Recent content by pbandjay

The gist of it is that the complex numbers form a field (just like the reals), so are equipped with the same properties as the reals (associative, commutative, closure under an addition and a multiplication, existence of identities w.r.t. the operations, inverses, distributive). A vector space...

I was never able to watch the saw movies very well either, but Dexter is my favorite show! Even right away in season one, the plot is amazing. My favorite seasons are one and two, personally. But a lot of my friends liked season four the most. They're all good.

Operations on infinite decimal representations need to be considered more carefully.

I should think something along these lines: (f*g)(t) \stackrel{\mathrm{def}}{=} \displaystyle\int_{-\infty}^\infty f(x)g(t - x) dx (h*(f*g))(t) = \displaystyle\int_{-\infty}^\infty h(y)(f*g)(t - y) dy = \displaystyle\int_{-\infty}^\infty h(y) \left( \displaystyle\int_{-\infty}^\infty...

Object Oriented Programming Database Systems Networking Software Engineering Artificial Intelligence Geometric Transformations Topology I am very nervous about it, but I always overload myself and tend to turn out okay.

Doesn't the series definition only correspond to the Riemann Zeta function for Re(s) > 1?

Are you trying to differentiate h(x) = sin [(x2 + 1)2] ? I'm currently having a hard time following your procedure (with the switching around of the h's and f's and u's and g's).

One of my professors recommended "The Linear Algebra a Beginning Graduate Student Ought to Know" by Jonathan Golan. I am currently working through it right now, and I am enjoying it thoroughly, as it is a little more involved than the textbook I had for my undergraduate linear algebra course...

Yes, it is easy to draw a graph that represents a relation. Unfortunately, I can't find a link to any good examples at the moment. It's not too difficult, just pick up a piece of paper and try this. Let's say you have a set S = {a, b, c} and a relation R = {(a,b), (a,c)} on S. First, you want...

Your language is kind of confusing to me with that "never" and those "nots". (I have dyslexia.) Basically, if you have a symmetric relation, then if you see (x,y) in your relation, you will also see a (y,x). Note that x and y might not be distinct. So if you have (x,x), it counts because you...

http://en.wikipedia.org/wiki/Antisymmetric_relation From what I can tell, if you have a relation R on a set, then it is anti-symmetric if the following holds: If x,y are in the set and both (x,y) and (y,x) are elements of R, then x = y, or \mathrm{If} \ (x,y) \in R \ \mathrm{and} \ (y,x) \in...

An equation of the form y(x) = c_1 e^{i\sqrt{k}x} + c_2 e^{-i\sqrt{k}x} would also solve the ODE, but that technique made use of the definitions \cos x = \frac{e^{ix} + e^{-ix}}{2} \sin x = \frac{e^{ix} - e^{-ix}}{2i} to get rid of the imaginary units.

Take this with a grain of salt, as I am doing it completely from memory. If you have y'' = -ky, then y = erx is a solution since y'' = r2erx, and substituting this into the original ODE you have r2erx = -kerx ==> r2 = -k ==> r = +/- sqrt(-k) then r = +/- i sqrt(k) therefore let y_1 =...

My professors have always used only the term Kernel, in both linear algebra and abstract algebra. Of course when referring to the vector space R^n and matrices, I can see how the term Null Space would go well with Vector Space, Column Space, etc.

Every element of a set is unique, therefore {1,2,2,3,3,1,1,1} is the same as {1,2,3}.