Vector Calculus Download Ebook PDF Epub Online

Author : Paul C. Matthews
Publisher : Springer Science & Business Media
Release : 2012-12-06
Page : 182
Category : Mathematics
ISBN 13 : 1447105974
Description :


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.


Author : Miroslav Lovric
Publisher : Wiley
Release : 2007-01-03
Page : 640
Category : Mathematics
ISBN 13 : 0471725692
Description :


This book gives a comprehensive and thorough introduction to ideas and major results of the theory of functions of several variables and of modern vector calculus in two and three dimensions. Clear and easy-to-follow writing style, carefully crafted examples, wide spectrum of applications and numerous illustrations, diagrams, and graphs invite students to use the textbook actively, helping them to both enforce their understanding of the material and to brush up on necessary technical and computational skills. Particular attention has been given to the material that some students find challenging, such as the chain rule, Implicit Function Theorem, parametrizations, or the Change of Variables Theorem.


Author : P. R. Baxandall
Hans Liebeck
Publisher :
Release : 1986
Page : 550
Category : Mathematics
ISBN 13 : 9780198596523
Description :


An introduction to the differential and integral calculus of functions of several variables for students wanting more than a superficial account of the subject. Topics covered include inverse function theorem, the implicit function theorem, and the integration theorems of Green, Stokes, and Gauss.


Author : Thomas H. Barr
Publisher : Pearson College Division
Release : 2001
Page : 458
Category : Mathematics
ISBN 13 :
Description :


This brief book presents an accessible treatment of multivariable calculus with an early emphasis on linear algebra as a tool. Its organization draws strong analogies with the basic ideas of elementary calculus (derivative, integral, and fundamental theorem). Traditional in approach, it is written with an assumption that the student reader may have computing facilities for two- and three-dimensional graphics, and for doing symbolic algebra. KEY TOPICS: Chapter topics include coordinate and vector geometry, differentiation, applications of differentiation, integration, and fundamental theorems. MARKET: For those with knowledge of introductory calculus in a wide range of disciplines including--but not limited to--mathematics, engineering, physics, chemistry, and economics.


Author : Antonio Galbis
Manuel Maestre
Publisher : Springer Science & Business Media
Release : 2012-03-29
Page : 375
Category : Mathematics
ISBN 13 : 1461422000
Description :


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 : Bill Cox
W. Cox
Publisher : Butterworth-Heinemann
Release : 1998
Page : 244
Category : Computers
ISBN 13 : 0340677414
Description :


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.


Author : Jerrold E. Marsden
Anthony Tromba
Publisher :
Release : 2012
Page : 545
Category : Mathematics
ISBN 13 : 9781429224048
Description :


This vector calculus text helps students gain a solid, intuitive understanding of this important subject. The book's careful balance between theory, application, and historical development, provides readers with insights into how mathematics progresses and is in turn influenced by the natural world. A special feature of this textbook is the early introduction of vector fields, divergence and curl in Chapter 4, before integration. The new edition offers a streamlined, contemporary design, an increased number of practice exercises, and content changes based on reviewer feedback, giving this classic text a modern appeal.


Author : Jerrold Franklin
Publisher : Courier Dover Publications
Release : 2020-02-12
Page : 112
Category : Mathematics
ISBN 13 : 0486835901
Description :


This concise text is a workbook for using vector calculus in practical calculations and derivations. Part One briefly develops vector calculus from the beginning; Part Two consists of answered problems. 2020 edition.


Author : Jerrold E. Marsden
Anthony Tromba
Publisher : W. H. Freeman
Release : 2011-12-16
Page : 545
Category : Mathematics
ISBN 13 : 9781429215084
Description :



Author : Susan Jane Colley
Publisher : Pearson College Division
Release : 2012
Page : 603
Category : Mathematics
ISBN 13 : 9780321780652
Description :


Normal 0 false false false Vector Calculus, Fourth Edition, uses the language and notation of vectors and matrices to teach multivariable calculus. It is ideal for students with a solid background in single-variable calculus who are capable of thinking in more general terms about the topics in the course. This text is distinguished from others by its readable narrative, numerous figures, thoughtfully selected examples, and carefully crafted exercise sets. Colley includes not only basic and advanced exercises, but also mid-level exercises that form a necessary bridge between the two.


Author : Alan Macdonald
Publisher : Createspace Independent Pub
Release : 2012
Page : 198
Category : Mathematics
ISBN 13 : 9781480132450
Description :


This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. It is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one. Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways. Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world. Differential geometry is used today in many disciplines. A final chapter is devoted to it. Visit the book's web site: http: //faculty.luther.edu/ macdonal/vagc to download the table of contents, preface, and index. This is a third printing, corrected and slightly revised. From a review of Linear and Geometric Algebra Alan Macdonald's text is an excellent resource if you are just beginning the study of geometric algebra and would like to learn or review traditional linear algebra in the process. The clarity and evenness of the writing, as well as the originality of presentation that is evident throughout this text, suggest that the author has been successful as a mathematics teacher in the undergraduate classroom. This carefully crafted text is ideal for anyone learning geometric algebra in relative isolation, which I suspect will be the case for many readers. -- Jeffrey Dunham, William R. Kenan Jr. Professor of Natural Sciences, Middlebury College


Author : Paul C. Matthews
Publisher : Springer Science & Business Media
Release : 2000-01-14
Page : 182
Category : Mathematics
ISBN 13 : 9783540761808
Description :


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.


Author : Alice Gorguis
Publisher : Xlibris Corporation
Release : 2013-07-31
Page : 120
Category : Mathematics
ISBN 13 : 1483672581
Description :


This text is intended for a one-semester course in the Calculus of functions of several variables and vector analysis taught at college level. This course is, normally known as , vector calculus, or multi variable calculus, or simply calculus-III. The course usually is preceded by a beginning course in linear algebra. The prerequisite for this course is the knowledge of the fundamen- tal of one-variable calculus, differentiation and integration of the standard functions. The text includes most of the basic theories as well as many related examples and problems. There are many exercises throughout the text, which in my experience are more than enough for a semester course in this subject. I include enough examples for each topics in each section to illustrate and help the student to practice his/her skills. Also, added problems that ask the student to reflect on and explore in his/her own words some of the important ideas of Vector Calculus. I have included material enough to be covered during a simple semester with- out a hassle, and it should be possible to work through the entire book with reasonable care. Most of the exercises are relatively routine computations to moderate and productive problems, to help the students understand the concept of each topic. Each section in a chapter is concluded with a set of exercises that review and extend the ideas that was introduced in the chapter, or section. Computer softwares were not included in this book. Most of the exercises can be solved easily by hand, but I advise the students to use Mathematica, or Maple to graph the functions in each problem to visualize the problem, and understand it better. Some of the homework might require the use of Mathematica.


Author : Anil Kumar Sharma
Publisher : Discovery Publishing House
Release : 2010
Page : 306
Category : Vector analysis
ISBN 13 : 9788183560948
Description :


Contents: Differentiation and Integration of Vectors, Multiple Vectors, Gradient, Divergence and Curl, Green s Gauss s and Stoke s Theorem.


Author : Dr T.K.V. Iyengar & Dr B. Krishna Gandhi & S. Ranganadham & Dr M.V.S.S.N. Prasad
Publisher : S. Chand Publishing
Release :
Page :
Category : Science
ISBN 13 : 9352838262
Description :


In this book, how to solve such type equations has been elaborately described. In this book, vector differential calculus is considered, which extends the basic concepts of (ordinary) differential calculus, such as, continuity and differentiability to vector functions in a simple and natural way. This book comprises previous question papers problems at appropriate places and also previous GATE questions at the end of each chapter for the


Author : Zine Boudhraa
Sanjay Rai
Publisher : World Scientific
Release : 2020-07-24
Page : 252
Category : Mathematics
ISBN 13 : 9811222584
Description :


Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.


Author : Steven Tan
Publisher : Lulu.com
Release :
Page :
Category :
ISBN 13 : 1387758624
Description :



Author : Kesra Nermend
Publisher : Springer Science & Business Media
Release : 2009-04-29
Page : 174
Category : Business & Economics
ISBN 13 : 9783790821796
Description :


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.


Author : J N Sharma
Publisher : Krishna Prakashan Media
Release : 1976
Page :
Category :
ISBN 13 :
Description :



Author : ZINE. RAI BOUDHRAA (SANJAY. QUINN, TERRANCE J.)
Terrance J. Quinn (Professor of mathematics)
Publisher : World Scientific Publishing Company
Release : 2020
Page : 250
Category : Mathematics
ISBN 13 : 9789811222566
Description :


Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.