Derivative of a definite integral (FTIC)
$\displaystyle \left.\frac{d}{dx}\right|_{x=\pi} \int_{t=0}^{x} \frac{\cos 3t}{\sqrt{1+t}} \,dt$ What would be the correct way to solve this? I'd rea...
19 Apr 2026 1 READS
Archive: News
Expressing Powers in Terms of Falling Powers
The falling power $n^\underline{k}$ (read $n$ to the falling $k$) is defined as follows: $$n^\underline{k}=n(n-1)(n-2)\cdots(n-k+1)$$ These are important ...
19 Apr 2026 1 READS
Factorization of quartic polynomial.
I want to know other ways of factorization to get quadratic factors in this polynomial: $$x^4+2x^3+3x^2+2x-3$$ Thanks in advance for your suggestions. The...
19 Apr 2026 1 READS
Inverse of $y = x^3 + x $?
Can you help me find the inverse function for $y = x^3 + x$? This question was posed at the beginning of AP Calculus, so we can't use any math beyond...
19 Apr 2026 1 READS
What is the intuitive meaning of 'order of accuracy' and 'order of approximation' with respect to a numerical method?
I have been studying numerical methods in order to get a better understanding of CFD and the algorithms used in CFD codes. Where I am stuck is I don'...
19 Apr 2026 1 READS
Prove $ne^{-n}$ converges to zero
How would I prove that $ne^{-n}$ converges to zero? I've tried $ne^{-n}<{\epsilon}$ and then logging both sides but no further progress could be m...
19 Apr 2026 1 READS
What is a stabilizer of a matrix (group action is multiplication)
I have the group $GL(3,\mathbb R)$ (the group of invertible 3x3 matrices) acting on $M_{33}(\mathbb R)$ (the set of 3x3 real matrices) by $A\cdot M=AM$. L...
18 Apr 2026 1 READS
Determining the rate of change of a radius as a sphere loses volume
Problem: A spherical balloon leaks $0.2\mathrm m^3 / \mathrm{min}$. How fast does the radius of the balloon decrease the moment the radius is $0.5\mathrm ...
18 Apr 2026 1 READS
Definition of a piecewise smooth path
In Apostol's "Mathematical Analysis" $($page 435$)$, a piecewise smooth path in the complex plane, say $f$, is defined as a path in the complex plane...
18 Apr 2026 1 READS
Time varying State transition matrix integration with orbit
Update 1 My question is this. How do I numerically integrate for the state transition matrix using the differential equations. Should I be using the Jacob...
18 Apr 2026 1 READS
