[PDF] Geometry Vector Calculus eBook

Author : Alan Macdonald
Publisher : Createspace Independent Publishing Platform
Page : 0 pages
File Size : 45,92 MB
Release : 2012
Category : Calculus
ISBN : 9781480132450

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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 : Gilbert de B. Robinson
Publisher : Courier Corporation
Page : 194 pages
File Size : 18,93 MB
Release : 2013-10-10
Category : Mathematics
ISBN : 0486321045

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Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.

Author : Melvin Hausner
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 41,23 MB
Release : 2018-10-17
Category : Mathematics
ISBN : 0486835391

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A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.

Author : Paul C. Matthews
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 11,76 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 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.

Author : Michael J. Crowe
Publisher : Courier Corporation
Page : 306 pages
File Size : 16,83 MB
Release : 1994-01-01
Category : Mathematics
ISBN : 0486679101

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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 : Antonio Galbis
Publisher : Springer Science & Business Media
Page : 383 pages
File Size : 11,93 MB
Release : 2012-03-29
Category : Mathematics
ISBN : 1461422000

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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 : Zbigniew Nitecki
Publisher : American Mathematical Soc.
Page : 417 pages
File Size : 21,82 MB
Release : 2018-10-16
Category : Mathematics
ISBN : 1470443600

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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 : C. E. Springer
Publisher : Courier Corporation
Page : 258 pages
File Size : 37,39 MB
Release : 2013-09-26
Category : Mathematics
ISBN : 048632091X

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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.