Here's the question. $\frac{∂^2}{∂t^2 } u(x,t)=c^2 \frac{∂^2}{∂x^2 } u(x,t)$ We are supposed to use this form of Fourier transform to solve our PDE $...

I understand how $\pi$ is calculated, but I am interested in references that explain when and how the natural exponent $e$ was developed. What mathematica...

Here I am referring to the notation $x \wedge y = \min \{ x,y \}$ and $x \vee y = \max \{ x,y \}$. These seem to reference the corresponding usages in log...

How do I solve the integral $$\int \frac{(x^3+6x^2+3x+16)}{(x^3+4x)} dx? $$ This integral gets very messy. Can I get a step by step break down of how to s...

How do you prove a triangle is equiangular with 5 steps? All I know is that triangle abc is equilateral? I need to prove it with a 2 column proof. These a...

There's an exercise in my book asking me to show that for $R$-submodules $A,B$ of an $R$-module $M$ the following is true $$(A+B)/A \cong B/A \cap B$...

How do we prove $\cos(\pi/5) - \cos(2\pi/5) = 0.5$ without using a calculator. Related question: how do we prove that $\cos(\pi/5)\cos(2\pi/5) = 0.25$, al...

Exercise 2.5 of Izenman's Modern Multivariate Statistical Techniques: Consider a hypercube of dimension $r$ and sides of length $2A$ and inscribe in ...

Assume $X_1, X_2, ..., X_n$ is a random sample of a uniform random variable $X$ on the interval $(0,\theta)$. What is the density function for $X$ and the...

The problem: Find $\ Df(x,y,z)$ if $\ f(x,y,z) = (xz, y^2+z)$ I got confused, is it asking me for the domain in which the function is defined or about som...