updates
Stiffness matrix for 3-nodes beam elements FEM (M+N)
Considering a 2-nodes beam element, having 3 dofs per node, making it 6 per element, this element will be studied according to a M+N model, where both ben...
Apr 18, 2026
Archive: Updates
updates
What is a fitting parameter in least-squares?
I was doing some least-squares homework when I saw this term "fitting parameters". I was asked to implement the leas-squares fit using polynomials of $p-t...
Apr 18, 2026
updates
Calculus: Area under the graph of a Heart-shaped curve
I'm currently stuck with this question and would appreciate any tips on how I can approach this question. Right now, my intuition is to split the are...
Apr 18, 2026
updates
What exactly are Cayley-Klein geometries?
Everywhere I see Cayley-Klein geometries discussed, they're presented in a manner that seems wholly disconnected from the rest of geometry. Just what...
Apr 18, 2026
updates
Find the remainder when you divide $x^{81} + x^{49} + x^{25} + x^{9} + x$ by $x^{3}-x$.
Find the remainder when you divide $x^{81} + x^{49} + x^{25} + x^{9} + x$ by $x^{3}-x$. Attempt: Let $f(x) = x^{81} + x^{49} + x^{25} + x^{9} + x$, then t...
Apr 18, 2026
updates
Solving for n in the equation
I found an equation like this $$5^2 \times 5^4 \times 5^6 \times 5^8 \times \cdots \times 5^{2n} = (0.008)^{-30}$$ Can someone explain me how to find the ...
Apr 18, 2026
updates
Find the remainder when $10^{400}$ is divided by 199?
I am trying to solve a problem Find the remainder when the $10^{400}$ is divided by 199? I tried it by breaking $10^{400}$ to $1000^{133}*10$ . And when 1...
Apr 18, 2026
updates
Upper and lower limits of integration
I have a small confusion in setting the limits of integration. My question is, if an integration is expressed in the following:$$\int_{1}^{b}f(x)dx$$ $1.$...
Apr 18, 2026
updates
How many solutions does this system of equations have?
I have $2$ equations : $$-\frac{a}{2}x-\frac{b}{2}+cx+d=x+2$$ $$-2ax-2b+cx+d=2x+1$$ with $a, b, c, x \neq 0$ We have to find all possible solutions of $a,...
Apr 18, 2026
updates
Trace Norm / Nuclear Norm: How to verify?
The nuclear norm is defined by this [from wikipedia]: $$\|A\|_* = \text{trace} \left( \sqrt{A^*A} \right) = \sum_{i=i}^{\min\{m,n\}}\sigma_i(A)$$ I get th...
Apr 18, 2026
