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Synopsis
Excerpt from Elements of Vector Analysis: Arranged for the Use of Students in Physics
(The three letters, i, j, k, will make an exception, to be mentioned more particularly hereafter.
2. Def. - Vectors are said to be equal when they are the same both in direction and in magnitude. The reader will observe that this vector equation is the equivalent of three scalar equations.
A vector is said to be equal to zero, when its magnitude is zero. Such vectors may be set equal to one another, irrespectively of any considerations relating to direction.
3. Perhaps the most simple example of a vector is afforded by a directed straight line, as the line drawn from A to B. We may use the notation AB to denote this line as a vector, i. e., to denote its length and direction without regard to its position in other respects. The points A and B may be distinguished as the origin and the terminus of the vector. Since any magnitude may be represented by a length, any vector may be represented by a directed line; and it will often be convenient to use language relating to vectors, which refers to them as thus represented.
Reversal of Direction, Scalar Multiplication and Division.
4. The negative sign (-) reverses the direction of a vector. (Sometimes the sign + may be used to call attention to the fact that the vector has not the negative sign.)
Def. - A vector is said to be multiplied or divided by a scalar when its magnitude is multiplied or divided by the numerical value of the scalar and its direction is either unchanged or reversed according as the scalar is positive or negative. These operations are represented by the same methods as multiplication and division in algebra, and are to be regarded as substantially identical with them. The terms scalar multiplication and scalar division are used to denote multiplication and division by scalars, whether the quantity multiplied or divided is a scalar or a vector.
5. Def. - A un…
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Présentation de l'éditeur
Excerpt from Elements of Vector Analysis: Arranged for the Use of Students in Physics
(The three letters, i, j, k, will make an exception, to be mentioned more particularly hereafter.
2. Def. - Vectors are said to be equal when they are the same both in direction and in magnitude. The reader will observe that this vector equation is the equivalent of three scalar equations.
A vector is said to be equal to zero, when its magnitude is zero. Such vectors may be set equal to one another, irrespectively of any considerations relating to direction.
3. Perhaps the most simple example of a vector is afforded by a directed straight line, as the line drawn from A to B. We may use the notation AB to denote this line as a vector, i. e., to denote its length and direction without regard to its position in other respects. The points A and B may be distinguished as the origin and the terminus of the vector. Since any magnitude may be represented by a length, any vector may be represented by a directed line; and it will often be convenient to use language relating to vectors, which refers to them as thus represented.
Reversal of Direction, Scalar Multiplication and Division.
4. The negative sign (-) reverses the direction of a vector. (Sometimes the sign + may be used to call attention to the fact that the vector has not the negative sign.)
Def. - A vector is said to be multiplied or divided by a scalar when its magnitude is multiplied or divided by the numerical value of the scalar and its direction is either unchanged or reversed according as the scalar is positive or negative. These operations are represented by the same methods as multiplication and division in algebra, and are to be regarded as substantially identical with them. The terms scalar multiplication and scalar division are used to denote multiplication and division by scalars, whether the quantity multiplied or divided is a scalar or a vector.
5. Def. - A un…
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
- ÉditeurForgotten Books
- Date d'édition2020
- ISBN 10 1332010679
- ISBN 13 9781332010677
- ReliureBroché
- Langueanglais
- Nombre de pages89
- Coordonnées du fabricantnon disponible
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EUR 20,28
EUR 1,09 expédition depuis Etats-Unis vers France
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Elements of Vector Analysis Arranged for the Use of Students in Physics Classic Reprint
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Elements of Vector Analysis Arranged for the Use of Students in Physics Classic Reprint
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
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Elements of Vector Analysis: Arranged for the Use of Students in Physics
impression à la demandeVendeur : Forgotten Books, London, Royaume-Uni
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Paperback. Etat : New. Print on Demand. This book delves into the intricate world of vector analysis, a mathematical framework for understanding quantities with both magnitude and direction. Building upon familiar concepts from algebra and geometry, the author develops a unique and powerful notation for expressing relationships between vectors and scalars. This approach offers a fresh perspective on the subject, diverging from traditional treatments found in quaternion theory. Instead, the focus lies on establishing a clear and concise system for manipulating and analyzing vectors, making it particularly well-suited for applications in physics and other scientific fields. Through rigorous definitions and detailed explanations, the book explores fundamental operations such as vector addition, subtraction, multiplication, and differentiation. It goes on to tackle more advanced topics, including surface and line integrals, and delves into the profound connections between vector calculus and the behavior of physical phenomena. Ultimately, this book provides a deep and insightful understanding of vector analysis, equipping readers with the tools to unlock its vast potential in various scientific and mathematical pursuits. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N° de réf. du vendeur 9781332010677_0
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Elements of Vector Analysis: Arranged for the Use of Students in Physics (Classic Reprint)
impression à la demandeVendeur : Revaluation Books, Exeter, Royaume-Uni
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Paperback. Etat : Brand New. 88 pages. 9.00x6.00x0.20 inches. This item is printed on demand. N° de réf. du vendeur zk1332010679
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