Vectors in Physics: A Practical Guide with Problems and Solutions (Undergraduate Lecture Notes in Physics)

This book provides a rigorous and comprehensive exposition of vectors and vector fields, designed for advanced undergraduate students in physics.It presents detailed derivations of essential vector identities, relations involving quantum vector operators, and vector calculus theorems commonly encountered in undergraduate and graduate physics coursework.A complete catalogue of vector identities-spanning both classical and quantum contexts-is presented using index notation and the Einstein summation convention, fostering fluency with tensorial methods and streamlining complex derivations. Core topics include vector algebra, differential and integral vector calculus, and three-dimensional Taylor expansions, supported by careful treatments of the essential underlying mathematical tools.Advanced subjects-such as the Dirac delta function, Green’s functions, multipole expansions, and Cartesian tensors-are introduced with a balance of formal clarity and pedagogical accessibility.A dedicated ch