Recent content by PLAGUE

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?

This says, If so, then why wouldn't two inductors provide two walls and make the current lag by 180 degrees? I know, people come up with answers such as, if it were the case that two inductors make current lag by 180 degrees, then it would be possible that you cut down a big inductor, which...