Mathematics of Linear and Nonlinear Systems
Published on 19. April 1990
Book
Hardback
317 pages
978-0-19-856332-7 (ISBN)
Description
This book is an attempt to present much of the necessary mathematical background needed to study the modern developments in linear and nonlinear system theory in a way in which will be more acceptable to the nonmathematician. The first six chapters concern those algebraic topics which have been instrumental in the establishment of linear system theory. These topics include groups, rings, modules and vector spaces. The last five chapters deal with those parts of analysis which lead to a geometric approach to nonlinear system theory that has been particularly successful in yielding important results since about 1970.
More details
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
College/higher education
Professional and scholarly
Illustrations
137 line drawings, bibliography, index
ISBN-13
978-0-19-856332-7 (9780198563327)
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Schweitzer Classification
Content
Part 1 Introduction to synamic systems: mathematical models; sets of mathematical objects; the space RxR; optimal control problems; the space R/n. Part 2 Aspects of set theory: unions and intersections; equivalence relations and classes; congruence modulo. Part 3 Mappings: general, special and inverse mappings. Part 4 Semigroups and groups: binary operations; semigroups; groups; isomorphisms and homomorphisms; cosets, normal subgroups and quotient. Part 5 Rings and fields: rings; the polynomial ring; homomorphisms, ideals and quotient rings; fields. Part 6 Vector spaces and modules: vector spaces; linear independence and bases; modules; submodules and module homomorphisms; torsion modules and free modules; state-space module. Part 7 Metric and normed spaces: metric and normed spaces. Part 8 Limits, convergence and boundedness: convergence of sequences and series; supremum and infirmum; cauchy sequences and completeness; uniform convergence; generalizations; other topics, including Zorn's lemma and the contraction-mapping theorem. Part 9 Sets, convexity and topology: open and closed sets; convex, compact and null sets; topological spaces. Part 10 Continuity and differentiability: continuity; differentiation; differentiable mappings; implicit functions. Part 11 Manifolds and lie algebras: vector fields; manifolds; lie groups; the singular-control problem; linear algebras.