- July 9, 2005: The potential formula for trivial Lagrangians.
- July 2, 2005: Bicomplex structure in CE
_{0}and expicit computation of the d_{1}differential. - May 25, 2005: Computing cohomologies L
_{p}(κ) of the subcomplex CDiff_{(p)}^{alt}(κ;) of CDiff_{(p)}(κ;) via the action of the symmetric group S_{p}. - May 19, 2005: Computing cohomologies of the complex
Diff(P
_{1},...,P_{1};Λ^{*}). - May 12, 2005: Techniques for computing the E
_{1}term of the C-spectral sequence and its differential. Skew-adjoint multi-C-differential operators acting on κ. Generalized Euler operators. Solution of the inverse problem of the Calculus of Variations, and historical facts. - April 21, 2005: Action of differential operators on the Berezin module. property of adjoint operators and the linear Green formula. Application of the C-Green formula to variational problems.
- April 14, 2005: Introducing the E
_{1}term of the C-spectral sequence and its differential. Euler operator and Euler-Lagrange equations. Theory of adjoint operators, arising as cochain maps of suitable differential operators complexes. First and second class constraints, restricted symplectic form, Dirac bracket, modified Poisson bracket. Relationship between Legendre transformation and Green formula. Secondary Poisson structures. - April 07, 2005: Introducing "common" conservation laws, and conserved currents.
Generalized conservation laws. Control problem in PDEs. Basic operations
on the E
_{0}term of the C-spectral sequence. The distribution of cones associated with a constrained Lagrangian system. A counterexample to Dirac's conjecture. - March 23, 2005: Describing the first column of the E
_{0}-term of the C-Spectral Sequence of J^{∞}(π) as the horizontal de Rham complex. Description of the other columns via horizontal forms-valued C-differential operators acting on κ, and computation of the corresponding cohomologies. Adjoint modules and operators. - March 16, 2005: Conditions of tangency of the relative vector
field X
_{L}to the constrain manifold. Secondary constraints. First and second class functions. Total Hamiltonians. Understanding variational problems in the framework of C-Spectral Sequence. Analogous considerations for conservations laws, with an example regarding KdV. - March 10, 2005: Finding the analogues of Hamilton equations for a gauge system.
- March 03, 2005: Basic facts of Calculus of Variations, describing the Euler-Lagrange equation by means of the universal linearization operator, Noether theorem. Facts about the quantization procedure of gauge systems in Hamiltonian form. Conjectures on the quantum observability. Constrain manifold of a gauge system, Lagrange multipliers.
- February 24, 2005: Hamiltonian mechanics. Geometrical counterparts
of physical constraints and forces. Singular Hamiltonians and transition principle.
Lagrangian formalism, relation between nondegeneracy of Legendre transformation and
formal integrability of the corresponding Euler-Lagrange equations.
Canonical relative vector field X
_{L}associated with a degenerate Lagrangian L. Geometrical procedure for discovering higher order constraints and making Euler-Langrange equations formally integrable. - February 17, 2005: Computation of symmetries for PDE. Universal linearization operator, understood as a secondary universal derivation. Higher symmetries of PDE, with examples.
- February 4, 2005: Contact fields. Lie fields on J
^{∞}. Coordinate description. Generating functions and generating sections. Evolutionary derivations and corresponding Poisson bracket. Introducing the Lie algebra κ of higher symmetries of J^{∞}, and C-differential operators. - January 20, 2004: Some topics in Differential Topology.
- January 14, 2005: Introducing the Cartan distribution
on J
^{∞}and the corresponding C-spectral sequence.

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