In Chap. 4 , key mathematical techniques such as three-dimensional Taylor series expansions are used to manipulate vector fields. The concept of the Dirac delta function as a limiting sequence of proper functions is developed. The Dirac delta function is then shown to be of critical importance in generalizing vector calculus formulas to regions that include the origin or where singularities exist. In-chapter examples and end-of-chapter problems are included to reinforce introduced concepts and to give readers a chance to practice the relevant mathematics.