About Vectors (eBook)

Banesh Hoffmann (Autor)

eBook Download: EPUB

2012
134 Seiten
Dover Publications (Verlag)
978-0-486-15169-4 (ISBN)

Infos

No calculus needed, but this is not an elementary book. Introduces vectors, algebraic notation and basic ideas, vector algebra and scalars. Includes 386 exercises.

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From his unusual beginning in "e;Defining a vector"e; to his final comments on "e;What then is a vector?"e; 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.

Autor

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.

Inhalt

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 questions2 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 fields3 VECTOR ALGEBRA 1. Components 2. Unit orthogonal triads 3. Position vectors 4. Coordinates 5. Direction cosines 6. Orthogonal projections 7. Projections of areas4 SCALARS. SCALAR PRODUCTS 1. Units and scalars 2. Scalar products 3. Scalar products and unit orthogonal triads5 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 vectors6 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

Produkt-Details

• Erscheint lt. Verlag: 24.5.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 0-486-15169-7 / 0486151697
• ISBN-13: 978-0-486-15169-4 / 9780486151694