000 04229nam a22006015i 4500
001 978-3-030-12025-2
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020 _a9783030120252
_9978-3-030-12025-2
024 7 _a10.1007/978-3-030-12025-2
_2doi
050 4 _aTA329-348
072 7 _aTBJ
_2bicssc
072 7 _aTEC009000
_2bisacsh
072 7 _aTBJ
_2thema
082 0 4 _a620.00151
_223
100 1 _aMartínez-Guerra, Rafael.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_938658
245 1 0 _aAlgebraic and Differential Methods for Nonlinear Control Theory
_h[electronic resource] :
_bElements of Commutative Algebra and Algebraic Geometry /
_cby Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García.
250 _a1st ed. 2019.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2019.
300 _aXIV, 196 p. 13 illus., 11 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematical and Analytical Techniques with Applications to Engineering,
_x1559-7466
505 0 _aMathematical Background -- Group Theory -- Rings -- Matrices and linear equations systems -- Permutations and Determinants -- Vector and Euclidean Spaces -- Linear Transformations -- Matrix Diagonalization and Jordan Canonical Form -- Differential Equations -- Differential Algebra for Nonlinear Control Theory -- Appendix -- Index.
520 _aThis book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.
650 0 _aEngineering mathematics.
_93254
650 0 _aNonlinear Optics.
_911414
650 0 _aControl engineering.
_931970
650 0 _aSystem theory.
_93409
650 0 _aControl theory.
_93950
650 1 4 _aEngineering Mathematics.
_93254
650 2 4 _aNonlinear Optics.
_911414
650 2 4 _aControl and Systems Theory.
_931972
650 2 4 _aSystems Theory, Control .
_931597
700 1 _aMartínez-Fuentes, Oscar.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_938659
700 1 _aMontesinos-García, Juan Javier.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_938660
710 2 _aSpringerLink (Online service)
_938661
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030120245
776 0 8 _iPrinted edition:
_z9783030120269
776 0 8 _iPrinted edition:
_z9783030120276
830 0 _aMathematical and Analytical Techniques with Applications to Engineering,
_x1559-7466
_938662
856 4 0 _uhttps://doi.org/10.1007/978-3-030-12025-2
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c76401
_d76401