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1 Beaverton Mathematics- Advanced

About Vectors

by

About Vectors Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

No calculus needed, but this is not an elementary book. Introduces vectors, algebraic notation and basic ideas, vector algebra, and scalars. Covers areas of parallelograms, triple products, moments, angular velocity, areas and vectorial addition, and more. Concludes with discussion of tensors. Includes 386 exercises.

About the Author

Banesh Hoffmann (1906-86) received his PhD from Princeton University. At Princeton's Institute for Advanced Study, he collaborated with Albert Einstein and Leopold Infeld on the classic paper "Gravitational Equations and the Problem of Motion." Hoffmann taught at Queens College for more than 40 years.

Table of Contents

1

  INTRODUCING VECTORS

  1. Defining a vector

  2. The parallelogram law

  3. Journeys are not vectors

  4. Displacements are vectors

  5. Why vectors are important

  6. The curious incident of the vectorial tribe

  7. Some awkward questions

2

  ALGEBRAIC NOTATION AND BASIC IDEAS

  1. Equality and addition

  2. Multiplication by numbers

  3. Subtraction

  4. Speed and velocity

  5. Acceleration

  6. Elementary statics in two dimensions

  7. Couples

  8. The problem of location. Vector fields

3

  VECTOR ALGEBRA

  1. Components

  2. Unit orthogonal triads

  3. Position vectors

  4. Coordinates

  5. Direction cosines

  6. Orthogonal projections

  7. Projections of areas

4

  SCALARS. SCALAR PRODUCTS

  1. Units and scalars

  2. Scalar products

  3. Scalar products and unit orthogonal triads

5

  VECTOR PRODUCTS. QUOTIENTS OF VECTORS

  1. Areas of parallelograms

  2. "Cross products of i, j, and k"

  3. "Components of cross products relative to i, j, and k"

  4. Triple products

  5. Moments

  6. Angular displacements

  7. Angular velocity

  8. Momentum and angular momentum

  9. Areas and vectorial addition

  10. Vector products in right- and left-handed reference frames

  11. Location and cross products

  12. Double cross

  13. Division of vectors

6

  TENSORS

  1. How components of vectors transform

  2. The index notation

  3. The new concept of a vector

  4. Tensors

  5. Scalars. Contraction

  6. Visualizing tensors

  7. Symmetry and antisymmetry. Cross products

  8. Magnitudes. The metrical tensor

  9. Scalar products

  10. What then is a vector?

  INDEX

Product Details

ISBN:
9780486604893
Author:
Hoffmann, Banesh
Publisher:
Dover Publications
Author:
Mathematics
Author:
Hoffmann, Banesh
Location:
New York :
Subject:
Calculus
Subject:
Vector Analysis
Subject:
General Mathematics
Subject:
Mathematics : Vector Analysis
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
19750631
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
144
Dimensions:
8.5 x 5.38 in 0.47 lb

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Related Subjects

Humanities » Philosophy » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Vector Analysis

About Vectors Used Trade Paper
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Product details 144 pages Dover Publications - English 9780486604893 Reviews:
"Synopsis" by ,
No calculus needed, but this is not an elementary book. Introduces vectors, algebraic notation and basic ideas, vector algebra, and scalars. Covers areas of parallelograms, triple products, moments, angular velocity, areas and vectorial addition, and more. Concludes with discussion of tensors. Includes 386 exercises.

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