Applied exterior calculus

This book gives an applied introduction to exterior calculus for upper division undergraduates and beginning graduate students. Development is operational with an emphasis on computation proficiency and elementary geometric notions. Consideration is limited to local questions. The book also features fully worked out examples and problems with answers. Much of the modern literature, both in mathematics and in the quantified sciences, employs exterior calculus as an expository vehicle. This text provides upper-level undergraduates and graduate students with access to the exterior calculus, developing most of the theory without recourse to global concepts. Using only local notions, the text places moderate demands on students with previous exposure to upper-division algebra and analysis courses.

The three-part treatment begins with coverage of the essential elements of the exterior calculus together with a number of abbreviated applications. The second part deals with specific detailed applications of the exterior calculus-both to group-theoretic questions in nonlinear second-order partial differential equations, and to problems in the calculus of variations. The final part consists of three chapters that provide in-depth studies of physical disciplines via the exterior calculus, consisting of examinations of classical and irreversible thermodynamics, electrodynamics with both electric and magnetic charges, and the modern theory of gauge fields.