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Author: Jerrold Franklin
Publisher: Courier Dover Publications
Published: 2021-01-13
Total Pages: 113
ISBN-13: 048684885X
DOWNLOAD EBOOKThis 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: Paul C. Matthews
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 189
ISBN-13: 1447105974
DOWNLOAD EBOOKVector 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: P. R. Baxandall
Publisher:
Published: 2008
Total Pages: 0
ISBN-13: 9780486466200
DOWNLOAD EBOOKThis 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.
Author: Terrance J Quinn
Publisher: World Scientific
Published: 2020-07-24
Total Pages: 250
ISBN-13: 9811222584
DOWNLOAD EBOOKBasic 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: Stanley J. Miklavcic
Publisher: Springer Nature
Published: 2020-02-17
Total Pages: 319
ISBN-13: 3030334597
DOWNLOAD EBOOKThis 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: Harry Moritz Schey
Publisher: W W Norton & Company Incorporated
Published: 2005
Total Pages: 163
ISBN-13: 9780393925166
DOWNLOAD EBOOKThis 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.
Author: Homer E. Newell
Publisher: Courier Corporation
Published: 2012-05-04
Total Pages: 226
ISBN-13: 0486154904
DOWNLOAD EBOOKThis 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.
Author: Miroslav Lovric
Publisher: John Wiley & Sons
Published: 2007-01-03
Total Pages: 638
ISBN-13: 0471725692
DOWNLOAD EBOOKThis 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: Michael J. Crowe
Publisher: Courier Corporation
Published: 1994-01-01
Total Pages: 306
ISBN-13: 0486679101
DOWNLOAD EBOOKPrize-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: Antonio Galbis
Publisher: Springer Science & Business Media
Published: 2012-03-29
Total Pages: 383
ISBN-13: 1461422000
DOWNLOAD EBOOKThe 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.
