Chris White
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 Feb8 comment Geometric meaning of $\nabla_{[i}(x^i \nabla_{j]}x^j)$ and $(\nabla_{[i}x^i )\nabla_{j]}x^j$ The determinant is just a coincidence. In general, if $A$ is a matrix with components $\nabla_i x^j$, then what you have is $(\operatorname{Tr}A)^2-\operatorname{Tr}(A^2)$. Apart from a factor of $2$, this is the sum of all products of 2 elements on the diagonal of $A$, minus the sum of all products of pairs of elements that are in reflected positions across the diagonal ($A_{12}A_{21} + A_{13}A_{31} + \cdots$). I'm not sure this is particularly useful though, or that it has a physical interpretation. Dec10 awarded Caucus Oct2 awarded Yearling Sep30 awarded Commentator Sep30 comment Very *mathematical* general physics book I'm just saying the OP may not know what they're asking for. Someone who's being taught out of that book is not in a position to understand any of the physics in the books you've mentioned, and probably very little of the math. Sep30 comment Very *mathematical* general physics book You should know, since it appears you've not read it, that Resnick et al. is a middle school level heuristic survey of random topics in physics used to write GRE questions and nothing else. Physics for poets, basically. One need not go so advanced as the things you've listed in order to get something "mathematical" compared to it. Sep24 awarded Autobiographer Sep16 comment Notation regarding the continuity equation for conservation of mass Mathjax supports \iint and \oint but not \oiint. In a pinch there's \unicode{x222F} for $\unicode{x222F}$, but it doesn't scale beyond inline math. Aug9 awarded Citizen Patrol Mar3 awarded Student Mar3 asked What is the generalization of Gauss's Theorem to a manifold? Dec22 awarded Enlightened Dec22 awarded Nice Answer Nov1 answered How can a single integral equal a triple integral? Oct29 awarded Quorum Oct2 awarded Yearling Aug26 comment Solving ODE with negative expansion power series @dingo_d Well, Math Overflow is generally only for research-level math. If your question is just needing an application of well-known ODE theory, it belongs on Math Stackexchange. If it calls upon physical principles in some meaningful way (beyond just "this came up while doing physics"), then it is okay here. But I doubt it will be particularly well-received on Math Overflow. In general, though, if you feel the question should be moved, you can ping a moderator and request they migrate it for you, to avoid cross-site duplication. Jun28 comment Analytical Solution for Elastic Bar under applied end velocity Existence of solutions sounds more like a math topic, unless you want to know if the setup is physically reasonable enough to admit a solution. I suggest migrating to mathematics, though in that case the users there should take into account that the word "analytical" here probably means "in terms of common functions" rather than simply "converges to its Taylor series." May31 comment Uniqueness of the vector in $\mathbb{R}^n$ specified by the curl, divergence and the normal component Though no doubt used in physics a lot, this is most certainly a pure math question (with a pure math answer). May19 comment Mathematicians conceived of black holes long before astronomers actually found any?How? A word of caution about the looseness of that claim: Most everyone involved in developing the theory of black holes would be described primarily as a theoretical physicist/astrophysicist, not a mathematician. You could ask how does any theorist make predictions prior to having observations, but that's just what a prediction is, and it's exactly what theoretical scientists do all day long.