A vector space is a set of vectors that satisfies certain properties. We will discuss various concepts in vector spaces, including basis, dimension, and orthogonality.
A typical search for V Balakrishnan Mathematical Physics PDF will yield a document (usually derived from his NPTEL video lectures) covering the following syllabus:
Part 1: Analysis
Part 2: Linear Algebra & Functional Analysis
Part 3: Differential Equations
Part 4: Integral Equations & Transforms
Part 5: Group Theory for Physicists
Vector calculus is a branch of mathematics that deals with the study of vectors and their properties. We will discuss various concepts in vector calculus, including vector algebra, gradient, divergence, and curl.