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.
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ALGEBRAIC NOTATION AND BASIC IDEAS
SCALARS SCALAR PRODUCTS
VECTOR PRODUCTS QUOTIENTS OF VECTORS
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algebraic angle angular displacements angular velocities arrow-headed line segment axes axis base vectors called combine according component vectors Consider contravariant vector couple covariant cross products definition denote diagram dimensions direction cosines entities equal magnitudes Equation 2.3 equilibrium equivalent example Exercise 3.1 fact Figure force F forces acting formula free vectors ft./sec geometrically gyroscope horizontal i x j idea inches instantaneous velocity left-handed length line of action magnitude and direction mathematical means metrical tensor momentum move Note opposite directions origin parallel parallelepiped parallelogram defined parallelogram law particle perpendicular plane position vector projection Prove pure numbers quaternion r x F radians rectangle reference frame relation relative resultant rigid body rotation scalar product shift Show speed starting theorem tion triangle turning effect unit orthogonal triad vector product vectors represented vertically whole numbers write x-axis zero