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Applied Algebra and Functional Analysis (Dover Books on Mathematics), by Anthony N. Michel, Charles J. Herget, Mathematics
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"The treatment is thorough; the book will certainly serve as a valuable reference." — American Scientist.
Written for graduate and advanced undergraduate students in engineering and science, this book focuses primarily on set theory, algebra, and analysis. Useful both for self-study and as a reference, the text provides the readers with appropriate mathematical background for advanced study in engineering or science, a basis for more advanced mathematical study, and an overview of modern mathematics.
The book is essentially divided into three parts: set theory (Chapter 1), algebra (Chapters 2‒4), and analysis (Chapters 5‒7). The first two chapters deal with the fundamental concepts of sets, functions, relations, and equivalence relations, and algebraic structures. Chapters 3 and 4 cover vector spaces and linear transformations, and finite-dimensional vector spaces and matrices. The last three chapters investigate metric spaces, normed spaces (Banach spaces) and inner product spaces (Hilbert spaces), and linear operators. A generous number of exercises have been integrated into the text and a section of references and notes is found at the end of each chapter. 1981 edition.
- Sales Rank: #1373749 in Books
- Published on: 2011-11-30
- Released on: 2011-11-02
- Original language: English
- Number of items: 1
- Dimensions: 8.44" h x .94" w x 5.40" l, 1.12 pounds
- Binding: Paperback
- 512 pages
Most helpful customer reviews
6 of 6 people found the following review helpful.
really useful discussion of the material
By JVerkuilen
My advanced mathematical training is in statistics, which is a field that relies HEAVILY on linear algebra. One undergraduate course in linear algebra is really insufficient to understand the mathematics necessary for the more advanced courses and some knowledge of functional analysis is also useful. This book is--thanks to Dover--an inexpensive way to fill the gap through self-study. It is highly useful for explaining a number of more advanced results without being too technical. Enhancing its utility to people working in applied fields, it has a number of useful examples and applications illustrating the utility (well, mathematical utility :) of the concepts discussed, e.g., applications to least squares problems, Fourier series, etc.
6 of 6 people found the following review helpful.
Very useful for robotics
By J. Kuffner
This book was recommended to me as a starting point to both review and learn advanced mathematics useful for robotics scientists and engineers. It covers linear differential equations, algebras (including Lie algebra), and metric spaces.
I found the text reasonable readable, and would recommend it to anyone looking to improve their understanding of the mathematical fundamentals useful for robotics and control research.
3 of 3 people found the following review helpful.
Excellent for self-study.
By H. Richter
I specialize in Dynamics and Controls. I found this book great for acquiring (some of) the necessary mathematics to get into a more serious study of mathematical control theory. It also boosted my capacity to closely follow some journal articles in control theory. People with the average graduate preparation in controls may skip the first four chapters and start with metric spaces. The book is not, however, adequate for studying Lie algebra as needed in controls (and robotics) as pointed out by the reviewer from Japan. It only defines Lie algebra in a very general way, and does not get into Lie algebras of vector fields, which is what we need for geometric control. The book contains, however, valuable applications of the theory to optimal control and estimation, as well as a clear exposition of existence and uniqueness of solutions to ODEs.
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