Vector calculus is the fundamental language of mathematical physics. It provides a way to describe physical quantities like displacement, velocity of a body in straight line motion; electric, magnetic and gravitational fields; the flux of a field through a surface, the mass of a particle, the electric charge, etcetera and the way in which these quantities vary. Many topics in physics can be analysed mathematically using the techniques of vector calculus.
These are my handwritten notes on vector calculus. Here is a listing (and brief description) of the material that is in this set of notes.
Vector addition – In this section, we look at how vectors are added – the triangle law, parallelogram law and polygon law of vector addition. We learn how to find a point \(P\) that divides a line segment \(AB\) into two parts \(AP\), \(PB\) in a fixed ratio. We derive interesting results in Euclidean geometry, for example, the medians of a triangle are concurrent at a point \(G\), the centroid.
Product of two vectors – In this section, we look at scalar and vector products and their geometric interpretation.