Fourier series coefficients proof
Can somebody help me understanding the fouries series coefficients? I know that if we have: $$f(t) = \sum_{n=1}^N A_n \sin(2\pi nt + Ph_n) \tag{where $Ph_...
Apr 20, 2026 2 VIEWS
Topic: General
5104 Articles 
Hydrostatic Pressure in Feet, Inches and PSI.
I am looking at this example from my engineering manual. Is there anyone that understands each step of the math so that the answer 0.866 can be reached. I...
Apr 20, 2026 1 VIEWS
irrationality of $\sqrt{2}^{\sqrt{2}}$.
The fact that there exists irrational number $a,b$ such that $a^b$ is rational is proved by the law of excluded middle, but I read somewhere that irration...
Apr 20, 2026 1 VIEWS
What tools are used when images are displayed in a scatter plot?
I have seen a lot of scatter plots where the data inside the scatter plot has come from images. But an image is like a matrix. It has a height and a width...
Apr 20, 2026 1 VIEWS
What do brackets mean for mod operation?
I'm solving equation 5 = (6 * 8 + 9 * b)(mod 10). I tried to use wolframalpha and it gives me answer b = 3. But if I remove brackets around mod 5 = (...
Apr 20, 2026 1 VIEWS
Find a 2d unit vector perpendicular to a given vector
So I'm given the vector 5i-12j and I need to find a unit vector perpendicular to this line. I know I need to use the dot product in some way, shape, ...
Apr 20, 2026 1 VIEWS
The sum of an uncountable number of positive numbers
Claim: If $(x_\alpha)_{\alpha\in A}$ is a collection of real numbers $x_\alpha\in [0,\infty]$ such that $\sum_{\alpha\in A}x_\alpha<\infty$, then $x_\a...
Apr 20, 2026 1 VIEWS
Are $\cos^2 \theta$ and $\cos \theta^2$ the same?
Are $\cos^2 \theta$ and $\cos \theta^2$ the same? I mean be it $\sin,\cos, \tan ,\cot ,\sec,\csc$. Are they same? Please help a maths noob here.
Apr 20, 2026 1 VIEWS
Solving symbolic linear equations with maple
How can I solve linear equations of the following type in Maple? $$\begin{pmatrix} 1 & 1 & 1 & 1\\ b-c & c-b & a-b &0 \\ b-d &...
Apr 20, 2026 1 VIEWS
definition and example of standard topology
Let $X$ be a topological space. Then trivial topology $T$ is $\{\phi,X\}$ discrete topology $T$ is the family of all subsets of $X$. standard topology $T$...
Apr 20, 2026 3 VIEWS
Oleinik's entropy condition, physical explanation
Consider the scalar conservation law $$u_t+f(u)_x=0, \hspace{0.4 cm} \text{in $\hspace{0.2 cm}$ $\mathbb{R} \times (0,\infty)$}$$ where $f \in C^{2}(\math...
Apr 20, 2026 1 VIEWS
Fill in a $5 \times 5$ square to make equal products in rows and columns
Let's say you fill in a $5 \times 5$ square with $1, 2,\dots, 25$. Is there a way to fill it so that the product of the first row is equal to the pro...
Apr 20, 2026 1 VIEWS