If $A$ and $B$ are singular and nonsingular respectively, where both are square, is $A+B$ always nonsingular? Suppose that $A$ is a singular matrix and th...

Can someone please help with this homework problem: Given the equations \begin{align} x^2 - y^2 - u^3 + v^2 + 4 &= 0 \\ 2xy + y^2 - 2u^2 + 3v^4 + 8 &a...

Integrating $\arctan^2(x)$ has been a mystery to me since I first learned to compute indefinite integrals. When I plug it into integral calculator or Wolf...

I recently completed an introductory course on multivariate calculus, and I'm still trying to come to grips with the concepts taught in the vector ca...

I was reading a blogpost here: http://mzargar.wordpress.com/2009/07/19/cauchys-method-of-induction/ (Wayback Machine) One thing that threw me off was that...

How to prove that the composition of 2 rotations about an axis $l_1$ and $l_2$ is the rotation? I know that we can represent rotation about the axis $l$ 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 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...

When $\theta$ is very small, why is sin $\theta$ taken to be JUST $\theta$?

How do you define-: (a) Angle between curves (b) Angle between straight line and a curve (c) Angle between tangent and a curve