Symmetry reductions of PDEs using Lie group method of infinitesimal transformations
202607
log into www.wikipedia.org and search for lie group...there is a detailed description and all the formulas as well and its free.
394234
T = 2pisqrt(l/g)\nl = g(T/(2pi))^2 = 9.80(1.0/(2pi))^2 = 0.25 m\n\n(The object's weight is irrelevant for small oscillations.)
29345
these are data from end fixing of the structure you should introduce to solve the system of equations, otherwise you would get infinite solutions or (rigide body motion)-Good Luck
280036
Try this:\n\nStructure and Interpretation of Classical Mechanics\nhttp://mitpress.mit.edu/SICM/\nbook-Z-H-20.html#%_chap_2
14091
An especially significant property of chaotic systems is great sensitivity to initial conditions.  Move the tiniest amount in x,y in Mandelbrot and you have a radically different outcome.
259743
I LOVE U\n\nFirst line:\n= I [ (L+N)² - N(2L+N) ] O / L\n= I [ L² + 2LN + N² ) - ( 2LN + N² ) ] O / L\n= I [ L² ] O / L\n= I L O\n\nSecond line:\n= [(v+r)(v-r)][E/V(U³/U²)]  (Note: that is U^3/U^2)\n= [v² - r²] [E/V(U)]\n\nNow we know that we "r" (are) nothing without each other, so r = 0\n\n= [V²] [E/V(U)]\n= V E U\n\nAll together our equation is I LOVE U
98400
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
547958
Start here:\nhttp://www.math.pitt.edu/~sussmanm/2071Spring05/lab07/lab07.html#TheGramSchmidtMethod
422571
Using one of the equations of motion\n\n(v*v) - (u*u) = 2*a*s\n\nwhere \nv is final velocity\nu is initial velocity\na is accleration\ns is displacement\n\n\nOR \nuse \n\nv * (dv / ds) = a
2514
∫xSec(x²)²dx = .5Sin(x²)/Cos(x²)
199785
what you are looking for is called Phase Space or Phase Portrait in analytical mechanics.\n\njust an example:\nhttp://www.cds.caltech.edu/~shawn/LCS-tutorial/motivation.html
76377
also try  http://mathworld.wolfram.com/ImplicitDifferentiation.html
73250
Assuming you mean over R, solve the equation s*t + r*sin(t) = 0 for r and s for all t that is not the trivial solution (r,s)=(0,0). \nIn other words, if f(t)=sin(t) and g(t)=t were linearly dependent, then there is some non-zero slope s, s*g(t) = s*t and some non-zero amplitude r, r*f(t) = r*sin(t) such that the graphs of these functions completely coincide for all t. Since f is non-linear and g is, this is nonsense and the functions are linearly independent.
432353
THe VdW equation is P= nRT/(V-nb) - a(n/V)^2, just plug and chug.  But dont forget to switch your T into Kalvin
464788
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.
198935
you should try this site http://www.oberlin.edu/physics/dstyer/SolvingProblems.html
504577
domain\nall real x\nx intercept\nputting y=0\n0=x+rt{x]\n-x=rtx\nx^2=x\nx(x-1)=0\nx=0 or 1\nx intercept=(0,0) and (1,0)\ny intercept\nsetting x=0\ny=0\ny intercept=(0,0)\nno symmetry exhibited