Exterior Algebra and Differential Forms
Differential forms play an important part in the theory of Hamiltonian systems, but his theory is not universally known by scientists and mathematicians. It gives the natural higher-dimensional generalization of the results of classical vector calculus. We give a brief introduction with some, but not all, proofs and refer the reader to Flanders (1963) for another informal introduction but a more complete discussion with many applicatons, or to Spivak (1965) or Abraham and Marsden (1978) for more complete mathematical discussion. The reader conversant with the theory of differential forms can skip this chapter, and the reader not conversant with the theory should realize that what is presented here is not meant to be a complete development but simply an introduction to a few results that will be used sparingly later.
KeywordsVector Field Tangent Vector Differential Form Exterior Algebra Symplectic Basis
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