Differentials and 1-forms
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Differential forms: three or more dimensions
All these results and proofs immediately generalise to functions of three, or indeed functions of n variables (assuming that the functions are differentiable). That is, in three-dimensions, if [Equation goes here - download the original to see it.] then [Equation goes here - download the original to see it.] which is computed by [Equation goes here - download the original to see it.] All of these are equivalent expressions for the same process. Example (2) [Equation goes here - download the original to see it.] Find [Equation goes here - download the original to see it.] Solution [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.]
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Contents of
Differentials and 1-forms
1 Differentials in one dimension
2 Summary – differentials in one dimension
3 Differentials in two-dimensions
4 Example: differential forms and directional derivatives
5 Differential forms: three or more dimensions
6 1-forms
7 Definition of the differential of a function f
8 Duals
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