## Cohomological Analysis of Partial Differential Equations and Secondary Calculus |

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### Contents

From Symmetries of Partial Differential Equations | 1 |

Elements of Differential Calculus | 25 |

Geometry of FiniteOrder Contact Structures | 57 |

Geometry of Infinitely Prolonged Differential | 95 |

Cspectral Sequence and Some Applications | 127 |

Introduction to Secondary Calculus | 189 |

237 | |

### Common terms and phrases

acyclic analog c-density C-field C-spectral sequence C-theory called canonical Cartan distribution CDiff Chapter characteristic classes classical cochain mapping cohomology classes coincides compute conservation laws Consider constructions contact structure coordinates Corollary corresponding defined definition denoted Diff diffeomorphism differential calculus differential forms differential operators diffiety domain elements equivalent Euler operator fact fibers filtration first-order functions functor Green formula Hence homomorphism homotopy horizontal identified infinitesimal symmetries integral manifolds isomorphism Jk(n Lagrangian Lemma Lie algebra Lie derivative Lie field Lie transformation linear morphism n-dimensional natural 5-module nonlinear notation Note obtained obviously partial differential equations particular problem projective projective module PROOF Proposition proved quotient representing object resp respect restriction rioc(7r scalar Secondary Calculus secondary differential operators secondary module secondary vector shows smbl smooth solution spectral Spencer submanifold submodule Subsection tangent term theory trivial vector fields