wath is the mathematical definition of the free modes for a system of partial differential equations?
84965
What you are describing is what some people like to refer to as Degrees of freedom.\n\nFor example in statics, there are 6 degrees of freedom;  The degrees of freedom in this case would be "movement in and rotation about all three axis.  However, not all six would be concidered a free mode.  Think of a wheel on a car.  The wheel can rotate about the transverse axis(how the car moves, and rotate about the vertical axis (this is how the car turns).  However the wheel could not move in any direction (relitive to the car) or rotate in the longitudinal axis (in normal condition).
962855
should be e^u*du/dx\n\nd[e^(x^2)] = e(x^2)*2*x
146531
This site is constructed well and has a high level of detail (up to degree level).\n\n\nhttp://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
457083
I think you mean Burger's equation.  Go to any good book on partial differential equations and you will see it there.  Richard Haberman has a good book for PDE's.
932600
http://en.wikipedia.org/wiki/States_of_matter
676950
A few that come to mind at Euler, Maxima and Octave. Unfortunately, I don't think any of the free packages come close to Mathematica or Matlab, but maybe one of them will still meet your needs.
1107625
I assume you are able to take partial derivatives. So take the partial derivatives that appear in the heat equation (you did look up the heat equation, right?) and plug them in to see if you get equality.\n\nSo, the partial derivative with respect to t is\n-lambda^2 k*u(x,t). This is the same as k times the second partial derivative with respect to x. Looks right to me!
1139073
Differential Equations
267038
You might try reading Whitehead and Russell's Principia Mathematica.  I can't promise it will help, as I haven't read it, but I've been told that this issue is addressed.
1074016
Detailed information as well as equations are available on the following page : \n\nhttp://www.jwave.vt.edu/crcd/kriz/modules/module06/formulation/edge_formulation.html
438946
A way to estimate a derivative and define a general way of solving differential equations numerically. See the links for more information.
787521
Example:\nIf z=f(u,v),\nu=g(x,y) and\nv=h(x,y), then\n(all derivatives are supposed to be partial derivatives)\ndz/dx=dz/du*du/dx+dz/dv*dv/dx\ndz/dy=dz/du*du/dy+dz/dv*dv/dy\n\nAlternatively, you can set of the matrices\n[[dz/du dz/dv]]\nand\n[[ du/dx du/dy]\n[dv/dx dv/dy]]\nand get that\n[[dz/dx dz/dy]]\nis the product of the two matrices.
121167
http://hyperphysics.phy-astr.gsu.edu/Hbase/surten.html
99672
honestly....good luck\n\ntry www.mathworld.com\n\ndo a search for differential equations, i think that would be your best bet...but that can get confusing...good luck
492128
I'm a third year physics student and I know what a Laplacian differential operator is, I just don't understand your question. Could you clarify?
655567
the first link explains system boundary and the second is an explanation of computer simulations in the context of "conceptualizing a system".  hope this helps
865054
Let u=ln t, e^u=t, du=dt/t, dt=t du\nThen:\n∫ln² t dt = ∫t u² du = ∫u² e^u du\nIntegrating by parts:\nu² e^u - ∫2u e^u du\nu² e^u - 2u e^u + ∫2e^u du\nu² e^u - 2u e^u + 2e^u + C\nt ln² t - 2t ln t + 2t +C\nAnd we are done.