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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

Library of Congress subject headings for this publication:

Vector analysis.