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Lecture 1: The meaning of vectors. Because we inhabit a world with more than one spatial dimension, physical phenomena frequently require us to distinguish between. Scalar : a quantity specified by a single number; Vector : a quantity specified by a number (magnitude) and a direction;
•A quantity with magnitude and direction is a vector. •A quantity with magnitude but no direction is a scalar. •Vector addition can be done either graphically or using components. •The sum is called the resultant vector. •Projectile motion is the motion of an object near the Earth’s surface under the influence of gravity.
Vector quantity: quantity with a magnitude and a direction. It can be represented by a vector. Examples: displacement, velocity, acceleration. Same displacement. Displacement does not describe the object’s path.
OUTLINE : 1. INTRODUCING VECTORS. 1.1 Scalars 1.2 Vectors 1.3 Unit vectors 1.4 Vector algebra 1.5 Simple examples. 2. 1.1 Scalars. IA scalar is a quantity with magnitude but no direction, any mathematical entity that can be represented by a number. IExamples: Mass, temperature, energy, charge ...
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.
Vectors. Two vectors are equal if their magnitudes are equal and their directions are the same. The vectors do not have to be in the same place! We add, subtract, and multiply vectors according to laws of vector algebra, which are different from those of ordinary algebra.
1. Revision of vector algebra, scalar product, vector product. 2. Triple products, multiple products, applications to geometry. 3. Differentiation of vector functions, applications to mechanics. 4. Scalar and vector fields. Line, surface and volume integrals, curvilinear co-ordinates . 5. Vector operators — grad, div and curl. 6.
