𝔖 Scriptorium
✦   LIBER   ✦
📁

Algebraic and Differential Methods for Nonlinear Control Theory: Elements of Commutative Algebra and Algebraic Geometry

✍ Scribed by Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García

Publisher
Springer International Publishing
Year
2019
Tongue
English
Leaves
201
Series
Mathematical and Analytical Techniques with Applications to Engineering
Edition
1st ed.
Category
Library
⬇  Acquire This Volume

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xiv
Mathematical Background (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 1-17
Group Theory (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 19-30
Rings (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 31-47
Matrices and Linear Equations Systems (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 49-64
Permutations and Determinants (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 65-73
Vector and Euclidean Spaces (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 75-91
Linear Transformations (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 93-107
Matrix Diagonalization and Jordan Canonical Form (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 109-123
Differential Equations (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 125-161
Differential Algebra for Nonlinear Control Theory (Rafael Martínez-Guerra, Oscar Martínez-Fuentes, Juan Javier Montesinos-García)....Pages 163-182
Back Matter ....Pages 183-196

✦ Subjects

Engineering; Engineering Mathematics; Applications of Nonlinear Dynamics and Chaos Theory; Control; Systems Theory, Control

📜 SIMILAR VOLUMES

Algebraic and Geometric Methods in Nonli
📁 Algebraic and Geometric Methods in Nonlinear Control Theory
✍ Bronisław Jakubczyk (auth.), M. Fliess, M. Hazewinkel (eds.) 📂 Library 📅 1986 🏛 Springer Netherlands 🌐 English

<p>Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown '

Algebraic and geometric methods in nonli
📁 Algebraic and geometric methods in nonlinear control theory
✍ Fliess M., Hazewinkel M. (eds.) 📂 Library 📅 1986 🏛 Springer;D Reidel 🌐 English

<p>Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown '

Algebraic Geometry and Commutative Algeb
📁 Algebraic Geometry and Commutative Algebra
✍ Siegfried Bosch 📂 Library 📅 2012 🏛 Springer 🌐 English

Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algeb

Algebraic geometry and commutative algeb
📁 Algebraic geometry and commutative algebra
✍ S Bosch 📂 Library 📅 2013 🏛 Springer 🌐 English

Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck's schemes invented in the late 1950s allowed the application of alge

Algebraic Geometry and Commutative Algeb
📁 Algebraic Geometry and Commutative Algebra
✍ Siegfried Bosch (auth.) 📂 Library 📅 2013 🏛 Springer-Verlag London 🌐 English

<p><p>Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of