what is poincare normal form?
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You might find this paper useful\nhttp://arxiv.org/abs/math-ph/0106027
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In brief, follow as many normal forms as possible in sequence. (possibly with an exception of 1NF)
1053820
Stationary in reference to what fixed point?
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Base on the Mathematics for STPM, Penerbit Fajar Bakti SDN.BHD. ,written by Ong Beng Sim...From the cphater 5,Coordinate Geometry, the actual standard form is ax/2+y/2=1.\n\nTo change the form:\n\nfind the axis-y & axis-x first,\n\nwhen y=0, x=2/a (axis-x)\nwhen x=0, y=2   (axis-y)\n\nBase on the standard form of linear funtion is x/a+y/b=1, where, a is axis-x and b is axis-y.\n\nso, substitute the axis-x & axis-y into the standard form of linear function...\n\nTherefore, the standard form of the linear funtion for y=-ax+2 is ax/2+y/2=1
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I like the joke!  To play along, I define:\nr = metric r  and \nd = metric d\n\nV = (pi/3)*(d^2)*(3r - d)\n\nThis will work for the tank being any fraction of a sphere, not just 1/2
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It's the standard form of a quadratic function.
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u(x, y) = e^(pi) e^x cos(ny)\n\nu_x (x, y) = e^(pi) e^x cos(ny)\n\nu_xx (x, y) = e^(pi) e^x cos(ny)     since e^(pi) cos(ny) is "constant" with respect to x\n\nu_y (x, y) = e^(pi) e^x (-nsin(ny))\n\nu_yy (x, y) = e^(pi) e^x (-n^2cos(ny))\n\nu_xx (x, y) + u_yy (x, y) = 0\n= e^(pi)(e^x)cos(ny)(1 - n^2)\n\nTherefore, u(x, y) is harmonic only if 1 - n^2 = 0, which is equivalent to n = 1 or n = -1.  For other values of n, we see that u(x, y) is, in general, not harmonic.\n\nTo find the harmonic conjugate v(x, y) of u(x, y) (for each of the cases n = 1 and n = -1), use the Cauchy-Riemann equations.\n\nThen use f(z) = f((z,0)) = u(z,0) + i v(z,0) to try to express w = u + iv in terms of z = x + iy (i.e. set y = 0 in u(x,y) and v(x,y), substitute into w = u(x, 0) + i v(x, 0)).
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in the plane,\nthere are two kinds of curvature,\nthe regular one, which is the norm of the second derivative, if the curve has unit tangent.\nand the signed curvature, which in addition measures if the first derivative and the second derivative preserve orientation.\ns
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The standard FDM is analogous to the FEM if linear approximations are used in the FEM for Dirichlet problems \nThe FEM satisfies the Neumann boundary conditions via an integral form exactly. This is not true of FDM. \nMath errors are more rigorously handled in the FEM.
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What is the standard way to describe motion ?
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Standard form of a parabola that opens left or right is\n\nx = c(y - h)^2 + k\n\nFor your equation, complete the square to get it in standard form:\n\nx = 3y^2 + 6y + 4\n= 3(y^2 + 2y) + 4\n= 3(y^2 + 2y + 1) + 4 - 3\n= 3(y + 1)^2 + 1
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If you mean Hermite see\nhttp://mathworld.wolfram.com/HermiteDifferentialEquation.html
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Domain\n(-∞, ∞)\n\nRange\n[-3, ∞)
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Please use the search function. This question was asked 5 days ago:\n\nA proper polar coordinate system (one that assigns each point in the plane a unique coordinate) will always leave out a ray of points. For example, the standard polar system that identifies the open set (0, oo) X (0, 2Pi) with R^2 - {0} by the function f(r, t) = (rcos(t), rsin(t)) ( = (x, y) ) does not correspond to any points on the positive x-axis and necessarily leaves out the origin (there is no way to include the origin uniquely). This is usually glossed over in a basic calculus or physics course as one actually uses an atlas of polar coordinate charts (this atlas never includes the origin, but at least covers the plane minus the origin); you use whichever chart is convenient for the problem at hand. Some definitions will disregard the need for a homeomorphism and include the positive x-axis by considering a domain that is not open, (0, oo)X[0, 2Pi)
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Orthocentre = point where altitudes intersect (An altitude is the line from the vertex to the opposite side (extended if necessary))\n\nIncentre = centre of the incircle = point where perpendicular bisectors of each of the sides intersect. \nRadius of incircle = √[(s-a)(s-b)(s-c)/s] where s = semiperimeter\n\nCentroid = point where medians meet (Median is the line joining a vertex to the midpoint of the opposite sides) The centroid is the centre of gravity of the triangle and the centroid divides each median in the ratio 2:1 On a numberplane the centroid of a triangle is the point which is at the average of the sum of the three x- and y-coordinates of its vertices)\n\nOne other is:\nCircumcentre = centre of the circumcircle = point where angular bisectors meet.\nDiameter of circumcircle = a/sinA = b /sinB = c/sinC
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2 X pi X  r = cirumference\n\npi X r squared = area
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In mathematics, a symplectic manifold is a smooth manifold M equipped with a closed, nondegenerate, 2-form ω called the symplectic form. The study of symplectic manifolds is called symplectic topology. Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds, e.g. in the Hamiltonian formulation of classical mechanics, which provides one of the major motivations for the field: The set of all possible configurations of a system is modelled as a manifold, and this manifold's cotangent bundle describes the phase space of the system.\n\nAny real-valued differentiable function H on a symplectic manifold can serve as an energy function or Hamiltonian. Associated to any Hamiltonian is a Hamiltonian vector field; the integral curves of the Hamiltonian vector field are solutions to the Hamilton-Jacobi equations. The Hamiltonian vector field defines a flow on the symplectic manifold, called a Hamiltonian flow or symplectomorphism. By Liouville's theorem, Hamiltonian flows preserve the volume form on the phase space.