Introduction To Vector Analysis
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Author | : John Cragoe Tallack |
Publisher | : Cambridge University Press |
Total Pages | : 310 |
Release | : 1970 |
Genre | : Vector analysis |
ISBN | : 0521079993 |
The first eight chapters of this book were originally published in 1966 as the successful Introduction to Elementary Vector Analysis. In 1970, the text was considerably expanded to include six new chapters covering additional techniques (the vector product and the triple products) and applications in pure and applied mathematics. It is that version which is reproduced here. The book provides a valuable introduction to vectors for teachers and students of mathematics, science and engineering in sixth forms, technical colleges, colleges of education and universities.
Author | : Louis Brand |
Publisher | : Courier Corporation |
Total Pages | : 306 |
Release | : 2012-06-22 |
Genre | : Mathematics |
ISBN | : 048615484X |
This text was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into the subjects' manifold applications. 1957 edition. 86 figures.
Author | : Pramod S. Joag |
Publisher | : Cambridge University Press |
Total Pages | : 548 |
Release | : 2016-10-13 |
Genre | : Science |
ISBN | : 1316870472 |
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.
Author | : Antonio Galbis |
Publisher | : Springer Science & Business Media |
Total Pages | : 383 |
Release | : 2012-03-29 |
Genre | : Mathematics |
ISBN | : 1461422000 |
The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables. Key topics include vectors and vector fields, line integrals, regular k-surfaces, flux of a vector field, orientation of a surface, differential forms, Stokes' theorem, and divergence theorem. This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables. The book can also be useful to engineering and physics students who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.
Author | : C. E. Springer |
Publisher | : Courier Corporation |
Total Pages | : 258 |
Release | : 2013-09-26 |
Genre | : Mathematics |
ISBN | : 048632091X |
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
Author | : Robert C. Wrede |
Publisher | : Courier Corporation |
Total Pages | : 436 |
Release | : 2013-01-30 |
Genre | : Mathematics |
ISBN | : 0486137112 |
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.
Author | : D. E. Bourne |
Publisher | : Academic Press |
Total Pages | : 271 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483260704 |
Vector Analysis and Cartesian Tensors, Second Edition focuses on the processes, methodologies, and approaches involved in vector analysis and Cartesian tensors, including volume integrals, coordinates, curves, and vector functions. The publication first elaborates on rectangular Cartesian coordinates and rotation of axes, scalar and vector algebra, and differential geometry of curves. Discussions focus on differentiation rules, vector functions and their geometrical representation, scalar and vector products, multiplication of a vector by a scalar, and angles between lines through the origin. The text then elaborates on scalar and vector fields and line, surface, and volume integrals, including surface, volume, and repeated integrals, general orthogonal curvilinear coordinates, and vector components in orthogonal curvilinear coordinates. The manuscript ponders on representation theorems for isotropic tensor functions, Cartesian tensors, applications in potential theory, and integral theorems. Topics include geometrical and physical significance of divergence and curl, Poisson's equation in vector form, isotropic scalar functions of symmetrical second order tensors, and diagonalization of second-order symmetrical tensors. The publication is a valuable reference for mathematicians and researchers interested in vector analysis and Cartesian tensors.
Author | : John Vince |
Publisher | : Springer Science & Business Media |
Total Pages | : 260 |
Release | : 2007-06-18 |
Genre | : Computers |
ISBN | : 1846288037 |
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.
Author | : Murray R. Spiegel |
Publisher | : McGraw Hill Professional |
Total Pages | : 242 |
Release | : 1959 |
Genre | : Calculus of tensors |
ISBN | : 9780070602281 |
Author | : Paul C. Matthews |
Publisher | : Springer Science & Business Media |
Total Pages | : 189 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1447105974 |
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.