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- What is a differential form? - Mathematics Stack Exchange
At this point, however, I think that the best way to approach the daunting concept of differential forms is to realize that differential forms are defined to be the thing that makes Stokes' Theorem true In other words, you can approach understanding forms in two different ways:
- differential geometry - divergence of a vector field on a manifold . . .
$\begingroup$ This (the formula for the derivative of the metric tensor) seems to be a direct consequence of corrollary 7 in chapter 6 of the second volume of Spivak's comprehensive introduction to differential geometry $\endgroup$ –
- what does ∇ (upside down triangle) symbol mean in this problem
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- differential topology - Regular values and maps of degree 0 . . .
There is an elementary phenomenon in differential topology, that I've never quite understood: It is well known that the mapping degree (Brouwer degree) $\operatorname{deg}(f) = \operatorname{deg}(f
- Different approaches to differentiability in $L^2$
You can find the proof of the equivalences above in most books that talk about Sobolev spaces (for example, in "Functional Analysis, Sobolev Spaces and Partial Differential Equations" by Haim Brezis and in "Partial Differential Equations" by Lawrence C Evans)
- Mathematics Stack Exchange
Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
- Itos chain rule and multidimensional derivation
In the book "Quant Job Interview: Questions and Answers" by M Joshi in the derivation of the final Black-Scholes formula he makes usage of Ito's chain rule
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