About Vectors

From his unusual beginning in "Defining a vector" to his final comments on "What then is a vector?" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar products; vector products and quotients of vectors; and tensors. The author writes with a fresh, challenging style, making all complex concepts readily understandable. Nearly 400 exercises appear throughout the text. Professor of Mathematics at Queens College at the City University of New York, Banesh Hoffmann is also the author of The Strange Story of the Quantum and other important books. This volume provides much that is new for both students and their instructors, and it will certainly generate debate and discussion in the classroom.

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.

Realizing that matrices can be a confusing topic for the beginner, the author of this undergraduate text has made things as clear as possible by focusing on problem solving, rather than elaborate proofs. He begins with the basics, offering students a solid foundation for the later chapters on using special matrices to solve problems.The first three chapters present the basics of matrices, including addition, multiplication, and division, and give solid practice in the areas of matrix manipulation where the laws of algebra do not apply. In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. He also covers special matrices — including complex numbers, quaternion matrices, and matrices with complex entries — and transpose matrices; the trace of a matrix; the cross product of matrices; eigenvalues and eigenvectors; and infinite series of matrices. Exercises at the end of each section give students further practice in problem solving. Prerequisites include a background in algebra, and in the later chapters, a knowledge of solid geometry. The book was designed as an introductory text for college freshmen and sophomores, but selected chapters can also be used to supplement advanced high school classes. Professionals who need a better understanding or review of the subject will also benefit from this concise guide.

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.

From one of the most original voices in imaginative fiction comes a stunning novel of suspense and speculation, as a scientist seeking to uncover the mystery of human consciousness finds himself in a desperate search for immortality. Dr. Jonathan Briggs is a gifted neuroscientist researching the existence of the human soul. Working at one of the world’s top facilities, he has access to the latest technology. He also has the enthusiastic support of his lover, Alynn Reed, who made her fortune as a creator of virtual reality games that have broken every barrier. Alynn believes in reincarnation, which Jonathan scoffs at--until he begins to note strange anomalies in his research. Then Jonathan’s life is suddenly, shockingly turned upside down. No longer the dispassionate scientist, he begins a fevered, reckless effort to go beyond belief to proof. Ridiculed by his colleagues and the tabloid media, hounded by the police, Jonathan finds himself in a frenzied race against time, memory, and his own mortality. As he journeys deeper into the labyrinth of the human psyche, he moves nearer the place where past and future intersect, identities mingle, and death is the beginning of the most amazing adventure of all.

James Richardson is one of the finest poets now writing, and the best contemporary practitioner of the art of aphorism."--Publishers Weekly "Not since the appearance of W. S. Merwin's translations and adaptations of aphorisms in Asian Figures, some thirty years ago, has an American poet managed to put down so much delightful and compelling wisdom."--American Literary Review "No one theme or moral pervades these tesserae of specificity. Rather, Richardson's elegant compression invites the reader to fill in the blanks with personal experience... Richardson's knack for the quintessential, sustained for more than a hundred pages, left me satisfied yet hungry for more."-- Times Literary Supplement "Readers will be obsessed by this book; they will memorize passages, give copies to friends, proselytize. That's because Vectors so generously provides the best that poetry can offer. It is a masterpiece of practicality, beauty, and solace."-- Boston Review "James Richardson's Vectors... penetrates to the very heart of human nature. I stand looking in the mirror, alert to my own foibles, shaking my head as I tolerate what I know he knows about who I am."-- The Georgia Review "Almost every entry... introduces a new insight, provides a revelation, supplies a surprise... it is a book one wants to spend time with, a wonderfully friendly book, generous, witty and entertaining."-- Gulf Coast "Vectors is the kind of book you read, reread, thumb through, and pick up several extra copies because you want to share the joy you found in perusing it with friends."-- Barrow Street "James Richardson's Vectors is a book of subversive wonders. Stunningly precise, these brilliant aphorisms and ten-second essays show a mind assessing, reassessing, discovering, and interrogating assumptions in ways that feel diamond-sharp, at once good-natured, quietly sly at times, and always, always, very shrewd. 'It can never be satisfied, the mind, never,' wrote Wallace Stevens. Vectors is a remarkable testament to such questing, vivid minding, as these aphorisms alight on everything from the nature of perception, to God, success, fear, shame, self-consciousness, love and friendship."--Laurie Sheck

Ideal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. The first unit deals with basic formulation, both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation, and curvilinear coordinate systems like spherical polar and parabolic systems and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.

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.