Jerrold Franklin 
Understanding Vector Calculus 

This concise text was created as a workbook for learning to use vector calculus in practical calculations and derivations.  Its only prerequisite is a familiarity with one-dimensional differential and integral calculus.  Though it often makes use of physical examples, knowledge of physics itself is not required to study the mathematics of vector calculus. The approach is suitable for advanced undergraduates and graduate students in mathematics, physics, and other areas of science. The two-part treatment opens with a brief text that develops vector calculus from the very beginning and then addresses some more detailed applications. Topics include vector differential operators, vector identities, integral theorems, Dirac delta function, Green's functions, general coordinate systems, and dyadics. The second part consists of answered problems, all closely related to the development of vector calculus in the text. Those who study this book and work out the problems will find that rather than memorizing long equations or consulting references, they will be able to work out calculations as they go. Dover original publication.