Vector Calculus

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.

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.

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.

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.

Based on many years of experience of the author Complex Analysis with Vector Calculus provides clear and condensed treatment of the subject. It is primarily intended to be used by undergraduate students of engineering and science as a part of a course in engineering mathematics, where they are introduced to complex variable theory, through conceptual development of analysis. The book also introduces vector algebra, step by step, with due emphasis on various operations on vector field and scalar fields. Especially, it introduces proof of vector identities by use of a new approach and includes many examples to clarify the ideas and familiarize students with various techniques of problem solving.

Methods used for regional development analysis are employed mainly to make forecasts and comparisons. Forecasting models of various types (e.g. econometric models) are usually used for forecasting. Recently, vector-autoregressive models (VAR) have become popular. These models were proposed by Sims in 1980. On the contrary, taxonomic methods (that are in the center of attention as far as the present publication is concerned) are most often employed to make comparisons. Linear ordering methods, including standard methods, are the most popular among ta- nomic methods. They are based on different distance and similarity measures, which leads to the fact that they do not always provide reliable information. When, for example, one construes the standard for a base year and then compares it with data for other years, it may turn out that the measure determined will have worse values than the standard for a real object (region, micro region) although this object is better from the standard. Hence, one must look for new methods employed in regional development analysis or improve hitherto existing ones in such a way so that information obtained re?ects the reality to a larger extent. The main aim of the present publication is to work out methodological basis for regional development analysis based on vector calculus together with assumptions about computer system supporting the implementation of the method suggested.

This introductory text offers a rigorous, comprehensive treatment. Classical theorems of vector calculus are amply illustrated with figures, worked examples, physical applications, and exercises with hints and answers. 1986 edition.

This book is designed primarily for undergraduates in mathematics, engineering, and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. Furthermore, it can be used to impower the mathematical knowledge for Artificial Intelligence (AI) concepts. It also provides numerous computer illustrations and tutorials using MATLAB® and Maple®, that bridge the gap between analysis and computation. Partial solutions and instructor ancillaries available for use as a textbook. FEATURES Includes numerous computer illustrations and tutorials using MATLAB®and Maple® Covers the major topics of vector geometry, differentiation, and integration in several variables Instructors’ ancillaries available upon adoption