Harley Flanders.
Differential Forms with Applications to the Physical Sciences.
Dover. 1963
This excellent text introduces the use of exterior differential forms as a
powerful tool in the analysis of a variety of mathematical problems
in the physical and engineering sciences.
Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory,
it is directed primarily to engineers and physical scientists,
but it has also been used successfully to introduce modern differential geometry to students in mathematics.
Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory.