Recent content by Hariraumurthy

Homework Statement I am trying to read arken's section on integral equations because I need it for a problem I am trying to attack. I am stuck on a part of a page. I have attached the relevant excerpt from the book.(Not the whole book because it is copyrighted) Homework Equations I...

Thanks for your reply. I thought that everyone had forgotten about the question. I think I found a better analog after some time. If \phi is one half the angle subtended by the vertical by an inverted pendulum(see figure attached), and if the inverted pendulum is a uniform rod, with the...

remember {z_1} = {r_1}{e^{{\theta _1}\pi i}},{z_2} = {r_2}{e^{{\theta _2}\pi i}},{{\bar z}_2} = {r_2}{e^{ - {\theta _2}\pi i}} then the first condition is {\mathop{\rm Re}\nolimits} \left( {{r_1}{r_2}{e^{i\pi ({\theta _1} - {\theta _2})}}} \right) = {r_1}{r_2} i.e. \cos ({\theta _1} -...

Actually, I am a vadiraja's brother and I know that he spent the required effort to try for the solution. He was really beating himself up about it that he could not find the solution to a problem of this nature. He gave ME an idea about the tan-1 and then I did not want to show the solution...

since the value of the limit is dependent on the x,y path, this means the limit does not exist.

If x be the distance from one endpoint to the place the altitude intersects the base produced in both directions, and B be the angle opposite b, then the following equation holds. B=arctan(x/h) + arctan[(b - x)/h] where h = 2k/b This equation even holds if x is negative or larger than b...

The problem is not on page 16. It is on page 28.:) But anyway here is the way I would do it. Suppose that f(n) is defined recursively by specifying the value of f(1) and a rule for finding f(n+1) from f(n). We will prove by mathematical induction that such a function is well-defined...

U(x) is discontinuous at x=0 and therefore by the Fundemental Theorem of Integral Calculus, U(x) is not integrable.

thank you very much.

[b]1. The problem statement, all variables and given/known Given a function f satisfying the following two conditions for all x and y; (a)f(x+y) = f(x)*f(y) (b)f(x) = 1 + x*g(x) where the limit as x tends to 0 of g(x) =1 prove (a) the derivative f'(x) exists (b) f'(x)=f(x) [b]2...

Thanks but not quite what I meant. If you plot dx/dt on the axis normally labled y and x on the x-axis as usual, if you take x=0.1, sinx will be greater than 0 and therefore dx/dt will be greater than 0 and therefore if a particle starts from x=0.1, it will move more to the right. Likewise if a...

Homework Statement What is a mechanical analog for xDOT=sin(x) .?Explain how using this analog, it becomes obvious that x*=0 is an unstable fixed point and that x*=pi is a stable fixed point. Homework Equations dx/dt=sin(x) The analytical solution to this problem is...