Classical Field Theories

This exceptional textbook provides extensive discussions and worked exercises to accompany a field theory course at the advanced undergraduate or beginning graduate level. There are many questions that arise, both philosophical and practical, during a standard course in classical field theory that are addressed here in discussions between an advanced graduate student and her inquisitive undergrad friend. The discussion involves explicitly working out exercises and making pertinent remarks on the results and potential of the developed formalism. The book is ideal for readers who have taken or are taking the classical field theory course so that they already have a mathematical background in vector and tensor calculus and are willing to learn the basics of differential forms and exterior calculus to gain further insight into field theory formulation. The text can also be used to answer what you‘ve always wanted to know but never dared to ask about field theory.