On variational calculus via the variational bicomplex and the Euler-Lagrange complex:
Ian Anderson: The variational bicomplex, Utah State University (1989) [pdf]
Ian Anderson: Introduction to the variational bicomplex, in: Mathematical aspects of classical field theory, Contemp. Math. 132 (1992) 51–73 [doi:10.1090/conm/132/1188434, pdf, pdf]
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