Vector Analysis Versus Vector Calculus

Author : Antonio Galbis,Manuel Maestre
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 45,6 Mb
Release : 2012-03-29
Category : Mathematics
ISBN : 9781461422006

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Vector Analysis Versus Vector Calculus by Antonio Galbis,Manuel Maestre Pdf

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 : Antonio Galbis,Manuel Maestre
Publisher : Springer
Page : 375 pages
File Size : 51,9 Mb
Release : 2012-03-24
Category : Mathematics
ISBN : 1461421993

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Vector Analysis Versus Vector Calculus by Antonio Galbis,Manuel Maestre Pdf

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 : Springer
Publisher : Unknown
Page : 392 pages
File Size : 45,7 Mb
Release : 2012-03-30
Category : Electronic
ISBN : 1461422019

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Vector Analysis Versus Vector Calculus by Springer Pdf

Author : R. K. Pandey
Publisher : Discovery Publishing House
Page : 192 pages
File Size : 43,5 Mb
Release : 2007
Category : Developmental biology
ISBN : 8183562973

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Vector Analysis by R. K. Pandey Pdf

This book play a major role as basic tools in Differential geometry, Mechanics, Fluid Mathematics. The bulk of the book consists of five chapters on Vector Analysis and its applications. Each chapter is accompanied by a problem set. The problem sets constitute an integral part of the book. Solving the problems will expose you to the geometric, symbolic and numerical features of multivariable calculus. Contents: Algebra of Vectors, Differentiation of Vectors, Gradient Divergence and Curl, Vector Integration, Application of Vector Integration.

Author : Terrance J Quinn,Zine Boudhraa,Sanjay Rai
Publisher : World Scientific
Page : 250 pages
File Size : 42,6 Mb
Release : 2020-07-24
Category : Mathematics
ISBN : 9789811222580

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Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding by Terrance J Quinn,Zine Boudhraa,Sanjay Rai Pdf

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 : Louis Brand
Publisher : Courier Corporation
Page : 306 pages
File Size : 42,5 Mb
Release : 2012-06-22
Category : Mathematics
ISBN : 9780486154848

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Vector Analysis by Louis Brand Pdf

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 : Klaus Jänich
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 54,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475734782

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Vector Analysis by Klaus Jänich Pdf

This book presents modern vector analysis and carefully describes the classical notation and understanding of the theory. It covers all of the classical vector analysis in Euclidean space, as well as on manifolds, and goes on to introduce de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality. The material is accessible to readers and students with only calculus and linear algebra as prerequisites. A large number of illustrations, exercises, and tests with answers make this book an invaluable self-study source.

Author : Durgaprasanna Bhattacharyya
Publisher : Unknown
Page : 104 pages
File Size : 53,6 Mb
Release : 1920
Category : Calculus
ISBN : UOM:39015031083192

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Vector Calculus by Durgaprasanna Bhattacharyya Pdf

Author : Michael J. Crowe
Publisher : Courier Corporation
Page : 306 pages
File Size : 53,8 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 9780486679105

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A History of Vector Analysis by Michael J. Crowe Pdf

Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

Author : Paul C. Matthews
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447105978

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Vector Calculus by Paul C. Matthews Pdf

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 : John Hamal Hubbard,Barbara Burke Hubbard
Publisher : Unknown
Page : 284 pages
File Size : 50,7 Mb
Release : 2009
Category : Algebras, Linear
ISBN : 097157667X

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Student Solution Manual to Accompany the 4th Edition of Vector Calculus, Linear Algebra, and Differential Forms, a Unified Approach by John Hamal Hubbard,Barbara Burke Hubbard Pdf

Author : C. J. Eliezer
Publisher : Courier Dover Publications
Page : 160 pages
File Size : 52,8 Mb
Release : 2016-01-14
Category : Mathematics
ISBN : 9780486809236

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Concise Vector Analysis by C. J. Eliezer Pdf

This concise introduction to the methods and techniques of vector analysis is suitable for college undergraduates in mathematics as well as students of physics and engineering. Rich in exercises and examples, the straightforward presentation focuses on physical ideas rather than mathematical rigor. The treatment begins with a chapter on vectors and vector addition, followed by a chapter on products of vector. Two succeeding chapters on vector calculus cover a variety of topics, including functions of a vector; line, surface, and volume integrals; the Laplacian operator, and more. The text concludes with a survey of standard applications, including Poinsot's central axis, Gauss's theorem, gravitational potential, Green's theorems, and other subjects.

Author : Alice Gorguis
Publisher : Xlibris Corporation
Page : 121 pages
File Size : 48,8 Mb
Release : 2013-07-31
Category : Mathematics
ISBN : 9781483672588

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Vector Calculus by Alice Gorguis Pdf

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 : Stanley J. Miklavcic
Publisher : Springer Nature
Page : 319 pages
File Size : 50,6 Mb
Release : 2020-02-17
Category : Mathematics
ISBN : 9783030334598

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An Illustrative Guide to Multivariable and Vector Calculus by Stanley J. Miklavcic Pdf

This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 48,9 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.