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Author: K.T. Leung
Publisher: Hong Kong University Press
ISBN: 9622093604
Category : Mathematics
Languages : en
Pages : 357
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Book Description
This book is the last volume of a three-book series written for Sixth Form students and first-year undergraduates. It introduces the important concepts of finite-dimensional vector spaces through the careful study of Euclidean geometry. In turn, methods of linear algebra are then used in the study of coordinate transformations through which a complete classification of conic sections and quadric surfaces is obtained. The book concludes with a detailed treatment of linear equations in n variables in the language of vectors and matrices. Illustrative examples are included in the main text and numerous exercises are given in each section. The other books in the series are Fundamental Concepts of Mathematics (published 1988) and Polynomials and Equations (published 1992).
Author: K.T. Leung
Publisher: Hong Kong University Press
ISBN: 9622093604
Category : Mathematics
Languages : en
Pages : 357
Get Book Here
Book Description
This book is the last volume of a three-book series written for Sixth Form students and first-year undergraduates. It introduces the important concepts of finite-dimensional vector spaces through the careful study of Euclidean geometry. In turn, methods of linear algebra are then used in the study of coordinate transformations through which a complete classification of conic sections and quadric surfaces is obtained. The book concludes with a detailed treatment of linear equations in n variables in the language of vectors and matrices. Illustrative examples are included in the main text and numerous exercises are given in each section. The other books in the series are Fundamental Concepts of Mathematics (published 1988) and Polynomials and Equations (published 1992).
Author: Gilbert De B. Robinson
Publisher: Courier Corporation
ISBN: 0486481603
Category : Mathematics
Languages : en
Pages : 194
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Book Description
This concise undergraduate-level text explores the relationship between algebra and geometry. Topics include determinants and linear equations, matrices, linear transformations, projective geometry, geometry on the sphere, and much more. An elementary course in plane geometry is the sole requirement, and answers to the exercises appear at the end. 1962 edition.
Author: David Carruthers Murdoch
Publisher: New York : J. Wiley & Sons
ISBN:
Category : Geometry, Analytic
Languages : en
Pages : 320
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Book Description
Author: Melvin Hausner
Publisher: Courier Dover Publications
ISBN: 0486835391
Category : Mathematics
Languages : en
Pages : 417
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Book Description
A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
Author: Jacob T. Schwartz
Publisher: Courier Corporation
ISBN: 9780486420004
Category : Mathematics
Languages : en
Pages : 198
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Book Description
Concise undergraduate text focuses on problem solving, rather than elaborate proofs. The first three chapters present the basics of matrices, including addition, multiplication, and division. In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. 1961 edition. 20 black-and-white illustrations.
Author: Gilbert de B. Robinson
Publisher: Courier Corporation
ISBN: 0486321045
Category : Mathematics
Languages : en
Pages : 194
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Book Description
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: Miroslav Josipović
Publisher: Springer Nature
ISBN: 3030017567
Category : Mathematics
Languages : en
Pages : 241
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Book Description
This book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it, and undergraduate students can master it. The universality, the clear geometric interpretation, the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth.
Author: Michael Mortenson
Publisher: Industrial Press
ISBN: 9780831136550
Category : Technology & Engineering
Languages : en
Pages : 350
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Book Description
Author: Thomas Banchoff
Publisher: Springer Science & Business Media
ISBN: 1461243904
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.
Author: Max Jeger
Publisher: Interscience Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Translation of Einfèuhrung in die vektorielle Geometrie und lineare Algebra (fèur Ingenieure und Naturwissenschafter)
