I was originally given the value $(4,-2)$ as the vertex of a parabola and told that it also includes the value $(3,-5)$. From this point, I deduced that t...
I am a student taking engineering course and wish to learn more about Fourier Transforms. It seems very useful. Would highly appreciate it if anyone could...
I have the following two definitions in my notes: The spectrum of an operator: We define $\sigma(T)$, the spectrum of T, by, $$\sigma(T):=\{\lambda\in\mat...
Let $f(x)$ be a continuous function on the interval $[a,b]$, $(a<b)$ and let: $$a=x_0,x_1,x_2,...,x_{i-1},x_i,...,x_{n-1},x_n=b$$ be an arbitrary (rand...
From here is the following excerpt Suppose one is given a homogeneous symmetric polynomial $P$ and asked to prove that $P(x_1, \ldots , x_n) ≥ 0$ How shou...
How do I get $\frac{5x}{x+5}$ from simplifying the following? $$\frac{(\frac{1}{x}-\frac{1}{5} )}{( \frac{1}{x^2}-\frac{1}{25})}$$ My work: I multiplied t...
I know the letter $d$ is commonly used in calculus and represents a derivative. Does this $d$ act as a variable that can be simplified or as a function of...
Many arguments about the foundations or philosophy of mathematics centre on the question of whether or not there exist objects or entities (such as certai...
I am struggling to get some traction on this and need someone to show me how to calculate this. I have a GCSE question that asks: In the attached image I&...
Can $\frac{a}{0}$ be defined or solved?
We know that a Lie group G acts on itself by conjugation. That is, $g \rightarrow I_g = R_{g^{-1}}\circ L_g$ and that this action is an automorphism assoc...
I was asked to solve the following question prove $z=\overline{z}$ conditions : iff $z$ is real. To begin with I have no idea what $\overline{z}$ is suppo...