Fundamentals of Advanced Mathematics 2 - 1st Edition - ISBN: 9781785482496

Fundamentals of Advanced Mathematics 2

1st Edition

Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves

Authors: Henri Bourles
Hardcover ISBN: 9781785482496
Imprint: ISTE Press - Elsevier
Published Date: 1st April 2018
Page Count: 230
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Description

Fundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves begins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known).

In addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems.

Key Features

  • Present Galois Theory, transcendental field extensions, and Picard
  • Includes sections on Vessiot theory, differentially transcendental field extensions, topology, topological vector spaces, Radon measure, differential calculus in Banach spaces, sheaves, distributions, hyperfunctions, algebraic analysis, and local analysis of systems of linear differential equations

Readership

Graduate students in Systems Theory, Robotics, Physics or Mathematics, research engineers in Automation control and/or robotics, assistant professors and professors in Automation control and/or robotics

Table of Contents

  1. Field Extensions and Differential Field Extensions
  2. General Topology
  3. Topological Vector Spaces
  4. Measure and Integration, Function Spaces
  5. Sheaves

Details

No. of pages:
230
Copyright:
© ISTE Press - Elsevier 2018
Published:
Imprint:
ISTE Press - Elsevier
Hardcover ISBN:
9781785482496

About the Author

Henri Bourles

Henri Bourlès is Full Professor and Chair at the Conservatoire National des Arts et Métiers, Paris, France.

Affiliations and Expertise

Conservatoire National des Arts et Metiers, France