Recent content by bhatiaharsh

Hi, In the study of dynamical systems, phase portraits play an important role. However, in almost all related text, I only see some standard examples like prey-predator, pendulum etc. I have a rather unclear thought in my head regarding the role of real/imaginary eigenvalues in the system...

Thanks both of you. JJacquelin, I think you used (1-2x) instead of (1+2x) , and therefore calculation of c_1,c_2 are wrong. But I got the general idea. Thanks a lot.

Hi, I am trying to solve a Poisson equation \nabla^2 \phi = f in \Omega, with Dirichlet boundary condition \phi = 0 on \partial \Omega. My problem is that I am trying to understand the condition under which a solution exists. All the text I consulted says that the problem is solvable. However...

Thanks for the pointers. If I understand right, and am not worried about a unique solution I should be able to use the integral solution of the equation. I tried a simple example in 1D and 3D, but the 3D example doesn't work out fine, and I am not sure what the problem is. In either case, the...

Hi, I am working on finding a solution to Poisson equation through Green's function in both 2D and 3D. For the equation: \nabla^2 D = f, in 3D the solution is: D(\mathbf x) = \frac{1}{4\pi} \int_V \frac{f(\mathbf x')}{|\mathbf x - \mathbf x'|} d\mathbf{x}', and in 2D the solution is: D(\mathbf...

Well, isn't the no of unknowns greater than the no of equations ? u = f_1 + c_1 u = g_1 + c_2 u = h_1 + c_3 There are 4 unknowns and 3 equations.

So, if I know \frac{\partial u}{\partial x},\frac{\partial u}{\partial y},\frac{\partial u}{\partial z} can someone help me how can I find u ? Any pointers are appreciated.

Thanks for the pointer chiro. I followed on the link you gave and reached exact differential equations. Hopefully learning about that should give me a more clear understanding. But I can already see how separability can be an issue.

Hi, I remember having read in basic calculus that the following is true, but I don't know what this property is called and am having a hard time finding a reference to this. d u(x,y) = \frac{\partial u}{\partial x} dx + \frac{\partial u}{\partial y} dy Ques: Is this true ? Is this true for...