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About Vectors

About Vectors
Author: Banesh Hoffmann
Publisher: Courier Corporation
Total Pages: 150
Release: 2012-05-24
Genre: Mathematics
ISBN: 0486151697
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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.

Vectors and Their Applications

Vectors and Their Applications
Author: Anthony J. Pettofrezzo
Publisher: Courier Corporation
Total Pages: 146
Release: 2012-12-04
Genre: Mathematics
ISBN: 0486148890
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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.

Vectors

Vectors
Author: James Richardson
Publisher: Ausable Press
Total Pages: 126
Release: 2001
Genre: Literary Criticism
ISBN: 9780967266893
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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

Introduction to Matrices and Vectors

Introduction to Matrices and Vectors
Author: Jacob T. Schwartz
Publisher: Courier Corporation
Total Pages: 198
Release: 2012-05-23
Genre: Mathematics
ISBN: 0486143708
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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.

Geometrical Vectors

Geometrical Vectors
Author: Gabriel Weinreich
Publisher: University of Chicago Press
Total Pages: 132
Release: 1998-07-06
Genre: Mathematics
ISBN: 9780226890487
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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.

Vectors in Physics and Engineering

Vectors in Physics and Engineering
Author: Alan Durrant
Publisher: Routledge
Total Pages: 310
Release: 2019-02-25
Genre: Mathematics
ISBN: 1351405551
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This text is an introduction to the use of vectors in a wide range of undergraduate disciplines. It is written specifically to match the level of experience and mathematical qualifications of students entering undergraduate and Higher National programmes and it assumes only a minimum of mathematical background on the part of the reader. Basic mathematics underlying the use of vectors is covered, and the text goes from fundamental concepts up to the level of first-year examination questions in engineering and physics. The material treated includes electromagnetic waves, alternating current, rotating fields, mechanisms, simple harmonic motion and vibrating systems. There are examples and exercises and the book contains many clear diagrams to complement the text. The provision of examples allows the student to become proficient in problem solving and the application of the material to a range of applications from science and engineering demonstrates the versatility of vector algebra as an analytical tool.

A History of Vector Analysis

A History of Vector Analysis
Author: Michael J. Crowe
Publisher: Courier Corporation
Total Pages: 306
Release: 1994-01-01
Genre: Mathematics
ISBN: 0486679101
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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.

Calculus with Vectors

Calculus with Vectors
Author: Jay S. Treiman
Publisher: Springer
Total Pages: 399
Release: 2014-10-30
Genre: Mathematics
ISBN: 3319094386
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Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additionally, the material presented is intentionally non-specific to any software or hardware platform in order to accommodate the wide variety and rapid evolution of tools used. Technology is referenced in the text and is required for a good number of problems.

Introduction to Applied Linear Algebra

Introduction to Applied Linear Algebra
Author: Stephen Boyd
Publisher: Cambridge University Press
Total Pages: 477
Release: 2018-06-07
Genre: Business & Economics
ISBN: 1316518965
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A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

R for Data Science

R for Data Science
Author: Hadley Wickham
Publisher: "O'Reilly Media, Inc."
Total Pages: 521
Release: 2016-12-12
Genre: Computers
ISBN: 1491910364
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Learn how to use R to turn raw data into insight, knowledge, and understanding. This book introduces you to R, RStudio, and the tidyverse, a collection of R packages designed to work together to make data science fast, fluent, and fun. Suitable for readers with no previous programming experience, R for Data Science is designed to get you doing data science as quickly as possible. Authors Hadley Wickham and Garrett Grolemund guide you through the steps of importing, wrangling, exploring, and modeling your data and communicating the results. You'll get a complete, big-picture understanding of the data science cycle, along with basic tools you need to manage the details. Each section of the book is paired with exercises to help you practice what you've learned along the way. You'll learn how to: Wrangle—transform your datasets into a form convenient for analysis Program—learn powerful R tools for solving data problems with greater clarity and ease Explore—examine your data, generate hypotheses, and quickly test them Model—provide a low-dimensional summary that captures true "signals" in your dataset Communicate—learn R Markdown for integrating prose, code, and results