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Geometry of Differential Forms Shigeyuki Morita
Publisher: American Mathematical Society

Principal theorems and applications of differential. This is my attempt to explain the concept of a differential form in differential geometry and several variable calculus; which I view as an extension of the concept of the signed integral in single variable calculus. Differentiable manifolds abd the differential and integral calculus of their associated structures, such as vectors, tensors, and differential forms are of great. I understand what forms are, and understand their properties in R2 and R3 (exactn. So geometry killed the electric and magnetic fields. I'll also refer the interested reader to another classic text on cohomology, namely Bott and Tu's, Differential Forms in Algebraic Topology. Dr David Loeffler Modular and automorphic forms, Iwasawa theory, and p-adic analysis. Integrals of differential forms play a fundamental role in modern differential geometry. The study of Lie groups forms an important branch of group theory and is of relevance to other branches of mathematics. Stochastic analysis: stochastic differential equations on geometrical spaces, geometry of stochastic flows, infinite dimensional analysis. Early differential geometers studied such properties of curves and surfaces such as: .. This term, the main text is Morita's Geometry of Differential forms. It is only later on, when calculus became more algebraic in outlook that one can begin to make a meaningful separation between the subjects of calculus and differential geometry. Let us try to write the four Maxwell equations using the language of differential forms, exterior differentiation and the Hodge star duality operation. It's also important to remember that differential forms don't have to be real-valued. So I'm a little stuck on the concept of forms on a manifold.