The three volumes of this series of books, of which this is the first, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering.
This first volume focuses primarily on algebraic questions: categories and functors, groups, rings, modules and algebra. Notions are introduced in a general framework and then studied in the context of commutative and homological algebra; their application in algebraic topology and geometry is therefore developed. These notions play an essential role in algebraic analysis (analytico-algebraic systems theory of ordinary or partial linear differential equations).
The book concludes with a study of modules over the main types of rings, the rational canonical form of matrices, the (commutative) theory of elemental divisors and their application in systems of linear differential equations with constant coefficients.
1. Categories and Functors.
2. Elementary Algebraic Structures.
3. Modules and Algebras.
Henri Bourlès is Full Professor and Chair at the Conservatoire National des Arts et Métiers, Paris, France.
Table of Contents
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