An Introduction to Vectors, Vector Operators and Vector Analysis

An Introduction to Vectors, Vector Operators and Vector Analysis

Author: Pramod S. Joag

Publisher: Cambridge University Press

ISBN: 9781316870471

Category: Science

Page:

View: 286

Ideal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. The first unit deals with basic formulation, both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation, and curvilinear coordinate systems like spherical polar and parabolic systems and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.

An Introduction to Vector Analysis

An Introduction to Vector Analysis

Author: B. Hague

Publisher: Springer Science & Business Media

ISBN: 9789400958418

Category: Mathematics

Page: 122

View: 705

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 Computer Graphics

Vector Analysis for Computer Graphics

Author: John A. Vince

Publisher: Springer Nature

ISBN: 9781447175056

Category: Computer graphics

Page: 246

View: 222

This second edition has been completely restructured, resulting in a compelling description of vector analysis from its first appearance as a byproduct of Hamiltons quaternions to the use of vectors in solving geometric problems. The result provides readers from different backgrounds with a complete introduction to vector analysis. The author shows why vectors are so useful and how it is possible to develop analytical skills in manipulating vector algebra. Using over 150 full-colour illustrations, the author demonstrates in worked examples how this relatively young branch of mathematics has become a powerful and central tool in describing and solving a wide range of geometric problems. These may be in the form of lines, surfaces and volumes, which may touch, collide, intersect, or create shadows upon complex surfaces. The book is divided into eleven chapters covering the history of vector analysis, linear equations, vector algebra, vector products, differentiating vector-valued functions, vector differential operators, tangent and normal vectors, straight lines, planes, intersections and rotating vectors. The new chapters are about the history, differentiating vector-valued functions, differential operators and tangent and normal vectors. The original chapters have been reworked and illustrated.

Vector Analysis for Mathematicians, Scientists and Engineers

Vector Analysis for Mathematicians, Scientists and Engineers

Author: S. Simons

Publisher: Elsevier

ISBN: 9781483160214

Category: Mathematics

Page: 200

View: 207

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.

Concise Vector Analysis

Concise Vector Analysis

Author: C. J. Eliezer

Publisher: Courier Dover Publications

ISBN: 9780486809236

Category: Mathematics

Page: 160

View: 375

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.

Vector Calculus

Vector Calculus

Author: Susan Jane Colley

Publisher: Prentice Hall

ISBN: 0131858742

Category: Mathematics

Page: 551

View: 109

This text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. Accessible to anyone with a good background in single-variable calculus, it presents more linear algebra than usually found in a multivariable calculus book. Colley balances this with very clear and expansive exposition, many figures, and numerous, wide-ranging exercises. Instructors will appreciate Colley's writing style, mathematical precision, level of rigor, and full selection of topics treated. Vectors: Vectors in Two and Three Dimensions. More About Vectors. The Dot Product. The Cross Product. Equations for Planes; Distance Problems. Some n-Dimensional Geometry. New Coordinate Systems. Differentiation in Several Variables: Functions of Several Variables; Graphing Surfaces. Limits. The Derivative. Properties; Higher-Order Partial Derivatives; Newton's Method. The Chain Rule. Directional Derivatives and the Gradient. Vector-Valued Functions: Parametrized Curves and Kepler's Laws. Arclength and Differential Geometry. Vector Fields: An Introduction. Gradient, Divergence, Curl, and the Del Operator. Maxima and Minima in Several Variables: Differentials and Taylor's Theorem. Extrema of Functions. Lagrange Multipliers. Some Applications of Extrema. Multiple Integration: Introduction: Areas and Volumes. Double Integrals. Changing the Order of Integration. Triple Integrals. Change of Variables. Applications of Integration. Line Integrals: Scalar and Vector Line Integrals. Green's Theorem. Conservative Vector Fields. Surface Integrals and Vector Analysis: Parametrized Surfaces. Surface Integrals. Stokes's and Gauss's Theorems. Further Vector Analysis; Maxwell's Equations. Vector Analysis in Higher Dimensions: An Introduction to Differential Forms. Manifolds and Integrals of k-forms. The Generalized Stokes's Theorem. For all readers interested in multivariable calculus.

Vector and Tensor Analysis with Applications

Vector and Tensor Analysis with Applications

Author: Aleksandr Ivanovich Borisenko

Publisher: Courier Corporation

ISBN: 0486638332

Category: Mathematics

Page: 257

View: 307

Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

Vector Analysis for Computer Graphics

Vector Analysis for Computer Graphics

Author: John Vince

Publisher: Springer

ISBN: 1447175042

Category: Computers

Page: 246

View: 869

This book is a complete introduction to vector analysis, especially within the context of computer graphics. The author shows why vectors are useful and how it is possible to develop analytical skills in manipulating vector algebra. Even though vector analysis is a relatively recent development in the history of mathematics, it has become a powerful and central tool in describing and solving a wide range of geometric problems. The book is divided into eleven chapters covering the mathematical foundations of vector algebra and its application to, among others, lines, planes, intersections, rotating vectors, and vector differentiation.