Recent content by xorg

Pag 46 says: He begins to do a rethink about what is a function. Function is a rule? If it is a rule then: f(x) = x² and f(x) = x² +3x + 3 -3(x+1) are different. But that was not what we wanted. But he rewrites, this way: f(x) = x² and f(x) = x² +3x +3 -c(x+1) Apparently this was a small...

You are right. Misinterpreted. Thank you.

Pag 42 says: Seems inconsistent. in (9): p = x +x²+x.sin²x q = x.sin x + x.sin²x But by definition p and q are not polynomial functions. It is a mistake in the book?

For example: $$ y^{2} = 25- x^{2} $$ $$ y = \sqrt{25- x^{2}} , -5\leq x\leq 5 $$ This part: $$ , -5\leq x\leq 5 $$ What is the name of this?If it were a function, it would be the domain. And for equations, and resolutions of equations, what is the name? Other example, the equation: xy = 1...

Thank You! The solution: $$ \sqrt{1-x^{2}} - 2\sqrt{1-y} = C $$ Results: $$ y = \frac{3}{4} + \frac{x^{2}}{4} + \frac{C\sqrt{1-x^{2}}}{2} - \frac{C^{2}}{4} $$ (in your solution, yourC = C/2) Matlab Code x = linspace(-1,1,1000); clf; grid on; hold on; c=0; y=3/4+(x.^2)/4...

Yes, if the dy/dx go to ∞ when x go to 1, then i guess in particular solution this should be the trend. It is as if the particular solution and differential equation were conflicting. Imagine that someone will draw the solution curves, from the dy / dx, at each point, does not match the...

Hi. I'm reading the bookhttp://amzn.com/0486649407 , in self-study mode. In page 53 and 54, below: Apparently does not make sense, because, If the differential equation is: $$ \frac{\mathrm{d}y }{\mathrm{d} x} = x\frac{\sqrt{1-y}}{\sqrt{1-x^{2}}} $$ then dy/dx = ∞ when x = 1, and y < 0...

Suppose a function f (t) = 0 x (t) -y (t) = 0 with x = t y = t df/dt = 0 However ∂f/∂x = 1 This case may seem obvious to most of the regulars this forum, but took me by surprise when I was reading a math book that I needed to "derive from both sides" (I assumed that as a side was zero, or other...

First I tried to find a way to understand why H (s) is the Laplace of impulse response. The first thing I thought was that I should start by the convolution of x and h. Then you answered me in a way, and a few hours later I saw this on a website: $$ \mathcal {L} \{x (t) \ast h (t) \} =...

Another way: $$ y(t) = x(t) \ast h(t) $$ $$ \mathcal{L}\{y(t)\} = \mathcal{L}\{x(t) \ast h(t)\} $$ $$ \mathcal{L}\{y(t)\} = \mathcal{L}\{x(t)\}\mathcal{L}\{h(t)\} $$ $$ Y(s) = H(s)X(s) $$

Thanks, helped me.

I saw in some books, that: Y(s)/X(s) = H(s) where, Y(s) is the laplace of the output X(s) is the laplace of the input H(s) is the laplace of impulse response. How to prove it? In the book Benjamin Kuo, he only mentions it without proof, and did not find it in the book of Oppennheim.

For a sinusoidal input, the amplitude is the same as it would if ζ were positive, so the maximum is the same. And the angle is the same, but negative. I think that's it.

In the book Automatic Control Systems, Benjamin C.Kuo, 7th edition, on page 548, he says: https://imagizer.imageshack.us/v2/720x154q90/540/ML8zmu.jpg He is doing an analysis of the following transfer function: http://imagizer.imageshack.us/a/img911/4839/XPKxoO.gif Mr is the maximum value...

Hi, My question is very simple but I have not found on google. Why Decibel unit employs Deci? I know Deci = 0.1, but why not just use B rather than dB? Is there some historical reason? Thank you, enjoyed the forum, it is my first post.