Search Results for "vector-and-geometric-calculus"

Vector and Geometric Calculus

Vector and Geometric Calculus

  • Author: Alan Macdonald
  • Publisher: Createspace Independent Pub
  • ISBN: 9781480132450
  • Category: Mathematics
  • Page: 198
  • View: 4354
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This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. It is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one. 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. Visit the book's web site: http: //faculty.luther.edu/ macdonal/vagc to download the table of contents, preface, and index. This is a third printing, corrected and slightly revised. 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

Clifford Algebra to Geometric Calculus

Clifford Algebra to Geometric Calculus

A Unified Language for Mathematics and Physics

  • Author: D. Hestenes,Garret Sobczyk
  • Publisher: Springer Science & Business Media
  • ISBN: 9400962924
  • Category: Science
  • Page: 314
  • View: 8471
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Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebm' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.

Geometry & Vector Calculus

Geometry & Vector Calculus

  • Author: A. R. Vasishtha
  • Publisher: Krishna Prakashan Media
  • ISBN: 8182835372
  • Category:
  • Page: N.A
  • View: 683
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Vector Calculus, Linear Algebra, and Differential Forms

Vector Calculus, Linear Algebra, and Differential Forms

A Unified Approach

  • Author: John H. Hubbard,Barbara Burke Hubbard
  • Publisher: N.A
  • ISBN: 9780136574460
  • Category: Mathematics
  • Page: 687
  • View: 4527
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This text covers most of the standard topics in multivariate calculus and part of a standard first course in linear algebra. It focuses on underlying ideas, integrates theory and applications, offers a host of pedagogical aids, and features coverage of differential forms and an emphasis on numerical methods to prepare students for modern applications of mathematics. *Covers important material that is usually omitted. *Presents more difficult and longer proofs (e.g. Proofs of the Kantorovitch theorem, the implicit function theorem) in an appendix. *Makes a careful distinction between vectors and points. *Features an innovative approach to the implicit function theorem and inverse function theorem using Newton's method. *Always emphasizes the underlying meaning - what is really going on (generally, with a geometric interpretation) - eg. The chain rule is a composition of linear transformations; the point of the implicit function theorem is to guarantee that under certain circumstances, non-linear equations have solutions. *Integrates theory and applications. *Begins most chapters with a treatment of a linear problem and then shows how the 7 methods apply to corresponding non-linear p

Geometric Algebra Applications Vol. I

Geometric Algebra Applications Vol. I

Computer Vision, Graphics and Neurocomputing

  • Author: Eduardo Bayro-Corrochano
  • Publisher: Springer
  • ISBN: 3319748300
  • Category: Computers
  • Page: 742
  • View: 1968
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The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.

Vector Analysis

Vector Analysis

  • Author: R. K. Pandey
  • Publisher: Discovery Publishing House
  • ISBN: 9788183562973
  • Category: Vector analysis
  • Page: 178
  • View: 9603
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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.

Fundamentals of Grid Generation

Fundamentals of Grid Generation

  • Author: Stanley Steinberg
  • Publisher: CRC Press
  • ISBN: 9780849389870
  • Category: Mathematics
  • Page: 304
  • View: 3959
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Fundamentals of Grid Generation is an outstanding text/reference designed to introduce students in applied mathematics, mechanical engineering, and aerospace engineering to structured grid generation. It provides excellent reference material for practitioners in industry, and it presents new concepts to researchers. Readers will learn what boundary-conforming grids are, how to generate them, and how to devise their own methods. The text is written in a clear, intuitive style that doesn't get bogged down in unnecessary abstractions. Topics covered include planar, surface, and 3-D grid generation; numerical techniques; solution adaptivity; the finite volume approach to discretization of hosted equations; concepts from elementary differential geometry; and the transformation of differential operators to general coordinate systems. The book also reviews the literature on algebraic, conformal, orthogonal, hyperbolic, parabolic, elliptic, biharmonic, and variational approaches to grid generation. This unique volume closes with the author's original methods of variational grid generation.

New Foundations in Mathematics

New Foundations in Mathematics

The Geometric Concept of Number

  • Author: Garret Sobczyk
  • Publisher: Springer Science & Business Media
  • ISBN: 0817683844
  • Category: Mathematics
  • Page: 370
  • View: 7248
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The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.

Geometric Calculus

Geometric Calculus

According to the Ausdehnungslehre of H. Grassmann

  • Author: Giuseppe Peano
  • Publisher: Springer Science & Business Media
  • ISBN: 1461221323
  • Category: Mathematics
  • Page: 150
  • View: 7989
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Calcolo Geometrico, G. Peano's first publication in mathematical logic, is a model of expository writing, with a significant impact on 20th century mathematics. Kannenberg's lucid and crisp translation, Geometric Calculus, will appeal to historians of mathematics, researchers, graduate students, and general readers interested in the foundations of mathematics and the development of a formal logical language. The book has never been reprinted in its entirety, and only two chapters have ever been translated into English. Readers of this valuable translation will gain insight into the work of a distinguished mathematician and founder of mathematical logic.

Advanced Calculus

Advanced Calculus

Third Edition

  • Author: R. Creighton Buck
  • Publisher: Waveland Press
  • ISBN: 147860820X
  • Category: Mathematics
  • Page: 622
  • View: 8743
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Demonstrating analytical and numerical techniques for attacking problems in the application of mathematics, this well-organized, clearly written text presents the logical relationship and fundamental notations of analysis. Buck discusses analysis not solely as a tool, but as a subject in its own right. This skill-building volume familiarizes students with the language, concepts, and standard theorems of analysis, preparing them to read the mathematical literature on their own. The text revisits certain portions of elementary calculus and gives a systematic, modern approach to the differential and integral calculus of functions and transformations in several variables, including an introduction to the theory of differential forms. The material is structured to benefit those students whose interests lean toward either research in mathematics or its applications.