## Advanced Ordinary Differential Equations: (Mathematics 220) New York University, Spring 1947 |

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absolute values absolutely convergent analytic analytic functions approximate solution assume assumption Asymptotic Stability called choose consider constant contact transformation continuous functions coordinates corresponding curve z.(t defined definition direction field dx dx dx eigen eigenvalues expression finite number follows given periodic solution gives half-rectangle hence homogeneous variational equations identity initial conditions initial values integral curve integrating factor interval Jordan Curve Jordan Curve Theorem k=r+l lemma lie inside limit point linear combination linear homogeneous linear system linearly independent Lipschitz Condition main diagonal means method non-singular orbitally Ordinary Differential Equations partial derivatives point of accumulation point x,y prove quantities region result satisfy a Lipschitz segment shown Solving stability straight line strictly monotonie subinterval subspace successive approximation sufficiently small system of equations tangent tion trajectory triangular matrix unstable v/ill vector X-XQ zero