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May
17
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
Continuity alone is not sufficient. Continuity plus two different solutions give an infinity of solutions. Think that $f$ Lipschitz (which is continuous) implies unique solution.
May
17
comment Show that $ \int_{-\infty}^{\infty} \frac{x^3}{(x^2+4)(x^2+1)}\, dx$ does not converge
If $a=b$ you integrate an odd function on $[-a,a]$ so you get $0$.
May
16
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
I do not get the question regarding the sufficiency. Can you please detail what you mean?
May
16
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
@S.Panja-1729: Wikipedia is only as right as the people contributing to it. So the question "is wikipedia wrong?" can well be answered "Yes" in plenty of situations. You can see in the comments to your questions that the equation you mention has infinitely many solutions.
May
16
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
Two solutions means exactly that. One may be trivial, there's no problem.
May
15
comment Accelerating approximations for arccos
Could you develop what you mean by the fact that you accelerated drastically the accuracy of $\arccos$? What was the rate of convergence before? What is your rate of convergence?
May
15
comment Are my results realistic or is there an error somewhere?
You know, you could include all the details of your problem in your question. If someone is willing to help, making him/her go through another question (without details), which links to a book, is not really appealing. Make your question self-contained, so that someone looking at it can understand what you ask without going through other sites/books.
May
14
comment Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
Yes, but in your case, the family is not independent. Assume that there are $a,b,c$, such that the relation you wrote is true for all $x \in \Bbb{R}$. Now you choose three values for $x$, in order to find a system of equations satisfied by $a,b,c$. You can choose whatever values you like, since the relation is valid for all $x \in \Bbb{R}$. If the family is not dependent, you'll find, after a few tries, that $a=b=c=0$, and this means that you have independence.
May
11
comment Limit of sequence - hard one
I have put a factor $1/n$ before the sum.
Apr
27
comment Cavalieri’s Principle for calculating volume.
Yes, I did replace $z$ with height, since they mean the same thing (if you orient your $z$ axis up)
Apr
27
comment Does a bounded countably infinite union of sets with volume have volume?
What do you mean by "$A$ has volume"? Do you mean it is measurable? If so, then countable union of measurable sets is measurable.
Apr
19
comment inverse of sum of diagonal matrix and eigendecomposition
I don't think that you can compute the inverse of a sum, in terms of the inverses of the two matrices.
Apr
12
comment Set of points at which a function coincides with its convexification is compact?
Yes, I guess lower semicontinuous could work.
Apr
12
comment $x\over(1-x)$ $y\over(1-y)$ $z\over(1-z)$ >= 8 when $x ,y ,z $ are positive proper fractions and $x+y+z = 2$
What does proper fractions mean? Are they rational numbers?
Apr
11
comment Proving properties about matrix $A$ s.t. $A^2 = -I$
The equation you get for $\lambda$ is $\lambda^2 = -1$. This has roots $\pm i$. The sum of the eigenvalues is equal to the trace (the sum of the elements on the diagonal), and since $A$ has real entries, the trace is real.
Apr
11
comment For $n \ge 3$, every subgroup of $A_n$ with index $n$, is isomorphic to $A_{n-1}$
I guess you could use the fact that for $n \geq 5$, normal subgroups of $S_n$ are $\{e\},A_n,S_n$. Prove that a subgroup of $A_n$ with index $n$ is a normal subgroup of a group isomorphic to $S_{n-1}$. Then its cardinality implies that it can only be $A_{n-1}$.
Apr
10
comment Learning modern differential geometry before curves and surfaces
I don't see why what you are doing could not be "safe". But it's just like talking about derivatives, without actually finding a derivative of a concrete function like $\exp,\sin,\ln$. Differential geometry was not a success for me, and as I look back, is this lack of concrete examples and connection with the curves and surfaces which kept me from learning more. I liked this course on curves and surfaces: alpha.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf If you like differential geometry, you'll like curves and surfaces.
Apr
10
comment Learning modern differential geometry before curves and surfaces
If you're comfortable with geometry on manifolds, it costs nothing to take a look into curves and surfaces. How can you speak of the tangent space to a manifold without being able to work with tangents to curves, or tangent planes to surfaces? How do you compute the curvature of a curve, or the mean curvature of a surface at a point? These are basic questions you need to know from curves and surfaces...
Apr
9
comment Please help solve for the variables A and B
Replace B in the first equation. Then you'll have just an equation in A
Apr
9
comment Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square
@Elaqqad: The article you cite proves this only for polynomials, as far as I see.