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Author : A. R. Vasishtha
Publisher : Krishna Prakashan Media
Page : 581 pages
File Size : 55,9 Mb
Release : 2024-05-09
Category : Electronic
ISBN : 9788182835375
Author : Alan Macdonald
Publisher : Createspace Independent Publishing Platform
Page : 0 pages
File Size : 55,9 Mb
Release : 2012
Category : Calculus
ISBN : 1480132454
This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. This is the printing of August 2022. The book is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one. Its web page is at faculty.luther.edu/ macdonal/laga. 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. Download the book's table of contents, preface, and index at the book's web site: faculty.luther.edu/ macdonal/vagc. 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 : Zbigniew Nitecki
Publisher : American Mathematical Soc.
Page : 405 pages
File Size : 52,6 Mb
Release : 2018-10-16
Category : Calculus
ISBN : 9781470443603
Calculus in 3D is an accessible, well-written textbook for an honors course in multivariable calculus for mathematically strong first- or second-year university students. The treatment given here carefully balances theoretical rigor, the development of student facility in the procedures and algorithms, and inculcating intuition into underlying geometric principles. The focus throughout is on two or three dimensions. All of the standard multivariable material is thoroughly covered, including vector calculus treated through both vector fields and differential forms. There are rich collections of problems ranging from the routine through the theoretical to deep, challenging problems suitable for in-depth projects. Linear algebra is developed as needed. Unusual features include a rigorous formulation of cross products and determinants as oriented area, an in-depth treatment of conics harking back to the classical Greek ideas, and a more extensive than usual exploration and use of parametrized curves and surfaces. Zbigniew Nitecki is Professor of Mathematics at Tufts University and a leading authority on smooth dynamical systems. He is the author of Differentiable Dynamics, MIT Press; Differential Equations, A First Course (with M. Guterman), Saunders; Differential Equations with Linear Algebra (with M. Guterman), Saunders; and Calculus Deconstructed, AMS.
Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 624 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210689
This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.
Author : Frank M. Tiller
Publisher : Unknown
Page : 374 pages
File Size : 44,5 Mb
Release : 1963
Category : Análisis vectorial
ISBN : UOM:39015015207932
Author : Kevin R. Coombes,Ronald L. Lipsman,Jonathan M. Rosenberg
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461216988
Aiming to "modernise" the course through the integration of Mathematica, this publication introduces students to its multivariable uses, instructs them on its use as a tool in simplifying calculations, and presents introductions to geometry, mathematical physics, and kinematics. The authors make it clear that Mathematica is not algorithms, but at the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The sets of problems give students an opportunity to practice their newly learned skills, covering simple calculations, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numerical integration, and also cover the practice of incorporating text and headings into a Mathematica notebook. The accompanying diskette contains both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students, which can be used with any standard multivariable calculus textbook. It is assumed that students will also have access to an introductory primer for Mathematica.
Author : Theodore Shifrin
Publisher : John Wiley & Sons
Page : 514 pages
File Size : 48,6 Mb
Release : 2004-01-26
Category : Mathematics
ISBN : 9780471526384
Multivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs. * Contains plenty of examples, clear proofs, and significant motivation for the crucial concepts. * Numerous exercises of varying levels of difficulty, both computational and more proof-oriented. * Exercises are arranged in order of increasing difficulty.
Author : R. K. Pandey
Publisher : Discovery Publishing House
Page : 192 pages
File Size : 55,8 Mb
Release : 2007
Category : Developmental biology
ISBN : 8183562973
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 : Antonio Galbis,Manuel Maestre
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 48,6 Mb
Release : 2012-03-29
Category : Mathematics
ISBN : 9781461422006
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 : Anders Kock
Publisher : Cambridge University Press
Page : 245 pages
File Size : 55,8 Mb
Release : 2006-06-22
Category : Mathematics
ISBN : 9780521687386
This book, first published in 2006, details how limit processes can be represented algebraically.
Author : Terrance J Quinn,Zine Boudhraa,Sanjay Rai
Publisher : World Scientific
Page : 250 pages
File Size : 50,9 Mb
Release : 2020-07-24
Category : Mathematics
ISBN : 9789811222580
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 : C. E. Springer
Publisher : Courier Corporation
Page : 256 pages
File Size : 49,5 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486320915
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
Author : F. W. Bedford,Frederick Warren Bedford,Tryambakeshwar D. Dwivedi
Publisher : McGraw-Hill Companies
Page : 552 pages
File Size : 43,9 Mb
Release : 1970
Category : Vector analysis
ISBN : UOM:39076006351493
Author : Sarhan M. Musa
Publisher : Mercury Learning and Information
Page : 491 pages
File Size : 47,8 Mb
Release : 2023-02-08
Category : Mathematics
ISBN : 9781683929178
This book is designed primarily for undergraduates in mathematics, engineering, and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. Furthermore, it can be used to impower the mathematical knowledge for Artificial Intelligence (AI) concepts. It also provides numerous computer illustrations and tutorials using MATLAB® and Maple®, that bridge the gap between analysis and computation. Partial solutions and instructor ancillaries available for use as a textbook. FEATURES Includes numerous computer illustrations and tutorials using MATLAB®and Maple® Covers the major topics of vector geometry, differentiation, and integration in several variables Instructors’ ancillaries available upon adoption
Author : Gerard Walschap
Publisher : Walter de Gruyter GmbH & Co KG
Page : 365 pages
File Size : 50,7 Mb
Release : 2015-07-01
Category : Mathematics
ISBN : 9783110369540
This book offers an introduction to differential geometry for the non-specialist. It includes most of the required material from multivariable calculus, linear algebra, and basic analysis. An intuitive approach and a minimum of prerequisites make it a valuable companion for students of mathematics and physics. The main focus is on manifolds in Euclidean space and the metric properties they inherit from it. Among the topics discussed are curvature and how it affects the shape of space, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.