Recent content by PLAGUE

I quote from my book: But it doesn't show any proof that for stationary waves, we can separate the space as time part of a 3D wave equation. How can we show that for stationary waves, we can separate the space as time part of a 3D wave equation?

In this cycle, if $$X$$ has efficiency greater than $$X^{'}$$, then we can show that, heat flows from cold reservoir to the hot reservoir. But this contradicts our everyday observation and we conclude that $$X$$ can not have greater efficiency than $$X^{'}$$. But what if efficiency of $$X$$ is...

+ means or here. You may be familiar with |

https://en.wikipedia.org/wiki/Introduction_to_Automata_Theory,_Languages,_and_Computation Edition 3rd page 99

Sorry. The second expression should be, $$(R+SU^*T)^*SU^*$$

Sorry. The second expression should be $$(R+SU^*T)SU^*$$

Sorry. The second expression should be $$(R+SU^*T)SU^*$$

I was studying the given finite automata. Using $$R_{ij}^{(k)}$$ method, I found out that the Regular Expression that this automaton accepts is $$R^*S(U+TR^*S)^*$$. But my book says, the regular expression for the accepted strings can be described in various ways. One is $$(R+SU^*T)SU^*$$. How...

I recently learned of a multiplication method of signed numbers using 2's complement. Here is the answer. What I want to know is how does this multiplication work? I understand that two's complement is $2^n−N$. I understand how subtraction with complements works. But how does the multiplication...

I was studying doppler shift yesterday and found out that the speed of sound wave remains the same even if the source is moving. To compensate that, the wavelength and frequency are adjusted. I know that this is also true for light which results in red and blue shift. Then why in special...

Say, $$y_n (x) = a_0 + a_1(x -x_0) + a_2(x-x_1)(x - x_0) + ... +a_n(x-x_0)(x-x_1)...(x-x_{n-1})$$ Now, $$y_0(x_0) = a_0$$ $$y_1(x_1) = a_0 + a_1(x_1 - x_0)$$ or, $$a_1 = \frac{\Delta y_0}{h}$$ Here, $$h = \frac{x_i - x_0}{i}$$ Similarly, $$a_n = \frac{(\Delta)^n y_0}{h^n n!}$$ Next...

Can you suggest some study materials?

I was said that setting y equal to 0 is equivalent to setting ##z=\overline z## as done here. (see the lower half of the page) But it also doesn't make sense to me why you would set ##z = \overline z##

Perhaps I am missing something. I am giving the full answer here. They are taken from Schaum's Outline of Complex Variables, 2ed: Second Edition (Schaum's Outlines) by Murray SPIEGEL (Author)

I am given, $$u = e^{-x} (x sin y - y cos y)$$ and asked to find v such that, $$f(z) = u + iv$$. My book solves these problems and the answer is, $$v = e^{-x} (ysiny + x cos y) + c$$. I understand how it is done, using Cauchy-Riemann equations. Then, the book asks to find f(z). When doing that...