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1d
answered Can you add a scalar to a matrix?
2d
comment How to find $\int x^2e^{x^2}dx$?
This antiderivative can't be expressed in elementary functions.
2d
comment Poincaré-Bendixson theorem, periodic solutions/periodic orbits
A solution spiralling in towards a limit cycle is an example of a non-periodic solution whose omega-limit set (i.e., the limit cycle) is a periodic solution.
2d
revised Leibniz integral rule (singular)
[Edit removed during grace period]
2d
answered How to integrate $\int \frac{4}{x\sqrt{x^2-1}}dx$
Jul
28
comment A proviso in l'Hospitals rule
@vonbrand: Yes, I know.
Jul
26
comment Basic limits as part of $\omega$-limit sets of dynamical systems
Use that $x=\sqrt{x^2}$ (if $x$ is positive).
Jul
25
comment Shortcuts for computing the eigenvalues of a linear transformation
In general, you may not be able to avoid multiplying everything out. For tricks like this to work, one needs to be a bit lucky. Or the exercise needs to be rigged. ;-)
Jul
25
comment Is it possible to define $x+x+x+x…x$ times?
math.stackexchange.com/questions/1096/…
Jul
24
comment Applying the sum-of-digits operation to $4444^{4444}$ three times
Those are not bogus comment; they will give you the answer, if you just bother to follow the links and read...
Jul
24
answered Shortcuts for computing the eigenvalues of a linear transformation
Jul
24
comment Why does a symmetric matrix have a complete set of eigenvectors and eigenvalues?
... and also of the last theorem in the note that Alex R linked to above.
Jul
24
comment Why does a symmetric matrix have a complete set of eigenvectors and eigenvalues?
There are $n$ eigenvalues if you count with them with multiplicity. If they are all distinct, then you have at once a basis with $n$ orthogonal eigenvectors. The difficult thing to show is that if the matrix happens to have a (say) triple eigenvalue, then there really must be a corresponding eigenspace of dimension three (not just one or two), so that you can get three basis eigenvectors from this eigenspace. This is the point of the answer by user level1807 in the question that I linked to.
Jul
20
comment Undamped Pendulum Phase Plane Solution
By the way, your comment about $A \sin 2x + B \cos 2x$ is not right. You would get a solution of that form if the left-hand side of the equation were $d^2 y/dx^2$, but here it's $d^2 x/dt^2$, so it's not even a linear equation.
Jul
20
comment Undamped Pendulum Phase Plane Solution
mathematicalgarden.wordpress.com/2009/03/29/nonlinear-pendulum
Jul
20
comment Intuition behind calculus notation
See also the "Linked" section of the question David mentioned; you'll find that similar questions have been asked here many times, so I'm voting to close this as a duplicate.
Jul
19
comment Why do we need to check for more than $\frac{\infty}{\infty}$ or $\frac{0}{0}$ when applying L'Hospital?
Perhaps of interest: maa.org/programs/faculty-and-departments/…
Jul
14
comment Evaluate $\int_{-2}^2\int_{y^2-3}^{5-y^2}dydx$
Much better now. :-)
Jul
14
comment Evaluate $\int_{-2}^2\int_{y^2-3}^{5-y^2}dydx$
What I meant was that the statement "your attempt is correct" is not correct.
Jul
14
comment Evaluate $\int_{-2}^2\int_{y^2-3}^{5-y^2}dydx$
No, it's not correct. (Integral of $y$ with respect to $x$ equals a constant?)