Understanding Vector Calculus

Understanding Vector Calculus

Author: Jerrold Franklin

Publisher: Courier Dover Publications

Published: 2021-01-13

Total Pages: 113

ISBN-13: 048684885X

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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.


Vector Calculus

Vector Calculus

Author: Paul C. Matthews

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 189

ISBN-13: 1447105974

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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.


Div, Grad, Curl, and All that

Div, Grad, Curl, and All that

Author: Harry Moritz Schey

Publisher: W W Norton & Company Incorporated

Published: 2005

Total Pages: 163

ISBN-13: 9780393925166

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This new fourth edition of the acclaimed and bestselling Div, Grad, Curl, and All That has been carefully revised and now includes updated notations and seven new example exercises.


Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding

Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding

Author: Terrance J Quinn

Publisher: World Scientific

Published: 2020-07-24

Total Pages: 250

ISBN-13: 9811222584

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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.


Vector Calculus

Vector Calculus

Author: P. R. Baxandall

Publisher:

Published: 2008

Total Pages: 0

ISBN-13: 9780486466200

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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.


Advanced Calculus

Advanced Calculus

Author: Harold M. Edwards

Publisher: Springer Science & Business Media

Published: 1994-01-05

Total Pages: 532

ISBN-13: 9780817637071

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This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.


Vector Analysis

Vector Analysis

Author: Homer E. Newell

Publisher: Courier Corporation

Published: 2012-05-04

Total Pages: 226

ISBN-13: 0486154904

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This text combines the logical approach of a mathematical subject with the intuitive approach of engineering and physical topics. Applications include kinematics, mechanics, and electromagnetic theory. Includes exercises and answers. 1955 edition.


Vector Calculus

Vector Calculus

Author: Miroslav Lovric

Publisher: John Wiley & Sons

Published: 2007-01-03

Total Pages: 638

ISBN-13: 0471725692

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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.


Vector Calculus

Vector Calculus

Author: Jerrold E. Marsden

Publisher: Macmillan

Published: 2003-08

Total Pages: 712

ISBN-13: 9780716749929

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'Vector Calculus' helps students foster computational skills and intuitive understanding with a careful balance of theory, applications, and optional materials. This new edition offers revised coverage in several areas as well as a large number of new exercises and expansion of historical notes.