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Existence of solutions of quasilinear elliptic equations following from a priori estimates for the solutions and their gradient. Distance between two points.

Ideals in commutative rings. Anosov linear systems, Plykin atractor, solenoid.

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The rank theorem and normal forms for mappings between euclidean spaces. Linear difference equations of first order with constant coefficients.

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Global Stability of Dynamical Systems. Como desenvolver a autodisciplina: Courant Lecture Notes in Mathematics, 1.

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Vetores e Geometria Analítica

Basic notions of dynamics: Numbers, approximations of real numbers with sequences. Parametric equations of the line and plane. Maximum principles for nonlinear elliptic equations of second order.


Class functions, irreducible representations and conjugacy classes. Cartesian coordinates in plane and space. Second-order partial differential equations. Elliptic partial differential equations. A first course in the Numerical Analysis of Differential Equations. A Basic Course in Algebraic Topology. Topological groups, the classical groups, Lie groups, homomorphisms of Lie groups, subgroups, coverings, Lie algebra associated to a Lie group, simply connected Lie groups, exponential mapping, closed subgroups, elementary representation theory, adjoint representation, maximal tori, group actions, orbits and orbit spaces.

Morse, Morse-Smale, Witten-Morse theories and their discretization through piecewise-linear, finite elements and Forman approaches with applications to Computer Graphics. Integration in the sense of Riemann. State-of-The-Art Report, Eurographics