most chapters also include MATLAB to help with more complicated calculations.

Building on previous texts in the Modular Mathematics series, in particular 'Vectors in Two or Three Dimensions' and 'Calculus and ODEs', this book introduces the student to the concept of vector calculus. It provides an overview of some of the key techniques as well as examining functions of more than one variable, including partial differentiation and multiple integration. Undergraduates who already have a basic understanding of calculus and vectors, will find this text provides tools with which to progress onto further studies; scientists who need an overview of higher order differential equations will find it a useful introduction and basic reference.

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This book [earlier titled as Electromagnetism: Theory and Applications which is bifurcated into two volumes: Electromagnetism: Theory and Electromagnetism: Applications (Magnetic Diffusion and Electromagnetic Waves) has been updated to cover some additional aspects of theory and nearly all modern applications. The semi-historical approach is unchanged, but further historical comments have been introduced at various places in the book to give a better insight into the development of the subject as well as to make the study more interesting and palatable to the students. Key Features • Physical explanations of different types of currents • Concepts of complex permittivity and complex permeability; and anisotropic behaviour of constitute parameters in different media and different conditions • Vector co-ordinate system transformation equations • Halbach magnets and the theory of one-sided flux • Discussion on physical aspects of demagnetization curve of B-H loop for ferromagnetic materials • Extrapolation of Frohlich-Kennely equation used for the design and analysis of permanent magnet applications • Physical aspects of Faraday’s law of electromagnetic induction (i.e., Fourth Maxwell’s field equation) through the approach of special relativity • Extrapolation and elaboration of the concept of electromechanical energy conversion to both magnetic as well as electric field systems Appendices contain in-depth analysis of self-inductance and non-conservative fields (Appendix 6), proof regarding the boundary conditions (Appendix 8), theory of bicylindrical co-ordinate system to provide the physical basis of the circuit approach to the cylindrical transmission line systems (Appendix 10), and properties of useful functions like Bessel and Legendre functions (Appendix 9). The book is designed to serve as a core text for students of electrical engineering. Besides, it will be useful to postgraduate physics students as well as research engineers and design and development engineers in industries.

This book is the product of more than half a century of leadership and innovation in physics education. When the first edition of University Physics by Francis W. Sears and Mark W. Zemansky was published in 1949, it was revolutionary among calculus-based physics textbooks in its emphasis on the fundamental principles of physics and how to apply them. The success of University Physics with generations of (several million) students and educators around the world is a testament to the merits of this approach and to the many innovations it has introduced subsequently. In preparing this First Australian SI edition, our aim was to create a text that is the future of Physics Education in Australia. We have further enhanced and developed University Physics to assimilate the best ideas from education research with enhanced problem-solving instruction, pioneering visual and conceptual pedagogy, the first systematically enhanced problems, and the most pedagogically proven and widely used online homework and tutorial system in the world, Mastering Physics.

Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with fractals, rather than the typical line-drawing algorithms found in many standard texts. He also brings the turtle back from obscurity to introduce several major concepts in computer graphics. Supplying the mathematical foundations, the book covers linear algebra topics, such as vector geometry and algebra, affine and projective spaces, affine maps, projective transformations, matrices, and quaternions. The main graphics areas explored include reflection and refraction, recursive ray tracing, radiosity, illumination models, polygon shading, and hidden surface procedures. The book also discusses geometric modeling, including planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, constructive solid geometry, boundary files, octrees, interpolation, approximation, Bezier and B-spline methods, fractal algorithms, and subdivision techniques. Making the material accessible and relevant for years to come, the text avoids descriptions of current graphics hardware and special programming languages. Instead, it presents graphics algorithms based on well-established physical models of light and cogent mathematical methods.

Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics. The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation. Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only). Numerous examples illuminate the mathematical theories Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach Each chapter concludes with an extensive set of exercises

Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. This text is an excellent book teaching guide. Contains exercises for student engagement as well as the integration and use of MATLAB Software Provides development of common solution methodologies and a systematic review of analytical solutions useful in applications of

For well over a decade, the numerical approach to field computation has been gaining progressively greater importance. Analytical methods offield compu tation are, at best, unable to accommodate the very wide variety of configura tions in which fields must be computed. On the other hand, numerical methods can accommodate many practical configurations that analytical methods cannot. With the advent of high-speed digital computers, numerical field computations have finally become practical. However, in order to implement numerical methods of field computation, we need algorithms, numerical methods, and mathematical tools that are largely quite different from those that have been traditionally used with analytical methods. Many of these algorithms have, in fact, been presented in the large number of papers that have been published on this subject in the last two decades. And to some of those who are already experienced in the art of numerical field computations, these papers, in addition to their own original work, are enough to give them the knowledge that they need to perform practical numerical field computations.

Covers multivariable calculus, starting from the basics and leading up to the three theorems of Green, Gauss, and Stokes, but always with an eye on practical applications. Written for a wide spectrum of undergraduate students by an experienced author, this book provides a very practical approach to advanced calculus—starting from the basics and leading up to the theorems of Green, Gauss, and Stokes. It explains, clearly and concisely, partial differentiation, multiple integration, vectors and vector calculus, and provides end-of-chapter exercises along with their solutions to aid the readers’ understanding. Written in an approachable style and filled with numerous illustrative examples throughout, Two and Three Dimensional Calculus: with Applications in Science and Engineering assumes no prior knowledge of partial differentiation or vectors and explains difficult concepts with easy to follow examples. Rather than concentrating on mathematical structures, the book describes the development of techniques through their use in science and engineering so that students acquire skills that enable them to be used in a wide variety of practical situations. It also has enough rigor to enable those who wish to investigate the more mathematical generalizations found in most mathematics degrees to do so. Assumes no prior knowledge of partial differentiation, multiple integration or vectors Includes easy-to-follow examples throughout to help explain difficult concepts Features end-of-chapter exercises with solutions to exercises in the book. Two and Three Dimensional Calculus: with Applications in Science and Engineering is an ideal textbook for undergraduate students of engineering and applied sciences as well as those needing to use these methods for real problems in industry and commerce.

Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. 1966 edition.

This handbook presents the first systematic account of corpus phonology - the employment of corpora for studying speakers' and listeners' acquisition and knowledge of the sound system of their native languages and the principles underlying those systems. The first part of the book discusses the design, compilation, and use of phonological corpora, while the second looks at specific applications. Part 3 presents the tools and methods used, while the final part examines a number of currently available phonological corpora in various languages. It will appeal not only to those working with phonological corpora, but also to researchers and students of phonology and phonetics more generally, as well as to all those interested in language variation, dialectology, language acquisition, and sociolinguistics.

Presented here is an integrated approach - perhaps the first in its class - of the basics of vector and matrix Algebra at College level, with the object-oriented C++ code that implements the vector and matrix objects and brings them to life. Thinking in terms of objects is the natural way of thinking. The concept of object has existed in Science for centuries. More recently, objects were introduced in Computation, and object-oriented programming languages were created. Yet the concept of object is not routinely used when teaching Science, and the idea that objects can come alive in a computer has not yet been fully exploited.This book integrates basic vector and matrix Algebra with object-oriented concepts and the actual code implementing them. It is both a textbook and a software release, complete withsoftware documentation and the mathematical background that supports the code. The source code is included by download and readers can use it for their own programming. The reader will need a basic knowledge of Mathematical notation, Algebra and Trigonometry, but familiarity with C++ is not required because a course on C++ is also included. You should read this book if you are a developer who needs a background in vector or matrix algebra, a science student who needs tolearn C++, a scientist who needs to write advanced code but can't waste time developing the basics, or you just need ready-to-use C++ source code for your project.

Theory of Random Functions and Its Application to Control Problems presents insights into a branch of probability theory, the theory of random functions, which studies and takes into account the effects of random factors on the functioning of control systems. The book does not require a high level of competency in the use of mathematical techniques and explains the basics of probability theory before focusing on the concepts of the theory of random functions. The selection also discusses in great detail the aspects of random functions and provides chapters that cover the determination and solution to problems of optimal systems. The text will be of value to telecommunications engineers, aeronautical engineers, meteorologists, seismologists, and other professionals engaged in applied sciences.