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Author: Rishi Kumar Jha, Anshuman Singh Publisher: Notion Press ISBN: 1642493600 Category : Mathematics Languages : en Pages : 101
Book Description
The book, Elements of Vector Algebra, is written for high school and engineering students who wish to gain elementary knowledge of vectors. Algebraic and geometric interpretations of vectors, along with examples and exercises in mathematical and engineering applications, have been provided to help develop a clear understanding of the vector concepts. The book provides thorough treatment of elementary vector operators and their algebra, product of two and three vectors and various engineering and scientific applications involving these concepts. At the end of each chapter, comprehensive exercises with varying degrees of difficulty have been provided to further hone the concepts. Interdisciplinary problems that have practical applications can also be found in this book catering to the ever-extending scope of vector algebra.
Author: Rishi Kumar Jha, Anshuman Singh Publisher: Notion Press ISBN: 1642493600 Category : Mathematics Languages : en Pages : 101
Book Description
The book, Elements of Vector Algebra, is written for high school and engineering students who wish to gain elementary knowledge of vectors. Algebraic and geometric interpretations of vectors, along with examples and exercises in mathematical and engineering applications, have been provided to help develop a clear understanding of the vector concepts. The book provides thorough treatment of elementary vector operators and their algebra, product of two and three vectors and various engineering and scientific applications involving these concepts. At the end of each chapter, comprehensive exercises with varying degrees of difficulty have been provided to further hone the concepts. Interdisciplinary problems that have practical applications can also be found in this book catering to the ever-extending scope of vector algebra.
Author: Stephen Boyd Publisher: Cambridge University Press ISBN: 1316518965 Category : Business & Economics Languages : en Pages : 477
Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author: John Browne Publisher: John M Browne ISBN: 1479197637 Category : Mathematics Languages : en Pages : 589
Book Description
Grassmann Algebra Volume 1: Foundations Exploring extended vector algebra with Mathematica Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, … multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be defined. Theorems of Projective Geometry are simply formulae involving these entities and the dual products. By introducing the (orthogonal) complement operation, the scalar product of vectors may be extended to the interior product of multivectors, which in this more general case may no longer result in a scalar. The notion of the magnitude of vectors is extended to the magnitude of multivectors: for example, the magnitude of the exterior product of two vectors (a bivector) is the area of the parallelogram formed by them. To develop these foundational concepts, we need only consider entities which are the sums of elements of the same grade. This is the focus of this volume. But the entities of Grassmann algebra need not be of the same grade, and the possible product types need not be constricted to just the exterior, regressive and interior products. For example quaternion algebra is simply the Grassmann algebra of scalars and bivectors under a new product operation. Clifford, geometric and higher order hypercomplex algebras, for example the octonions, may be defined similarly. If to these we introduce Clifford's invention of a scalar which squares to zero, we can define entities (for example dual quaternions) with which we can perform elaborate transformations. Exploration of these entities, operations and algebras will be the focus of the volume to follow this. There is something fascinating about the beauty with which the mathematical structures that Hermann Grassmann discovered describe the physical world, and something also fascinating about how these beautiful structures have been largely lost to the mainstreams of mathematics and science. He wrote his seminal Ausdehnungslehre (Die Ausdehnungslehre. Vollständig und in strenger Form) in 1862. But it was not until the latter part of his life that he received any significant recognition for it, most notably by Gibbs and Clifford. In recent times David Hestenes' Geometric Algebra must be given the credit for much of the emerging awareness of Grassmann's innovation. In the hope that the book be accessible to scientists and engineers, students and professionals alike, the text attempts to avoid any terminology which does not make an essential contribution to an understanding of the basic concepts. Some familiarity with basic linear algebra may however be useful. The book is written using Mathematica, a powerful system for doing mathematics on a computer. This enables the theory to be cross-checked with computational explorations. However, a knowledge of Mathematica is not essential for an appreciation of Grassmann's beautiful ideas.
Author: P.M. Cohn Publisher: Routledge ISBN: 1351452843 Category : Mathematics Languages : en Pages : 241
Book Description
This volume presents a thorough discussion of systems of linear equations and their solutions. Vectors and matrices are introduced as required and an account of determinants is given. Great emphasis has been placed on keeping the presentation as simple as possible, with many illustrative examples. While all mathematical assertions are proved, the student is led to view the mathematical content intuitively, as an aid to understanding.The text treats the coordinate geometry of lines, planes and quadrics, provides a natural application for linear algebra and at the same time furnished a geometrical interpretation to illustrate the algebraic concepts.
Author: A. I. Borisenko Publisher: Courier Corporation ISBN: 0486131904 Category : Mathematics Languages : en Pages : 292
Book Description
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Author: Hari Kishan Publisher: Atlantic Publishers & Dist ISBN: 9788126908066 Category : Calculus Languages : en Pages : 452
Book Description
The Present Book Aims At Providing A Detailed Account Of The Basic Concepts Of Vectors That Are Needed To Build A Strong Foundation For A Student Pursuing Career In Mathematics. These Concepts Include Addition And Multiplication Of Vectors By Scalars, Centroid, Vector Equations Of A Line And A Plane And Their Application In Geometry And Mechanics, Scalar And Vector Product Of Two Vectors, Differential And Integration Of Vectors, Differential Operators, Line Integrals, And Gauss S And Stoke S Theorems.It Is Primarily Designed For B.Sc And B.A. Courses, Elucidating All The Fundamental Concepts In A Manner That Leaves No Scope For Illusion Or Confusion. The Numerous High-Graded Solved Examples Provided In The Book Have Been Mainly Taken From The Authoritative Textbooks And Question Papers Of Various University And Competitive Examinations Which Will Facilitate Easy Understanding Of The Various Skills Necessary In Solving The Problems. In Addition, These Examples Will Acquaint The Readers With The Type Of Questions Usually Set At The Examinations. Furthermore, Practice Exercises Of Multiple Varieties Have Also Been Given, Believing That They Will Help In Quick Revision And In Gaining Confidence In The Understanding Of The Subject. Answers To These Questions Have Been Verified Thoroughly. It Is Hoped That A Thorough Study Of This Book Would Enable The Students Of Mathematics To Secure High Marks In The Examinations. Besides Students, The Teachers Of The Subject Would Also Find It Useful In Elucidating Concepts To The Students By Following A Number Of Possible Tracks Suggested In The Book.
Author: Michael J. Crowe Publisher: Courier Corporation ISBN: 0486679101 Category : Mathematics Languages : en Pages : 306
Book Description
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: Melvin Hausner Publisher: Courier Dover Publications ISBN: 0486835391 Category : Mathematics Languages : en Pages : 417
Book Description
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: Rishi Kumar Jha, Anshuman Singh
Author: Rishi Kumar Jha, Anshuman Singh
Author: Stephen Boyd
Author: Ludwik Silberstein
Author: Josiah Willard Gibbs
Author: John Browne
Author: P.M. Cohn
Author: A. I. Borisenko
Author: Hari Kishan
Author: Michael J. Crowe
Author: Melvin Hausner