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Originally published as Mathematical Foundations in Engineering and Science by Prentice-Hall, Englewood Cliffs, NJ, USA, in 1981, a subsequent paperback edition under the title Applied Algebra and Functional Analysis was published by Dover, New York, NY, USA, in 1993. The following reviews may refer to one of the previous editions.
“ This book is a useful compendium of the mathematics of (mostly) finite-dimensional linear vector spaces (plus two final chapters on infinite-dimensional spaces), which do find increasing application in many branches of engineering and science…. The treatment is thorough; the book will certainly serve as a valuable reference.” -American Scientist “ The authors present topics in algebra and analysis for students in engineering and science….. Each chapter is organized to include a brief overview, detailed topical discussions and references for further study. Notes about the references guide the student to collateral reading. Theorems, definitions, and corollaries are illustrated with examples. The student is encouraged to prove some theorems and corollaries as models for proving others in exercises. In most chapters, the authors discuss constructs used to illustrate examples of applications. Discussions are tied together by frequent, well written notes. The tables and index are good. The type faces are nicely chosen. The text should prepare a student well in mathematical matters.” -Science Books and Films “ This is an intermediate level text, with exercises, whose avowed purpose is to provide the science and engineering graduate student with an appropriate modern mathematical (analysis and algebra) background in a succinct, but not trivial, manner. After some fundamentals, algebraic structures are introduced followed by linear spaces, matrices, metric spaces, normed and inner product spaces and linear operators…. While one can quarrel with the choice of specific topics and the omission of others, the book is quite thorough and can serve as a text, for self-study, or as a reference.” -Mathematical Reviews “ The authors designed a typical work from graduate mathematical lectures: formal definitions, theorems, corollaries, proofs, examples, and exercises. It is to be noted that problems to challenge students' comprehension are interspersed throughout each chapter rather than at the end.” -CHOICE Reviews from Amazon.com
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.
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.
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. |
really useful discussion of the material