Recent content by PLAGUE

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...

Or perhaps, i made mistake in my code: import math as mp def g(x): return (1-x**2)**(1/3) def pg(x): return (-2*x)*(1/3)*((1-x**2)**(-2/3)) x_0 =0.02 e = 0.0001 max_itr = 50 x_1 = g(x_0) n=0 while(n<max_itr): x_1 = g(x_0) print("{:<10} {:<10.6f} {:<10.6f} {:<10.6f}...

0 0.020000 0.999867 -0.013337 0.979867 1 0.999867 0.064367 -160.886288 0.935499 2 0.064367 0.998617 -0.043031 0.934250 3 0.998617 0.140340 -33.802368 0.858277 4 0.140340 0.993391 -0.094809 0.853052 5 0.993391...

Right! Missed that.

$$x = 3/2 + (cosx)/2$$ here, if you assume $$x_0=0$$, then the derivative becomes 0. Yet, it converges!

Finally, the savior! Thanks a lot.

I am new to numerical methods and am currently learning Fixed point iteration. I have learned that if you can express $$x = g(x)$$, and $$|g'(x_0)|<1$$, then the sequence, $$x_{n+1} = g(x_n)$$ converges to the root. I am solving $$x^3 = 1 - x^2$$ and wrote $$x = \sqrt[3]{1-x^2}$$. I took $$x_0...

Why along a characteristic curve dx/P = dy/Q = dz/R?

I am new to partial differential equations and today, I was introduced to Lagrange's method of solving PDE's. Here, is a proof that shows how Lagrange's method works. I understand the proof until it says, I mean why should, "if u(x, y, z) = c1 and v(x, y, z) = c2 are two independent solutions...

You mean something like this?