Vector Integration, Potential Theory

Celso Melchiades Doria ()
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Celso Melchiades Doria: Universidade Federal de Santa Catarina, Department of Mathematics, CFM

Chapter Chapter 5 in Differentiability in Banach Spaces, Differential Forms and Applications, 2021, pp 215-230 from Springer

Abstract: Abstract We will review some operations in vector calculus that will motivate using differential forms when integrating vector fields. The differential forms formalism allows us to generalize the Stokes Theorem to describe the conditions of integrability (Frobenius Theorem), and to write Maxwell’s equations succinctly to obtain topological invariants using differentiable tools and many other applications.

Date: 2021
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DOI: 10.1007/978-3-030-77834-7_5

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