Recent content by Devil Moo

Will you make a tree diagram and state the relationship between the equations or concepts?

As the title said, how do you memorize efficiently? For example, knowledge on your interested fields.

I once finished the part starting with Peano's axioms. Wow, it is inspiring.

Hi, all. I would like to read books about the topics - Geometry, Real Analysis and Electricity and Magnetism. And I find the followings. Are they decent and rigorous? Geometry The Real Numbers and Real Analysis Introduction to Electrodynamics Classical Electricity and Magnetism Electricity...

For the proof by contradiction about ##\sqrt 2## is a irrational number, we conclude that it is true once we find the contradiction. In this case, why can't I conclude that ##u + v \in W## is true? Is ##not (u + v \in U) = u + v \in W## wrong?

This is a linear algebra question which I am confused. 1. Homework Statement Prove that "if the union of two subspaces of ##V## is a subspace of ##V##, then one of the subspaces is contained in the other". The Attempt at a Solution Suppose ##U##, ##W## are subspaces of ##V##. ##U \cup W##...

Proof by contradiction starts by supposing a statement, and then shows the contradiction. 1. Homework Statement Now, there is a statement ##A##. Suppose ##A## is false. It leads to contradiction. So ##A## is true. My question: There are two statements ##A## and ##B##. Suppose ##A## is true...

By chain rule, ##\begin{align} \frac {d\sin(\theta/2)} {d(\theta /2)}\frac {d(\theta / 2)} {d\theta} & = \frac {1} {2} \cos\frac {\theta} {2} \frac {d\theta} {dt} \nonumber \\ |\frac {d\mathbf A} {dt} | & = A\cos\frac {\theta} {2} \frac {d\theta} {dt} \nonumber \end{align}## It seems they are...

Is Differentiation exact or just an approximation? I am wonder whether this question is meaningful or not. Slope is expressed as "it is approaching to a value as x is approaching 0" so it is inappropriate to ask such question. But when I deal with uniform circular motion, it is very confusing...

So if we have to define something, we have to calculate these laws before applying using the basic arithmetic rules.

Now it is defined as the angle between ##\mathbf A## and ##\mathbf B## where ##\theta## is smaller than or equal to ##\pi## and it is commutative. How do you find out that it is not distributive? Um... How are these two examples related to the derivation?

Is k served as a parameter to choose the center points of the circle passing through those two points, for k != -1?

So in Cartesian Coordinates System and Polar Coordinates System, the "rules" to express same vector is different. It is not appropriate to interpret the vector in Polar form as one in Cartesian. How do we define mathematical operations in Polar form, for example, differentiation? Is it by...

Scalar Product is defined as ##\mathbf A \cdot \mathbf B = | \vec A | | \vec B | \cos \theta##. With the construct of a triangle, the Law of Cosines is proved. ##\mathbf A## points to the tail of ##\mathbf B##. Well, ##\mathbf C## starts from the tail of ##\mathbf A## and points to somewhere...

Undergraduate level. What else biological areas are described in microscopic perspective?