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What are differential forms?
Is this what I'm going to learn about in my upcoming differential geometry class?
Is this what I'm going to learn about in my upcoming differential geometry class?
A classical course on differential geometry -- which includes many introductory courses -- may not cover and use differential forms at all.
quetzalcoatl9 said:The short (and least satisfying) answer is that an n-form is an antisymmetric tensor of rank (0,n) that enjoys some nice symmetry properties - these properties essentially make the indices of the tensor "disappear". They can be thought of as functions that take tangent vectors as input They are also well defined across something called "pullback", something that is not true of tensors in general, so in effect they transcendent tensors. They also can provide topological information.
... then I can recommend the book by Weintraub (sp? it may be Weintraube, I forget, he is a professor in Louisianna) called "Differential Forms: A Complement to Vector Calculus" or something like that.
mathwonk said:when is someone going to reveal that there is an entire thread devoted to this topic, called "a geometric approach to differential forms" by david bachman, just below here, with zillions of entries and a free book?
quetzalcoatl9 said:Try doing a search on this forum and you will see previous discussions.<snip>