عنوان

Algebraic and Differential Methods for Nonlinear Control Theory :

3030120252

9783030120252

3030120244

9783030120245

Algebraic and Differential Methods for Nonlinear Control Theory :

[Book]

Elements of Commutative Algebra and Algebraic Geometry /

Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García.

Cham, Switzerland :

Springer Nature,

[2019]

1 online resource

Mathematical and analytical techniques with applications to engineering

Includes bibliographical references and index.

Intro; Preface; Acknowledgements; Contents; Notations and Abbreviations; 1 Mathematical Background; 1.1 Introduction to Set Theory; 1.1.1 Set Operations and Other Properties; 1.2 Equivalence Relations; 1.3 Functions or Maps; 1.3.1 Classification of Functions or Maps; 1.4 Well-Ordering Principle and Mathematical Induction; References; 2 Group Theory; 2.1 Basic Definitions; 2.2 Subgroups; 2.3 Homomorphisms; 2.4 The Isomorphism Theorems; References; 3 Rings; 3.1 Basic Definitions; 3.2 Ideals, Homomorphisms and Rings; 3.3 Isomorphism Theorems in Rings; 3.4 Some Properties of Integers.

3.4.1 Divisibility3.4.2 Division Algorithm; 3.4.3 Greatest Common Divisor; 3.4.4 Least Common Multiple; 3.5 Polynomials Rings; References; 4 Matrices and Linear Equations Systems; 4.1 Properties of Algebraic Operations with Real Numbers; 4.2 The Set mathbbRn and Linear Operations; 4.2.1 Linear Operations in mathbbRn; 4.3 Background of Matrix Operations; 4.4 Gauss-Jordan Method; 4.5 Definitions; References; 5 Permutations and Determinants; 5.1 Permutations Group; 5.2 Determinants; References; 6 Vector and Euclidean Spaces; 6.1 Vector Spaces and Subspaces; 6.2 Generated Subspace.

6.3 Linear Dependence and Independence6.4 Bases and Dimension; 6.5 Quotient Space; 6.6 Cayley-Hamilton Theorem; 6.7 Euclidean Spaces; 6.8 GramSchmidt Process; References; 7 Linear Transformations; 7.1 Background; 7.2 Kernel and Image; 7.3 Linear Operators; 7.4 Associate Matrix; References; 8 Matrix Diagonalization and Jordan Canonical Form; 8.1 Matrix Diagonalization; 8.2 Jordan Canonical Form; 8.2.1 Generalized Eigenvectors; 8.2.2 Dot Diagram Method; References; 9 Differential Equations; 9.1 Motivation: Some Physical Origins of Differential Equations; 9.1.1 Free Fall.

9.1.2 Simple Pendulum Problem9.1.3 Friction Problem; 9.2 Definitions; 9.3 Separable Differential Equations; 9.4 Homogeneous Equations; 9.5 Exact Equations; 9.6 Linear Differential Equations; 9.7 Homogeneous Second Order Linear Differential Equations; 9.8 Variation of Parameters Method; 9.9 Initial Value Problem; 9.10 Indeterminate Coefficients; 9.11 Solution of Differential Equations by Means of Power Series; 9.11.1 Some Criterions of Convergence of Series; 9.11.2 Solution of First and Second Order Differential Equations; 9.12 Picard's Method; 9.13 Convergence of Picard's Iterations.

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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.

Springer Nature

com.springer.onix.9783030120252

Algebraic and Differential Methods for Nonlinear Control Theory.

9783030120245

Commutative algebra.

Geometry, Algebraic.

Nonlinear control theory.

Commutative algebra.

Geometry, Algebraic.

MATHEMATICS-- General.

Nonlinear control theory.

TECHNOLOGY & ENGINEERING-- Engineering (General)

MAT-- 000000

TEC-- 009000

Martínez-Guerra, Rafael

Martínez-Fuentes, Oscar

Montesinos-García, Juan Javier

20200823082811.0

pn

[Book]

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