Mathematical and Analytical Techniques with Applications to Engineering

Algebraic and Differential Methods for Nonlinear Control Theory

Elements of Commutative Algebra and Algebraic Geometry

Authors: Martinez-Guerra, Rafael, Martinez-Fuentes, Oscar, Montesinos-Garcia, Juan Javier

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  • Self-contained and concise primer
  • Geared towards applications in nonlinear control theory
  • Emphasizes tools from ​commutative algebra and algebraic geometry
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eBook $84.99
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  • ISBN 978-3-030-12025-2
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Hardcover $149.99
price for USA in USD
  • ISBN 978-3-030-12024-5
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About this book

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 (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-030-12025-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-3-030-12024-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic and Differential Methods for Nonlinear Control Theory
Book Subtitle
Elements of Commutative Algebra and Algebraic Geometry
Authors
Series Title
Mathematical and Analytical Techniques with Applications to Engineering
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-12025-2
DOI
10.1007/978-3-030-12025-2
Hardcover ISBN
978-3-030-12024-5
Series ISSN
1559-7458
Edition Number
1
Number of Pages
XIV, 196
Number of Illustrations
2 b/w illustrations, 11 illustrations in colour
Topics