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.
You may also like
Is there anything more beautiful than an A in Algebra Not to the Lial team! Marge Lial, John Hornsby, and Terry McGinnis write their textbooks and accompanying...
Is there anything more beautiful than an “A” in Algebra? Not to the Lial team! Marge Lial, John Hornsby, and Terry McGinnis write their textbooks and...
In Essentials of College Algebra, 12th Edition, the experience of master teachers helps students develop both the conceptual understanding and analytical...
- Elementary introduction to the Lebesgue integral by Steven G. Krantz PDF
- Organic Chemistry, 6th Edition By Marc Loudon PDF
- Finite Mathematics 7th Edition by Stefan Waner PDF
- Mathematical Physics with Partial Differential Equations by James Kirkwood PDF
- University Physics with Modern Physics 12th Edition by Hugh D. Young PDF