I am given the eigenvalues of a square, 8x8, matrix. They are all non-zero. I have determined that the matrix is diagonalizable and has an inverse. In one...

I'm writing a controller for an inverted pendulum in which the state vector isn't completely measurable. The state vector is $\mathbf{x}\in\math...

I'm going to learn Affine plane as well as affine Geometry. Unfortunately, my text book (not in English) is not good at all, so please recommend some...

$$\lim_{x\to 0} \frac{\ln(1+x)}x$$ The process I want to take to solving this is by using the definition of the limit, but I am getting confused. ( withou...

I am not sure if I am doing the right thing here in setting up the integrals using cylindrical coordinates. I need to set up the integral using cylindrica...

We know that $\vec{i}$ and $\vec{j}$ are unit vectors along $x$-axis and $y$-axis respectively. So angle between them is $90°$. But let $\vec{a}$ and $\ve...

I heard there are 48 regular polyhedrons. With what Jan Misali calls regular polyhedrons, are there any more? Assumptions: A polyhedron must lie in 3D Euc...

Let $n\in\mathbb{Z}^+ $ I have a simple discrete function: $$ \mathrm{acc}(n) = 8n $$ The discrete integral (is that the right term?) of that is: $$ \math...

How would I integrate the following: .$$\int\frac{\sin^3x}{\cos x}\,\mathrm dx.$$ I am not sure what to do. I could split $\sin^3x=(1-\cos^2x)(\sin x)$ Th...

I would like to know if there is a general method to solve equation looking like this: $$\tan(\sec^{-1} 4)$$ without using a calculator (you have to find ...