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| Author | : Gilbert de B. Robinson |
| Publisher | : Courier Corporation |
| Total Pages | : 194 |
| Release | : 2013-10-10 |
| Genre | : Mathematics |
| ISBN | : 0486321045 |
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 |
| Total Pages | : 417 |
| Release | : 2018-10-17 |
| Genre | : Mathematics |
| ISBN | : 0486835391 |
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 | : Gabriel Weinreich |
| Publisher | : University of Chicago Press |
| Total Pages | : 132 |
| Release | : 1998-07-06 |
| Genre | : Mathematics |
| ISBN | : 9780226890487 |
Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition. Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.
| Author | : Seymour Schuster |
| Publisher | : |
| Total Pages | : 213 |
| Release | : 1962-01-01 |
| Genre | : Geometry |
| ISBN | : 9780471764946 |
| Author | : Miroslav Josipović |
| Publisher | : Springer Nature |
| Total Pages | : 258 |
| Release | : 2019-11-22 |
| Genre | : Mathematics |
| ISBN | : 3030017567 |
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 | : Serge Lang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 624 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210682 |
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 | : David Carruthers Murdoch |
| Publisher | : New York : J. Wiley & Sons |
| Total Pages | : 320 |
| Release | : 1966 |
| Genre | : Geometry, Analytic |
| ISBN | : |
| Author | : D. E. Rutherford |
| Publisher | : Courier Corporation |
| Total Pages | : 148 |
| Release | : 2012-04-27 |
| Genre | : Mathematics |
| ISBN | : 048615453X |
This text offers both a clear view of the abstract theory as well as a concise survey of the theory's applications to various branches of pure and applied mathematics. 1957 edition.
| Author | : Anthony J. Pettofrezzo |
| Publisher | : Courier Corporation |
| Total Pages | : 146 |
| Release | : 2012-12-04 |
| Genre | : Mathematics |
| ISBN | : 0486148890 |
Geared toward undergraduate students, this text illustrates the use of vectors as a mathematical tool in plane synthetic geometry, plane and spherical trigonometry, and analytic geometry of two- and three-dimensional space. Its rigorous development includes a complete treatment of the algebra of vectors in the first two chapters. Among the text's outstanding features are numbered definitions and theorems in the development of vector algebra, which appear in italics for easy reference. Most of the theorems include proofs, and coordinate position vectors receive an in-depth treatment. Key concepts for generalized vector spaces are clearly presented and developed, and 57 worked-out illustrative examples aid students in mastering the concepts. A total of 258 exercise problems offer supplements to theories or provide the opportunity to reinforce the understanding of applications, and answers to odd-numbered exercises appear at the end of the book.
| Author | : Alan Macdonald |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 0 |
| Release | : 2012 |
| Genre | : Calculus |
| ISBN | : 9781480132450 |
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
