general
how to do such stochastic integration $dS = a S^b dt + c S dW$?
How to do stochastic integration $dS = a S^b dt + c S dW$, where $a$, $b$ and $c$ are constant, $b > 0$, and $W$ is the Wiener process. I know how to d...
Apr 22, 2026
Archive: General
general
What can we say if the dot product of two vectors is equal to 1
The question really is in the title. I know what it means if the dot product equals 0 but I find it interesting thinking what it means when it equals exac...
Apr 22, 2026
general
Find the least squares solution of the linear system......
Hi I'm looking for the least squares solutions of.... $$ \begin{pmatrix} 1&-1 \\ -1&2 \\ -1&0 \end{pmatrix} \begin{pmatrix} x\\y \end{pma...
Apr 22, 2026
general
Finding the interval for an optimization problem involving a silo
The problem asks: A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per squ...
Apr 22, 2026
general
How does the middle term of a quadratic $ax^2 + bx + c$ influence the graph of $y = x^2$?
Every parabola represented by the equation $y = ax^2 + bx + c$ can be obtained by stretching and translating the graph of $y = x^2$. Therefore: The sign o...
Apr 22, 2026
general
the proof of implicit function theorem (Terence Tao)
Implicit function theorem: Let $E$ be an open subset of $\mathbb{R}^n$, let $f : E \to \mathbb{R}$ be continuously differentiable, and let $y = ( y_1, ......
Apr 22, 2026
general
Definition of "turning point"?
What is the definition of a "turning point"? For example, here's a definition that I feel doubtful about: The Concise Oxford Dictionary of Mathematic...
Apr 22, 2026
general
How to sample from unknown distribution
Let's just assume on the picture we have a prob. distribution of aliens height on a Mars. We know for sure, the area below the curve is 1. But I have...
Apr 22, 2026
general
Intuition behind quadratic approximation
I'm not looking for a proof of the taylor series, I want an intuition to why the quadratic term equals the orange part or if I was just wrong My teac...
Apr 22, 2026
general
Solving PDE with Laplace transform
Please help me to solve the following PDE with Laplace transform. In class we got less than 10 mins to study the topic (the semester ended and we were beh...
Apr 22, 2026
