LEADER 04438nam 22006015 450 001 9910337642503321 005 20200702171249.0 010 $a3-030-12025-2 024 7 $a10.1007/978-3-030-12025-2 035 $a(CKB)4100000007592156 035 $a(DE-He213)978-3-030-12025-2 035 $a(MiAaPQ)EBC5660214 035 $a(PPN)233800018 035 $a(EXLCZ)994100000007592156 100 $a20190130d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebraic and Differential Methods for Nonlinear Control Theory$b[electronic resource] $eElements of Commutative Algebra and Algebraic Geometry /$fby Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XIV, 196 p. 13 illus., 11 illus. in color.) 225 1 $aMathematical and Analytical Techniques with Applications to Engineering,$x1559-7458 311 $a3-030-12024-4 327 $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. 330 $aThis book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra. 410 0$aMathematical and Analytical Techniques with Applications to Engineering,$x1559-7458 606 $aEngineering mathematics 606 $aStatistical physics 606 $aControl engineering 606 $aSystem theory 606 $aEngineering Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/T11030 606 $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 615 0$aEngineering mathematics. 615 0$aStatistical physics. 615 0$aControl engineering. 615 0$aSystem theory. 615 14$aEngineering Mathematics. 615 24$aApplications of Nonlinear Dynamics and Chaos Theory. 615 24$aControl and Systems Theory. 615 24$aSystems Theory, Control. 676 $a620.00151 700 $aMartínez-Guerra$b Rafael$4aut$4http://id.loc.gov/vocabulary/relators/aut$0791790 702 $aMartínez-Fuentes$b Oscar$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMontesinos-García$b Juan Javier$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910337642503321 996 $aAlgebraic and Differential Methods for Nonlinear Control Theory$91954034 997 $aUNINA