Algebraic And Differential Methods For Nonlinear Control Theory: Elements Of Commutative Algebra And Algebraic Geometry: Elements Of Commutative Algebra And Algebra by Rafael Martínez-guerraAlgebraic And Differential Methods For Nonlinear Control Theory: Elements Of Commutative Algebra And Algebraic Geometry: Elements Of Commutative Algebra And Algebra by Rafael Martínez-guerra

Algebraic And Differential Methods For Nonlinear Control Theory: Elements Of Commutative Algebra…

byRafael Martínez-guerra, Oscar Martínez-fuente, Juan Javier Montesinos-garc

Hardcover | March 4, 2019

Pricing and Purchase Info

$212.95

Earn 1,065 plum® points

Prices and offers may vary in store

Quantity:

In stock online

Ships free on orders over $25

Not available in stores

about

This 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.

Title:Algebraic And Differential Methods For Nonlinear Control Theory: Elements Of Commutative Algebra…Format:HardcoverDimensions:196 pagesPublished:March 4, 2019Publisher:Springer NatureLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3030120244

ISBN - 13:9783030120245

Reviews

Table of Contents

Mathematical 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.