- Problem calculating surface integral over a cylinder
Problem: Find the surface integral $I=\\iint_S2x^2ydydz-y^2dzdx+4xz^2dxdy$, where $S$ is curved surface of the cylinder $y^2+z^2=9$ bounded by the planes $x=0,\\,x=2
- calculus - Integrating $e^ {f (x)}$ - Mathematics Stack Exchange
Interesting, I fired my old symbolic algebra program and typed the following $$ \int {\exp\left (C_ {0}+C_ {1}x-C_ {2}x^ {2}\right)}\,\mathrm {d}x= $$ and it gave the
- Meaning of dx, dy, du (u-substitution) - Mathematics Stack Exchange
I understand the meaning of $\frac {dy} {dx}$ and $\int f (x)dx$, but outside of that what do $dy, du, dx$ etc mean? When I took calc I, derivatives and integrals
- Sub division rings of division rings - Mathematics Stack Exchange
Update: Two things have happened: Rankeya has given a valid answer to the written question, but I realize now I was too vague Secondly, I looked up the correct exercise in Jacobson and found that the following exercise is precisely to show that it does hold for all division rings Stupid gut feelings I'm accepting this answer and reposting the correct question
- Show that a real symmetric matrix is always diagonalizable
As the eigenvalues are real, one need only consider real (generalised) eigenvectors, and so one needs transpose, rather than conjugate transpose Anyway, this does give a method to prove that the geometric and algebraic multiplicities ar the same
- Eigenvectors of real symmetric matrices are orthogonal
The statement is imprecise: eigenvectors corresponding to distinct eigenvalues of a symmetric matrix must be orthogonal to each other Eigenvectors corresponding to the same eigenvalue need not be orthogonal to each other However, since every subspace has an orthonormal basis, you can find orthonormal bases for each eigenspace, so you can find an orthonormal basis of eigenvectors
- calculus - dx (t) dx vs. dx dx - Mathematics Stack Exchange
its actually $\dot x$ or $\frac {dx} {dt}$, the term inside of the integral
- What do the symbols d dx and dy dx mean? - Mathematics Stack Exchange
Okay this may sound stupid but I need a little help What do $\\Large \\frac{d}{dx}$ and $\\Large \\frac{dy}{dx}$ mean? I need a thorough explanation Thanks
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