Mathematics of linear and nonlinear systems : for engineers and applied scientists
著者
書誌事項
Mathematics of linear and nonlinear systems : for engineers and applied scientists
（Oxford science publications）
Clarendon Press , Oxford University Press, 1990
- : pbk
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注記
Bibliography: p. [292]-294
Includes index
内容説明・目次
- 巻冊次
-
ISBN 9780198563327
内容説明
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.
目次
- 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.
- 巻冊次
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: pbk ISBN 9780198563631
内容説明
* Excellent introduction with exercises and solutions This book presents much of the necessary mathematical background needed to study the modern developments in linear and nonlinear system theory, in a way which will be more acceptable to the nonmathematician. This book is intended for postgraduate engineers and applied scientists; 3rd year undergraduate applied and pure mathematicians.
目次
- Introduction to dynamical systems
- Aspects of set theory
- Mappings
- Semigroups and groups
- Rings and fields
- Vector spaces and modules
- Metric and normed spaces
- Limits, convergence, and boundedness
- Sets, convexity, and topology
- Continuity and differentiability
- Manifolds and Lie algebras
- Solutions to exercises
- References
- Index.
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