An Introduction to Vector Analysis

For Physicists and Engineers

Author: B. Hague

Publisher: Springer Science & Business Media

ISBN: 9400958412

Category: Mathematics

Page: 122

View: 8422

The principal changes that I have made in preparing this revised edition of the book are the following. (i) Carefuily selected worked and unworked examples have been added to six of the chapters. These examples have been taken from class and degree examination papers set in this University and I am grateful to the University Court for permission to use them. (ii) Some additional matter on the geometrieaI application of veetors has been incorporated in Chapter 1. (iii) Chapters 4 and 5 have been combined into one chapter, some material has been rearranged and some further material added. (iv) The chapter on int~gral theorems, now Chapter 5, has been expanded to include an altemative proof of Gauss's theorem, a treatmeot of Green's theorem and a more extended discussioo of the classification of vector fields. (v) The only major change made in what are now Chapters 6 and 7 is the deletioo of the discussion of the DOW obsolete pot funetioo. (vi) A small part of Chapter 8 on Maxwell's equations has been rewritten to give a fuller account of the use of scalar and veetor potentials in eleetromagnetic theory, and the units emploYed have been changed to the m.k.s. system.

Vector Analysis for Mathematicians, Scientists and Engineers

The Commonwealth and International Library: Physics Division

Author: S. Simons

Publisher: Elsevier

ISBN: 1483160211

Category: Mathematics

Page: 200

View: 5809

Vector Analysis for Mathematicians, Scientists and Engineers, Second Edition, provides an understanding of the methods of vector algebra and calculus to the extent that the student will readily follow those works which make use of them, and further, will be able to employ them himself in his own branch of science. New concepts and methods introduced are illustrated by examples drawn from fields with which the student is familiar, and a large number of both worked and unworked exercises are provided. The book begins with an introduction to vectors, covering their representation, addition, geometrical applications, and components. Separate chapters discuss the products of vectors; the products of three or four vectors; the differentiation of vectors; gradient, divergence, and curl; line, surface, and volume integrals; theorems of vector integration; and orthogonal curvilinear coordinates. The final chapter presents an application of vector analysis. Answers to odd-numbered exercises are provided as the end of the book.

Analytical and Computational Methods of Advanced Engineering Mathematics

Author: Grant B. Gustafson,Calvin H. Wilcox

Publisher: Springer Science & Business Media

ISBN: 9780387982656

Category: Mathematics

Page: 733

View: 1914

This book focuses on the topics which provide the foundation for practicing engineering mathematics: ordinary differential equations, vector calculus, linear algebra and partial differential equations. Destined to become the definitive work in the field, the book uses a practical engineering approach based upon solving equations and incorporates computational techniques throughout.

Introduction to Vector and Tensor Analysis

Author: Robert C. Wrede

Publisher: Courier Corporation

ISBN: 0486137112

Category: Mathematics

Page: 418

View: 2584

Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.

Vector and Tensor Analysis

Author: George E. Hay

Publisher: Courier Corporation

ISBN: 0486601099

Category: Mathematics

Page: 193

View: 2097

"Remarkably comprehensive, concise and clear." — Industrial Laboratories "Considered as a condensed text in the classical manner, the book can well be recommended." — Nature Here is a clear introduction to classic vector and tensor analysis for students of engineering and mathematical physics. Chapters range from elementary operations and applications of geometry, to application of vectors to mechanics, partial differentiation, integration, and tensor analysis. More than 200 problems are included throughout the book.

Introduction to Engineering Physics For U.P.

Author: A S Vasudeva

Publisher: S. Chand Publishing

ISBN: 8121922178

Category: Science

Page: 484

View: 2255

Unit 1: Relativity And InterferenceTheory Of RelativityInterference Unit 2: Diffraction And PolarizationDiffractionPolarizationUnit 3: Fields And ElectrostaticsScalar And Vector FieldsElectric Fields And Gauss'S LawMaxwell'S Equations Unit 4: Magnetic Properties Of Materials And X-RaysMagnetic Properties Of MaterialsX-Rays And Compton Effect Unit 5: Quantum Theory And LasersMatter Waves And Uncertainty PrincipleQuantum TheoryLasersModel Test Papers

Functional Analysis for Physics and Engineering

An Introduction

Author: Hiroyuki Shima

Publisher: CRC Press

ISBN: 1482223031

Category: Mathematics

Page: 285

View: 4893

This book provides an introduction to functional analysis for non-experts in mathematics. As such, it is distinct from most other books on the subject that are intended for mathematicians. Concepts are explained concisely with visual materials, making it accessible for those unfamiliar with graduate-level mathematics. Topics include topology, vector spaces, tensor spaces, Lebesgue integrals, and operators, to name a few. Two central issues—the theory of Hilbert space and the operator theory—and how they relate to quantum physics are covered extensively. Each chapter explains, concisely, the purpose of the specific topic and the benefit of understanding it. Researchers and graduate students in physics, mechanical engineering, and information science will benefit from this view of functional analysis.



Publisher: PHI Learning Pvt. Ltd.

ISBN: 9788120327320

Category: Mathematics

Page: 272

View: 6512

This fully revised and thoroughly updated second edition takes into account the constructive suggestions received from teachers and students alike on the first edition. A new chapter on Generalized Coordinate System has been added to make the book complete. Some more examples have been provided to highlight the applicability of vectors in physics and engineering. The answers to all the end-of-chapter exercises have been given in this edition to enhance the utility of the book. Beginning with the basic concepts of vector methods and various operations of vector-valued functions such as continuity, differentiability, and integrability, the three fundamental differential operators-gradient, divergence, and curl-are fully explored. The text then moves on to provide the essentials of differential geometry with particular reference to curvature and torsion, and Serret-Frenet equations. The chapter on mechanics demonstrates the strength of vectors in tackling physical problems. The book concludes with a new chapter on notions of vectors in the generalized coordinate system. This book is primarily intended for use by undergraduate students of mathematics and science for a course in vector analysis. It will also be useful to engineering students, as part of a course in engineering mathematics, where they are introduced to vector algebra, so essential for assimilating a better understanding of the physical aspects of the theory.

Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica

Author: Kuzman Adzievski,Abul Hasan Siddiqi

Publisher: CRC Press

ISBN: 1466510579

Category: Mathematics

Page: 648

View: 4340

With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations. The authors use Mathematica® along with graphics to improve understanding and interpretation of concepts. They also present exercises in each chapter and solutions to selected examples. Topics discussed include Laplace and Fourier transforms as well as Sturm-Liouville boundary value problems.

Vector Analysis

A Physicist's Guide to the Mathematics of Fields in Three Dimensions

Author: N. Kemmer

Publisher: CUP Archive

ISBN: 9780521211581

Category: Mathematics

Page: 254

View: 2505

Vector analysis provides the language that is needed for a precise quantitative statement of the general laws and relationships governing such branches of physics as electromagnetism and fluid dynamics. The account of the subject is aimed principally at physicists but the presentation is equally appropriate for engineers. The justification for adding to the available textbooks on vector analysis stems from Professor Kemmer's novel presentation of the subject developed through many years of teaching, and in relating the mathematics to physical models. While maintaining mathematical precision, the methodology of presentation relies greatly on the visual, geometric aspects of the subject and is supported throughout the text by many beautiful illustrations that are more than just schematic. A unification of the whole body of results developed in the book - from the simple ideas of differentiation and integration of vector fields to the theory of orthogonal curvilinear coordinates and to the treatment of time-dependent integrals over fields - is achieved by the introduction from the outset of a method of general parametrisation of curves and surfaces.

Introduction to Vectors and Tensors

Author: Ray M. Bowen,Chao-cheng Wang

Publisher: Courier Corporation

ISBN: 048646914X

Category: Mathematics

Page: 520

View: 5397

This convenient single-volume compilation of two texts offers both an introduction and an in-depth survey. Geared toward engineering and science students rather than mathematicians, its less rigorous treatment focuses on physics and engineering applications. A practical reference for professionals, it is suitable for advanced undergraduate and graduate students. 1976 edition.

Concise Vector Analysis

Author: C. J. Eliezer

Publisher: Courier Dover Publications

ISBN: 0486809234

Category: Mathematics

Page: 160

View: 7455

This concise introduction to the methods and techniques of vector analysis is suitable for college undergraduates in mathematics as well as students of physics and engineering. Rich in exercises and examples, the straightforward presentation focuses on physical ideas rather than mathematical rigor. The treatment begins with a chapter on vectors and vector addition, followed by a chapter on products of vector. Two succeeding chapters on vector calculus cover a variety of topics, including functions of a vector; line, surface, and volume integrals; the Laplacian operator, and more. The text concludes with a survey of standard applications, including Poinsot's central axis, Gauss's theorem, gravitational potential, Green's theorems, and other subjects.

Tensor Calculus for Engineers and Physicists

Author: Emil de Souza Sánchez Filho

Publisher: Springer

ISBN: 331931520X

Category: Technology & Engineering

Page: 345

View: 9845

This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.

Vector Calculus

Author: Paul C. Matthews

Publisher: Springer Science & Business Media

ISBN: 9783540761808

Category: Mathematics

Page: 182

View: 7543

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.

Mathematical Techniques for Engineers and Scientists

Author: Larry C. Andrews,Ronald L. Phillips

Publisher: SPIE Press

ISBN: 9780819445063

Category: Mathematics

Page: 797

View: 8748

As technology continues to move ahead, modern engineers and scientists are frequently faced with difficult mathematical problems that require an ever greater understanding of advanced concepts. Designed as a self-study text for practicing engineers and scientists, as well as a useful reference, the book takes the reader from ordinary differential equations to more sophisticated mathematics--Fourier analysis, vector and tensor analysis, complex variables, partial differential equations, and random processes. The emphasis is on the use of mathematical tools and techniques. The general exposition and choice of topics appeals to a wide audience of applied practitioners.

Mathematical Methods for Scientists and Engineers

Author: Donald Allan McQuarrie

Publisher: University Science Books

ISBN: 9781891389245

Category: Mathematics

Page: 1161

View: 7953

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.