Library of American University of Madaba
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Seiler, Werner M.
Involution The Formal Theory of Differential Equations and its Applications in Computer Algebra / [electronic resource] : by Werner M. Seiler. - XXII, 650 p. online resource. - Algorithms and Computation in Mathematics, 24 1431-1550 ; .
Formal Geometry of Differential Equations -- Involution I: Algebraic Theory -- Completion to Involution -- Structure Analysis of Polynomial Modules -- Involution II: Homological Theory -- Involution III: Differential Theory -- The Size of the Formal Solution Space -- Existence and Uniqueness of Solutions -- Linear Differential Equations -- Miscellaneous -- Algebra -- Differential Geometry.
The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas. It presents for the first time in book form the theory of Pommaret bases, a special kind of Gröbner bases closely related to Koszul homology, and contains an extensive discussion of the existence and uniqueness of solutions of formally well-posed initial value problems and a novel presentation of Vessiot's dual version of the Cartan-Kähler theory. Special emphasis is put on a constructive approach leading to effective algorithms.
9783642012877
Mathematics.
Algebra--Data processing.
Algebra.
Differential Equations.
Differential equations, partial.
Mathematics.
Partial Differential Equations.
Ordinary Differential Equations.
Commutative Rings and Algebras.
Algebra.
Theoretical, Mathematical and Computational Physics.
Symbolic and Algebraic Manipulation.
QA370-380
515.353
Involution The Formal Theory of Differential Equations and its Applications in Computer Algebra / [electronic resource] : by Werner M. Seiler. - XXII, 650 p. online resource. - Algorithms and Computation in Mathematics, 24 1431-1550 ; .
Formal Geometry of Differential Equations -- Involution I: Algebraic Theory -- Completion to Involution -- Structure Analysis of Polynomial Modules -- Involution II: Homological Theory -- Involution III: Differential Theory -- The Size of the Formal Solution Space -- Existence and Uniqueness of Solutions -- Linear Differential Equations -- Miscellaneous -- Algebra -- Differential Geometry.
The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas. It presents for the first time in book form the theory of Pommaret bases, a special kind of Gröbner bases closely related to Koszul homology, and contains an extensive discussion of the existence and uniqueness of solutions of formally well-posed initial value problems and a novel presentation of Vessiot's dual version of the Cartan-Kähler theory. Special emphasis is put on a constructive approach leading to effective algorithms.
9783642012877
Mathematics.
Algebra--Data processing.
Algebra.
Differential Equations.
Differential equations, partial.
Mathematics.
Partial Differential Equations.
Ordinary Differential Equations.
Commutative Rings and Algebras.
Algebra.
Theoretical, Mathematical and Computational Physics.
Symbolic and Algebraic Manipulation.
QA370-380
515.353