Αποτελέσματα Αναζήτησης
Introduction to vectors. A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry.
It explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigenvectors and eigenvalues of a linear vector operator are discussed using vector algebra. Topics including Mohr’s algorithm, Hamilton’s theorem and Euler’s theorem are discussed in detail.
triangle law of addition, assigns meaning to Eq. (1.1) and is illustrated in Fig. 1.1. By completing the parallelogram, we see that C =A +B =B +A, (1.2) as shown in Fig. 1.2. In words, vector addition is commutative. For the sum of three vectors D =A +B +C, Fig. 1.3, we may first add A and B: A +B =E. 1
Course Content. •Introduction and revision of elementary concepts, scalar product, vector product. •Triple products, multiple products, applications to geometry. •Differentiation and integration of vector functions of a single variable. •Curvilinear coordinate systems. Line, surface and volume integrals. •Vector operators.
To distinguish between scalars and vectors we will denote scalars by lower case italic type such as a, b, c etc. and denote vectors by lower case boldface type such as u, v, w etc. In handwritten script, this way of distinguishing between vectors and scalars must be modified.
Three numbers are needed to represent the magnitude and direction of a vector quantity in a three dimensional space. These quantities are called vector quantities. Vector quantities also satisfy two distinct operations, vector addition and multiplication of a vector by a scalar.
Basic Concepts. A vector V in the plane or in space is an arrow: it is determined by its length, denoted V and its direction. Two arrows represent the same vector if they have the same length and are parallel (see figure 13.1). We use vectors to represent entities which are described by magnitude and direction.
