Algebraic and Differential Methods for Nonlinear Control Theory - Elements of Commutative Algebra and Algebraic Geometry (Paperback, 1st ed. 2019)

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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Mathematical and Analytical Techniques with Applications to Engineering
Release date:	October 2020
First published:	2019
Authors:	Rafael Martinez-Guerra • Oscar Martinez-Fuentes • Juan Javier Montesinos-Garcia
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	196
Edition:	1st ed. 2019
ISBN-13:	978-3-03-012027-6
Categories:	Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematics for scientists & engineers Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science Books > Professional & Technical > Electronics & communications engineering > Electronics engineering > Automatic control engineering > General
LSN:	3-03-012027-9
Barcode:	9783030120276

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