Algebra and Analysis for Engineers and Scientists
Authors: Michel, Anthony N., Herget, Charles J.
 Allows students in engineering or science to become familiar with a great deal of pertinent mathematics in a rapid and efficient manner without sacrificing rigor
 Gives readers a unified overview of applicable mathematics, enabling them to choose additional, advanced topical courses in mathematics more intelligently
 Offers many exercises integrated into the text
 Features applications of algebra and analysis having a broad appeal
 Supplementary material for students and instructors available on the web
 Useful as a course textbook, for selfstudy, or as a reference
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 About this Textbook

"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 nontrivial, manner.... [T]he book is quite thorough and can serve as a text, for selfstudy, or as a reference." —Mathematical Reviews
Written for graduate and advanced undergraduate students in engineering and science, this classic book focuses primarily on set theory, algebra, and analysis. Useful as a course textbook, for selfstudy, or as a reference, the work is intended to:
* provide readers with appropriate mathematical background for graduate study in engineering or science;
* allow students in engineering or science to become familiar with a great deal of pertinent mathematics in a rapid and efficient manner without sacrificing rigor;
* give readers a unified overview of applicable mathematics, enabling them to choose additional, advanced topical courses in mathematics more intelligently.
Whereas these objectives for writing this book were certainly pertinent over twenty years ago when the work was first published, they are even more compelling now. Today’s graduate students in engineering or science are expected to be more knowledgeable and sophisticated in mathematics than students in the past. Moreover, today’s graduate students in engineering or science are expected to be familiar with a great deal of ancillary material (primarily in the computer science area), acquired in courses that did not even exist a couple of decades ago.
The book is 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 finitedimensional vector spaces and matrices. The last three chapters investigate metric spaces, normed and inner product spaces, and linear operators. Because of its flexible structure, Algebra and Analysis for Engineers and Scientists may be used either in a one or twosemester course by deleting appropriate sections, taking into account the students’ backgrounds and interests.
A generous number of exercises have been integrated into the text, and a section of references and notes is provided at the end of each chapter. Applications of algebra and analysis having a broad appeal are also featured, including topics dealing with ordinary differential equations, integral equations, applications of the contraction mapping principle, minimization of functionals, an example from optimal control, and estimation of random variables.
Supplementary material for students and instructors is available at http://Michel.Herget.net.
 Reviews

"This book is a useful compendium of the mathematics of (mostly) finitedimensional linear vector spaces (plus two final chapters on infinitedimensional 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 selfstudy, 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
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Bibliographic Information
 Bibliographic Information

 Book Title
 Algebra and Analysis for Engineers and Scientists
 Authors

 Anthony N. Michel
 Charles J. Herget
 Copyright
 2007
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Birkhäuser Boston
 eBook ISBN
 9780817647070
 DOI
 10.1007/9780817647070
 Softcover ISBN
 9780817647063
 Edition Number
 1
 Number of Pages
 XIV, 486
 Number of Illustrations and Tables
 48 b/w illustrations
 Additional Information
 Originally published as "Mathematical Foundations in Engineering and Science" by PrenticeHall, 1981; reprinted as "Applied Algebra and Functional Analysis" by Dover, 1993
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