The final prices may differ from the prices shown due to specifics of VAT rules About this Textbook Vector calculus is the fundamental language of mathematical physics. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. 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. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications.

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Matthews Evans, J. Blackledge, P. Parker Further Linear Algebra T. Blyth and E. R Wallace Hyperbolic Geometry J. Anderson Information and Coding Theory G. Jones and J. Dyke Introduction to Ring Theory P. Coln Introductory Mathematics: Algebra and analysis G.

Smith Linear Functional Analysis B. Rynne and M. Capirksi and T. Evans, ]. Yardley Probability Models J. Haigh Real analysis J. Howie ts, Logic and Categories P. Smith ando. Tabachnikova Vector Calculus p c matthews P C. Springer undergraduate mathematics series 1. Vector analysis 2. Calculus of tensors ITitle Springer undergraduate mathematics series Includes index IsBN pbk. Series QAM The publisher makes no representation express or implied with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or ommissions that may be made Mathews: Vector Calculus C, Springer-Verlag London Limited All rights reserved.

No part of this publication may be reproduced, stored in any electronic or mechanical form, including photocopy, recording or otherwise, without the prior written Permission of the publisher. Prin ted in India by rashtriya Printers, Dehi P reface 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 diferentiation ntegration 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. In addition to the worked examples, a section of exercises is included at the middle and at the end of each chapter.

At the end of each chapter, a one-page summary is given, listing the most essential points of the chapter Vector Calculus The first chapter covers the basic concepts of vectors and scalars, the ways in which vectors can be multiplied together and some of the applications of vectors to physics and geometry Chapter 2 defines the ways in which vector and scalar quantities can be integrated, covering line integrals, surface integrals and volume integrals.

The key concepts of gradient, divergence and curl are defined, which provide the basis for the following chapters Chapter 4 introduces a new and powerful notation, suffix notation, for ma nipulating complicated vector expressions. Quantities that run to several lines using conventional vector notation can be written extremely compactly using suffix notation. These help to tie the subject together, by providing links between the different forms of integrals from Chapter 2 and the derivatives of vectors from Chapter 3 Chapter 6 covers the general theory of orthogonal curvilinear coordinate systems and describes the two most important examples, cylindrical polar co- ordinates and spherical polar coordinates Chapter 7 introduces a more rigorous, mathematical definition of vectors and scalars, which is based on the way in which they transform when the coordinate system is rotated.

This definition is extended to a more general class of objects known as tensors. Line, Surface and Volume Integrals 21 21 Applications and methods of integration. Gradient, Divergence and Curl 3. Sufix Notation and its Applications. Curvilinear Coordinates. Cartesian Tensors 7. Applications of Vector Calculus.

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## Vector Calculus

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.

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About this book Introduction Vector calculus is the fundamental language of mathematical physics. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. 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. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications.

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