Recent content by saminator910

So, I have an expression 0=A (f,x,\lambda) after setting \frac{\delta I}{\delta f}=\lambda \frac{\delta J}{\delta f} (where J is the functional that is set equal to constraint T), so I maximize what w.r.t. what? I really appreciate the help, I'm back from college for the summer so I don't have...

Ok, that makes sense. Now what I'm realizing is my functionals and constraint are such that the functional for the region will be maximized on the boundary.

Yeah, take a look at the bottom of my original question, I thought about using Lagrange multipliers, I just have no idea about how to get rid of the lambda? once I set the functional derivative of the constraint equal to the functional derivative of the boundary multiplied by lambda, and get a...

Ok, so from what I've read I set \frac{\delta I}{\delta f(x)}=\frac{\partial L}{\partial f}=0, the derivative is in this specific form because L is not a function of f'. Mathematically I don't know how to incorporate the constraint. So, if I don't arrive at a max that satisfies the constraint...

So, the extreme values are at the boundary?

My guess would be a functional derivative equal to 0, but all the problems I've looked at don't have a constraint.

Can anyone tell me straightforward information about a way to maximize a certain functional I[f]=\displaystyle\int_{X} L(f,x)dx such that the integral is bounded, T≥\displaystyle\int_{X}f(x)h(x)dx. I really know a minimal amount about functional analysis and calculus of variations, but I've...

I am trying to derive the Probability distribution of Geometric Brownian motion, and I don't know how to find the variance. start with geometric brownian motion dX=\mu X dt + \sigma X dB I use ito's lemma working towards the solution, and I get this. \ln X = (\mu - \frac{\sigma...

Oh, alright, let me get this straight. The equation itself will always be separable, but that does not necessarily imply that it will have a solution on any given boundary conditions. For that we must have the right combination of coordinate system and boundary? But I will be able to separate...

Ok, so what you are saying is that the coordinate system which the PDE is defined on will also effect whether it is separable. So, where the wave equation may be separable in Cartesian coordinates, it may not in Spherical coordinates?

Question about Solutions of second order linear PDEs I don't have very much formal knowledge of this topic, this is something I have been thinking about, so excuse me if my notation is off. I have a question about second order linear PDEs, do all have a separable solution? It seems that we can...

the s(t) is notation for the distance traveled, therefore, the change in distance with respect to time is the speed, as opposed to the velocity, which is displacement over time.

Ok, can someone check this for me? I must be doing something stupid but I don't know what I'm doing wrong, this has to be some special case \displaystyle\int \sqrt{1+\sin \theta} d \theta sub in. \theta = \sin^{-1}x d \theta = \displaystyle\frac{1}{\sqrt{1-x^{2}}}...

I recently had a breakthrough regarding this topic while I was thinking about something that didn't seem to be directly related. I thought about construction of the integral, and I thought about boxes under the curve. So, We get this. \displaystyle\sum f(x_{i})\Delta x \Leftrightarrow \int...

Do you have a Calculus textbook? I have a Stewart textbook and I really like the problems in there, and although they are not official college board, they are still that level. Also, I suggest Barrons if you don't have a textbook but you need practice. Usually they have a lot of practice tests...