Vector Calculus

Author: Paul C. Matthews

Publisher: Springer Science & Business Media

ISBN: 1447105974

Category: Mathematics

Page: 182

View: 8778

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.

Vector Calculus

Author: Bill Cox,W. Cox

Publisher: Butterworth-Heinemann

ISBN: 0340677414

Category: Computers

Page: 244

View: 401

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.

Vector Calculus

Author: J N Sharma

Publisher: Krishna Prakashan Media



Page: N.A

View: 5008

Vector calculus

Author: Thomas H. Barr

Publisher: Pearson College Div


Category: Mathematics

Page: 458

View: 3560

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. Chapter topics include coordinate and vector geometry, differentiation, applications of differentiation, integration, and fundamental theorems. For those with knowledge of introductory calculus in a wide range of disciplines including—but not limited to—mathematics, engineering, physics, chemistry, and economics.

Vector calculus

Author: Frederick Warren Bedford,Tryambakeshwar D. Dwivedi

Publisher: McGraw-Hill Companies


Category: Mathematics

Page: 528

View: 1350

Text Book Of Vector Calculus

Author: Anil Kumar Sharma

Publisher: Discovery Publishing House

ISBN: 9788183560948


Page: 306

View: 1986

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

Vector Analysis Versus Vector Calculus

Author: Antonio Galbis,Manuel Maestre

Publisher: Springer Science & Business Media

ISBN: 1461422000

Category: Mathematics

Page: 375

View: 7290

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

Author: Susan Jane Colley

Publisher: N.A


Category: Mathematics

Page: 558

View: 5246

Appropriate for 2nd year courses in multivariable calculus, this is an accessible text with a conceptual and geometric slant that assumes a background in single-variable calculus. The text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus.

Vector Calculus

For College Students

Author: Alice Gorguis

Publisher: Xlibris Corporation

ISBN: 1483672581

Category: Mathematics

Page: 120

View: 8745

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.

Vector Calculus, with Applications to Physics

Author: James Byrnie Shaw

Publisher: Sagwan Press

ISBN: 9781376763232

Category: History

Page: 332

View: 2748

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Vector Calculus in Regional Development Analysis

Comparative Regional Analysis Using the Example of Poland

Author: Kesra Nermend

Publisher: Springer Science & Business Media

ISBN: 9783790821796

Category: Business & Economics

Page: 174

View: 9588

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.

Linear Algebra and Vector Calculus (GTU 2016)

Author: Ravish R Singh,Mukul Bhatt

Publisher: McGraw-Hill Education

ISBN: 9339224787


Page: N.A

View: 1298

Linear Algebra and Vector Calculus is a key area in the study of an engineering course. It is the study of numbers, structures, and associated relationships using rigorously defined literal, numerical, and operational symbols. A sound knowledge of the subject develops analytical skills, thus enabling engineering graduates to solve numerical problems encountered in daily life, as well as apply vector principles to physical problems, particularly in the area of engineering. Features Each topic has been thoroughly covered from the examination point of view. The theory part of the text is explained in a lucid manner. For each topic, problems of all possible combinations have been worked out. This is followed by an exercise with answers. Objective-type questions provided in each chapter help students in mastering concepts. Salient features of the book are summarised below: • Exactly in-sync with the latest GTU syllabus of Linear Algebra and Vector Calculus (2110015) • Lucid writing style and tutorial approach throughout the book, i.e., teach-by-examples • Offers extensive opportunities to students for practice and self-evaluation through numerous step-by-step solved examples and exercises • Application-based problems for better comprehension of concepts • Solved GTU 2015, 2014, 2013, and 2012 examination papers • Exam-oriented rich pedagogy includes 86 Illustrations 400 Solved Examples 300 Exercise Problems

Mathematics for Engineers III

Vector Calculus

Author: Gerd Baumann

Publisher: Oldenbourg Verlag

ISBN: 3486714473

Category: Mathematics

Page: 434

View: 9466

This book is part of a four-volume textbook on Engineering Mathematics for undergraduates. Volume III treats vector calculus and differential equations of higher order. The text uses Mathematica as a tool to discuss and to solve examples from mathematics. The basic use of this language is demonstrated by examples.


Author: Klaus Jänich

Publisher: Springer-Verlag

ISBN: 366210752X

Category: Mathematics

Page: 276

View: 7690

Die Vektoranalysis handelt, in klassischer Darstellung, von Vektorfeldern, den Operatoren Gradient, Divergenz und Rotation, von Linien-, Flächen- und Volumenintegralen und von den Integralsätzen von Gauß, Stokes und Green. In moderner Fassung ist es der Cartansche Kalkül mit dem Satz von Stokes. Das vorliegende Buch vertritt grundsätzlich die moderne Herangehensweise, geht aber auch sorgfältig auf die klassische Notation und Auffassung ein. Das Buch richtet sich an Mathematik- und Physikstudenten ab dem zweiten Studienjahr, die mit den Grundbegriffen der Differential- und Integralrechnung in einer und mehreren Variablen sowie der Topologie vertraut sind. Der sehr persönliche Stil des Autors und die aus anderen Büchern bereits bekannten Lernhilfen, wie: viele Figuren, mehr als 50 kommentierte Übungsaufgaben, über 100 Tests mit Antworten machen, auch diesen Text zum Selbststudium hervorragend geeignet.

Vector Calculus

Author: Miroslav Lovric

Publisher: Wiley

ISBN: 0471725692

Category: Mathematics

Page: 640

View: 9020

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.