Module 1 : A Crash Course in Vectors Lecture 1 : Scalar And Vector FieldsObjectives In this lecture you will learn the followingLearn about the concept of field Know the difference between a scalar field and a vector field. Review your knowledge of vector algebraLearn how an area can be looked upon as a vector Define position vector and study its transformation properties under rotationSCALAR AND VECTOR FIELDS This introductory chapter is a review of mathematical concepts required for the course. It is assumed that the reader is already familiar with elementary vector analysis. Physical quantities that we deal with in electromagnetism can be scalars or vectors. A scalar is an entity which only has a magnitude. Examples of scalars are mass, time, distance, electric charge, electric potential, energy, temperature etc. A vector is characterized by both magnitude and direction. Examples of vectors in physics are displacement, velocity, acceleration, force, electric field, magnetic field etc. A field is a quantity which can be specified everywhere in space as a function of position. The quantity that is specified may be a scalar or a vector. For instance, we can specify the temperature at every point in a room. The room may, therefore, be said to be a region of ``temperature field" which is a scalar field because the temperature is a scalar function of the position. An example of a scalar field in electromagnetism is the electric potential.