Ebook: Analysis of Dirac Systems and Computational Algebra
- Tags: Partial Differential Equations, Linear and Multilinear Algebras Matrix Theory, Mathematical Methods in Physics, Numerical and Computational Physics
- Series: Progress in Mathematical Physics 39
- Year: 2004
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
The subject of Clifford algebras has become an increasingly rich area of research with a significant number of important applications not only to mathematical physics but to numerical analysis, harmonic analysis, and computer science.
The main treatment is devoted to the analysis of systems of linear partial differential equations with constant coefficients, focusing attention on null solutions of Dirac systems. In addition to their usual significance in physics, such solutions are important mathematically as an extension of the function theory of several complex variables. The term "computational" in the title emphasizes two main features of the book, namely, the heuristic use of computers to discover results in some particular cases, and the application of Gröbner bases as a primary theoretical tool.
Knowledge from different fields of mathematics such as commutative algebra, Gröbner bases, sheaf theory, cohomology, topological vector spaces, and generalized functions (distributions and hyperfunctions) is required of the reader. However, all the necessary classical material is initially presented.
The book may be used by graduate students and researchers interested in (hyper)complex analysis, Clifford analysis, systems of partial differential equations with constant coefficients, and mathematical physics.
The subject of Clifford algebras has become an increasingly rich area of research with a significant number of important applications not only to mathematical physics but to numerical analysis, harmonic analysis, and computer science.
The main treatment is devoted to the analysis of systems of linear partial differential equations with constant coefficients, focusing attention on null solutions of Dirac systems. In addition to their usual significance in physics, such solutions are important mathematically as an extension of the function theory of several complex variables. The term "computational" in the title emphasizes two main features of the book, namely, the heuristic use of computers to discover results in some particular cases, and the application of Gr?bner bases as a primary theoretical tool.
Knowledge from different fields of mathematics such as commutative algebra, Gr?bner bases, sheaf theory, cohomology, topological vector spaces, and generalized functions (distributions and hyperfunctions) is required of the reader. However, all the necessary classical material is initially presented.
The book may be used by graduate students and researchers interested in (hyper)complex analysis, Clifford analysis, systems of partial differential equations with constant coefficients, and mathematical physics.
The subject of Clifford algebras has become an increasingly rich area of research with a significant number of important applications not only to mathematical physics but to numerical analysis, harmonic analysis, and computer science.
The main treatment is devoted to the analysis of systems of linear partial differential equations with constant coefficients, focusing attention on null solutions of Dirac systems. In addition to their usual significance in physics, such solutions are important mathematically as an extension of the function theory of several complex variables. The term "computational" in the title emphasizes two main features of the book, namely, the heuristic use of computers to discover results in some particular cases, and the application of Gr?bner bases as a primary theoretical tool.
Knowledge from different fields of mathematics such as commutative algebra, Gr?bner bases, sheaf theory, cohomology, topological vector spaces, and generalized functions (distributions and hyperfunctions) is required of the reader. However, all the necessary classical material is initially presented.
The book may be used by graduate students and researchers interested in (hyper)complex analysis, Clifford analysis, systems of partial differential equations with constant coefficients, and mathematical physics.
Content:
Front Matter....Pages i-xv
Background Material....Pages 1-91
Computational Algebraic Analysis for Systems of Linear Constant Coefficients Differential Equations....Pages 93-138
The Cauchy-Fueter System and Its Variations....Pages 139-207
Special First Order Systems in Clifford Analysis....Pages 209-266
Some First Order Linear Operators in Physics....Pages 267-306
Open Problems and Avenues for Further Research....Pages 307-311
Back Matter....Pages 313-332
The subject of Clifford algebras has become an increasingly rich area of research with a significant number of important applications not only to mathematical physics but to numerical analysis, harmonic analysis, and computer science.
The main treatment is devoted to the analysis of systems of linear partial differential equations with constant coefficients, focusing attention on null solutions of Dirac systems. In addition to their usual significance in physics, such solutions are important mathematically as an extension of the function theory of several complex variables. The term "computational" in the title emphasizes two main features of the book, namely, the heuristic use of computers to discover results in some particular cases, and the application of Gr?bner bases as a primary theoretical tool.
Knowledge from different fields of mathematics such as commutative algebra, Gr?bner bases, sheaf theory, cohomology, topological vector spaces, and generalized functions (distributions and hyperfunctions) is required of the reader. However, all the necessary classical material is initially presented.
The book may be used by graduate students and researchers interested in (hyper)complex analysis, Clifford analysis, systems of partial differential equations with constant coefficients, and mathematical physics.
Content:
Front Matter....Pages i-xv
Background Material....Pages 1-91
Computational Algebraic Analysis for Systems of Linear Constant Coefficients Differential Equations....Pages 93-138
The Cauchy-Fueter System and Its Variations....Pages 139-207
Special First Order Systems in Clifford Analysis....Pages 209-266
Some First Order Linear Operators in Physics....Pages 267-306
Open Problems and Avenues for Further Research....Pages 307-311
Back Matter....Pages 313-332
....