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Electromagnetic Waves continues the applied approach used in the authors' successful Engineering Electromagnetics. The second book is appropriate for a second course in Electromagnetics that covers the topic of waves and the application of Maxwell's equations to electromagnetic events.
FEATURES/BENEFITS
Demonstrates how electromagnetic concepts are important to modern electrical engineering applications.
More examples and problems than competing booksAll include references to current literature or practical applications.
Footnotes and biographies.
An intuitive and progressive approachCovers topics in order of increasing complexity.
Emphasis on physical understanding and clarityWithout sacrificing rigor and completeness.
Detailed examples, selected application examples, abundant illustrations, and numerous end-of-chapter problems emphasizing practical applications.
Historical notes, abbreviated biographies, and hundreds of footnotes.
Written for advanced undergraduate physics and engineering students, this textbook is an introduction to electromagnetic waves which emphasizes physical understanding and practical applications. Starting with Maxwell's equations, the authors (electrical engineering at the U. of Portland and Stanford U., separately) discuss the propagation of waves in empty space or material media, their reflection and refraction at planar boundaries, their guiding within metallic or dielectric boundaries, their interaction with matter, and their generation by simple sources. Annotation c. Book News, Inc., Portland, OR (booknews.com)
More Reviews and RecommendationsUMRAN S. INAN is Professor of Electrical Engineering at Stanford University, where he serves as Director of the Space, Telecommunications, and Radioscience (STAR) Laboratory. He has received the 1998 Stanford University Tau Beta Pi Award for Excellence in Undergraduate Teaching, and actively conducts research in electromagnetic waves in plasmas, lightning discharges, ionospheric physics, and very low frequency remote sensing. Dr. Inan has served as the Ph.D. thesis advisor for 13 students and is a senior member of IEEE, a member of Tau Beta Pi, Sigma Xi, the American Geophysical Union, the Electromagnetics Academy, and serves as Secretary of U.S. National Committee of the International Union of Radio Science (URSI).
AZIZ S. INAN is Associate Professor of Electrical Engineering at the University of Portland, where he has also served as Department Chairman. A winner of the University's faculty teaching award, he conducts research in electromagnetic wave propagation in conducting and inhomogeneous media. He is a member of Tau Beta Pi and IEEE.
Electromagnetic Waves continues the applied approach used in the authors' successful Engineering Electromagnetics. The second book is appropriate for a second course in Electromagnetics that covers the topic of waves and the application of Maxwell's equations to electromagnetic events.
FEATURES/BENEFITS
Demonstrates how electromagnetic concepts are important to modern electrical engineering applications.
More examples and problems than competing booksAll include references to current literature or practical applications.
Footnotes and biographies.
An intuitive and progressive approachCovers topics in order of increasing complexity.
Emphasis on physical understanding and clarityWithout sacrificing rigor and completeness.
Detailed examples, selected application examples, abundant illustrations, and numerous end-of-chapter problems emphasizing practical applications.
Historical notes, abbreviated biographies, and hundreds of footnotes.
Written for advanced undergraduate physics and engineering students, this textbook is an introduction to electromagnetic waves which emphasizes physical understanding and practical applications. Starting with Maxwell's equations, the authors (electrical engineering at the U. of Portland and Stanford U., separately) discuss the propagation of waves in empty space or material media, their reflection and refraction at planar boundaries, their guiding within metallic or dielectric boundaries, their interaction with matter, and their generation by simple sources. Annotation c. Book News, Inc., Portland, OR (booknews.com)
This book provides engineering students with a solid grasp of electromagnetic waves, by emphasizing physical understanding and practical applications. Starting with Maxwell's equations, the text provides a comprehensive treatment of the propagation of electromagnetic waves in empty space or material media, their reflection and refraction at planar boundaries, their guiding within metallic or dielectric boundaries, their interaction with matter, and their generation by simple sources.
Electromagnetic Waves is designed for senior and first-year graduate college and university engineering and physics students, for those who wish to learn the subject through self-study, and for practicing engineers who need an up-to-date reference text. The student using this text is assumed to have completed a typical (third- or fourth-year) undergraduate course in electromagnetic fundamentals.
The key features of this textbook are
Progressive Chapter Organization
We use a physical, intuitive, and progressive approach, covering electromagneticwavephenomena in order of increasing complexity. Starting with Maxwell's equations (Chapter 1) as the experimentally based fundamental laws, we first (Chapter 2) study their most profound implications: the propagation of electromagnetic waves through empty space or unbounded simple media. We then (Chapter 3) discuss the reflection and refraction of electromagnetic waves from simple planar boundaries, followed by (Chapter 4) the guiding of electromagnetic waves within planar metallic or dielectric structures. Guiding of electromagnetic waves within cylindrical structures and electromagnetic resonators are discussed next (Chapter 5), followed by coverage of the interaction of electromagnetic waves with matter and their generation by simple sources (Chapter 6).
Emphasis on Physical Understanding
Future engineers and scientists need a clear understanding and a firm grasp of the basic principles so that they can understand, formulate, and interpret the results of complex practical problems. Engineers and scientists nowadays do not (and should not) spend time on working out formulas and obtaining numerical results by substitution. As most of the number crunching and formula manipulations are left to computers and packaged application and design programs, a solid grasp of fundamentals is now more essential than ever before. We maintain a constant link with established as well as new and emerging applications throughout the text, so that the reader's interest remains perked up, while at the same time emphasizing fundamental physical insight and solid understanding of basic principles. We strive to empower the reader with more than just a working knowledge of the manipulation of a dry set of vector relations and formulas. We supplement rigorous analyses with extensive discussions of the physical nature of the electromagnetic fields and waves involved, often from alternative points of view. In emphasizing physical understanding, we attempt to distill the essentials of physically based treatments available in physics texts, while presenting them in the context of traditional and emerging engineering applications.
Detailed Examples and Abundant Illustrations
We present the material in a clear and simple yet precise and accurate manner, with interesting examples illustrating each new concept. Many examples emphasize selected applications of electromagnetic waves. A total of 74 illustrative examples are detailed over six chapters, with two of the chapters having more than 20 examples. Each example is presented with an abbreviated topical title, a clear problem statement, and a detailed solution. Recognizing the importance of visualization in the reader's understanding, especially in view of the three-dimensional nature of electromagnetic wave phenomena, over 180 diagrams, graphs, and illustrations appear throughout the book.
Numerous End-of-Chapter Problems
Each chapter concludes with a variety of practice problems to allow the students to test their understanding of the material covered in the chapter, with a total of over 230 exercise problems spread over five chapters. The topical content of each problem is clearly identified in an abbreviated title (e.g., "Infrared antireflection coating" or "GPS signal transmission through the ionosphere"). Many of the problems explore interesting applications, and many practical "real-life" problems are included in each chapter to motivate students.
Historical Notes and Abbreviated Biographies
The history of the development of electromagnetic waves is laden with outstanding examples of pioneering scientists and development of scientific thought. Throughout our text we maintain a constant link with the pioneering giants and their work in order to bring about a better appreciation of the complex physical concepts and how they were discovered, which helps to motivate readers to keep their interest. We provide abbreviated biographies of the pioneers, emphasizing their scientific work in electromagnetics as well as in other fields, such as optics, heat, chemistry, and astronomy.
Emphasis on Clarity without Sacrificing Rigor and Completeness
This textbook presents the material at a simple enough level to be readable by senior undergraduate and first-year graduate students, but it is also rigorous in providing references and footnotes for in-depth analyses of selected concepts and applications. We provide the students with a taste of the rigor and completeness of classical reference texts, combined with a level of physical insight that was exemplified so well in some very old texts, while still maintaining the necessary level of organization and presentation clarity required for a modern textbook. We also provide not just a superficial but a sufficiently rigorous and in-depth exposure to a diverse range of applications of electromagnetic waves, in the body of the text, in examples, and in end-of-chapter problems.
Hundreds of Footnotes
In view of its fundamental physical nature, and its wide-encompassing generality, electromagnetic s is a subject that lends itself particularly well to alternative ways of thinking about physical and engineering problems and is also particularly rich in terms of available scientific literature and many outstanding textbooks. Almost every new concept encountered can be thought of in different ways, and its implications can be explored further by the interested reader. We encourage such scholarly pursuit of enhanced knowledge and understanding by providing tens to hundreds of footnotes in each chapter, providing further comments, qualifications of statements made in the text, and references for in-depth analyses of selected concepts and applications. A total of over 360 footnotes are spread over six chapters. These footnotes do not interrupt the flow of ideas and the development of the main topics, but they provide an unprecedented degree of completeness for a textbook at this level, with interesting and sometimes thought-provoking content to make the subject more appealing.
The organization as well as the philosophy of this textbook is motivated by our view of the current status of electromagnetic fundamentals and waves in engineering curricula. Electromagnetic Waves is designed specifically for what normally is the second fields and waves course in most schools, the first one being a course in electromagnetic fundamemals. This book is the second of a sequence of two books by the same authors, the first one, Engineering Electromagnetics, having been designed specifically for the one-semester first course.
Understanding electromagnetics and appreciating its applications require a generally higher level of abstraction than most other topics encountered by electrical engineering students. The first course in electromagnetics, which most students take after having had vector calculus, aims at the development and understanding of Maxwell's equations, which requires the utilization of the full three-dimensional vector form of the fields and their relationships. It is this very step that makes the subject of electromagnetics appear insurmountable to many students and turns off their interest, especially when coupled with a lack of presentation and discussion of important and stimulating applications and the physical (and experimental) bases of the fundamental laws of physics. In our first book, we attempt to overcome this difficulty by (i) using a modern chapter organization, starting with an initial exposure to transmission lines and transients on high-speed distributed circuits, to bridge electrical circuits and electromagnetics, and (ii) emphasizing a combination of physical understanding; practical applications; historical notes and biographies; clarity without sacrificing rigor; and abundant examples, illustrations, and end-of-chapter problems. A first course based on Engineering Electromagnetics provides the students with a working knowledge of transmission lines as well as a solid, physically based background and a firm understanding of Maxwell's equations and their experimental bases. At that point, the student is ready to study in detail the most important manifestation of Maxwell's equations: electromagnetic waves, which is the subject of the present book.
Since electromagnetics is a mature basic science, and the topics covered in introductory texts are well established, the various texts differ primarily in their organization as well as range and depth of coverage. In formulating our approach, we were cognizant of the many challenges and opportunities that lie ahead in teaching electromagnetic waves. Challenges include (i) the need to return to fundamentals (rather than rely on derived concepts), especially in view of the many emerging new applications that exploit unusual properties of materials and that rely on unconventional device concepts, and (ii) the need to maintain student interest, in spite of the reputation of electromagnetic s as a difficult and abstract subject. Opportunities are abundant, especially as the engineers working in electronics and computer science are now finding that as devices get smaller and faster, circuit theory is insufficient in describing system performance or facilitating design. The need for a basic understanding of electromagnetic waves and their guided propagation is underscored by the explosive expansion of the use of optical fibers and consideration of extremely high data rates (ranging to 10 Gb-s-1 ) and the emerging use of highperformance, high-density cables for communication within systems that will soon be required to carry digital signals at Gb-s-1 rates over distances of a few meters. The rapidly increasing demand for personal wireless communication systems similarly requires a thorough understanding of the electromagnetic propagation channel, varying from simple line of sight to one that is severely obstructed by buildings and foliage. In addition, issues of electromagnetic interference (EMI) and electromagnetic compatibility (EMC) are beginning to limit the performance of system-, board-, and chiplevel designs, and electrostatic discharge phenomena significantly impact the design and performance of integrated circuits.
This book is specifically designed for a one-term course in electromagnetic waves, nowadays typically the second (required or optional) fields and waves course in most electrical engineering curricula. The recommended course content for a regular three-unit one-semester course (42 contact hours) is provided in Table 1. The sections under "Cover" are recommended for complete coverage, including illustrative examples, while those marked "Skim" are recommended to be covered lightly, although the material provided is complete in case individual students want to go into more detail. The sections marked with a superscript asterisk are intended to provide flexibility to the individual instructor. For example, depending on the desired emphasis, one may want to choose between covering oblique reflection from lossy interfaces (Sec. 3.8), wave propagation in plasmas (Sec. 6.2), or ferrites (Sec. 6.4).
Table 1 also shows a recommended course content for a three-unit one-quarter course (27 contact hours) identical to the "Electromagnetic Waves" course (entry course for the fields and waves specialization for the BSEE degree) that one of us taught at Stanford for the past seven years. This topical coverage provides the students with a solid, physically based background and a working knowledge of electromagnetic wave phenomena and their applications.
| Quarter course (27 hours) | Semester course (42 hours) | |||||
|---|---|---|---|---|---|---|
| Chapter | Cover | Skim | Skip | Cover | Skim | Skip |
| 1 | All | All | ||||
| 2 | 2.1-2.6 | 2.7 | 2.4.4 | All | ||
| 3 | 3.1-3.7 | 3.1.1 | 3.8 | 3.1-3.7, 3.8* | ||
| 4 | All | All | ||||
| 5 | 5.1, 5.2.2 5.3.1 | 5.2.1 5.3.2, 5.3.3 | 5.2.3 | 5.1, 5.2 5.3 | 5.2.3* | |
| 6 | 6.1, 6.2.1 | 6.5.1, 6.5.2 | 6.2.2, 6.2.3 6.3-6.5, 6.5.3 | 6.1, 6.2*, 6.3* 6.4*, 6.5* |
As educators with a good deal of experience, we firmly believe that practice is the key to learning and that homework and exams are all instruments of teachingalthough they may not be regarded as such by the students at the time. In our own courses, we take pride in providing the students with detailed solutions of homework and exam problems, rather than cryptic and abbreviated answers. To aid the instructors who choose to use this text, we have thus taken it upon ourselves to prepare a well-laidout solutions manual, describing the solution of every end-of-chapter problem, in the same step-by-step detailed manner as our illustrative examples within the chapters. The solution for each end-of-chapter problem has been typeset by the authors themselves, with special attention to pedagogical detail. This instructor's manual is available to instructors upon request from Prentice Hall.
As authors of this book, we are looking forward to interacting with its users, both students and instructors, to collect and respond to their comments, questions, and corrections. We can most easily be reached by electronic mail at inan@nova.stanford.edu (URL: ...
This book provides engineering students with a solid grasp of electromagnetic waves, by emphasizing physical understanding and practical applications. Starting with Maxwell's equations, the text provides a comprehensive treatment of the propagation of electromagnetic waves in empty space or material media, their reflection and refraction at planar boundaries, their guiding within metallic or dielectric boundaries, their interaction with matter, and their generation by simple sources.
Electromagnetic Waves is designed for senior and first-year graduate college and university engineering and physics students, for those who wish to learn the subject through self-study, and for practicing engineers who need an up-to-date reference text. The student using this text is assumed to have completed a typical (third- or fourth-year) undergraduate course in electromagnetic fundamentals.
The key features of this textbook are
Progressive Chapter Organization
We use a physical, intuitive, and progressive approach, covering electromagnetic wavephenomena in order of increasing complexity. Starting with Maxwell's equations (Chapter 1) as the experimentally based fundamental laws, we first (Chapter 2) study their most profound implications: the propagation of electromagnetic waves through empty space or unbounded simple media. We then (Chapter 3) discuss the reflection and refraction of electromagnetic waves from simple planar boundaries, followed by (Chapter 4) the guiding of electromagnetic waves within planar metallic or dielectric structures. Guiding of electromagnetic waves within cylindrical structures and electromagnetic resonators are discussed next (Chapter 5), followed by coverage of the interaction of electromagnetic waves with matter and their generation by simple sources (Chapter 6).
Emphasis on Physical Understanding
Future engineers and scientists need a clear understanding and a firm grasp of the basic principles so that they can understand, formulate, and interpret the results of complex practical problems. Engineers and scientists nowadays do not (and should not) spend time on working out formulas and obtaining numerical results by substitution. As most of the number crunching and formula manipulations are left to computers and packaged application and design programs, a solid grasp of fundamentals is now more essential than ever before. We maintain a constant link with established as well as new and emerging applications throughout the text, so that the reader's interest remains perked up, while at the same time emphasizing fundamental physical insight and solid understanding of basic principles. We strive to empower the reader with more than just a working knowledge of the manipulation of a dry set of vector relations and formulas. We supplement rigorous analyses with extensive discussions of the physical nature of the electromagnetic fields and waves involved, often from alternative points of view. In emphasizing physical understanding, we attempt to distill the essentials of physically based treatments available in physics texts, while presenting them in the context of traditional and emerging engineering applications.
Detailed Examples and Abundant Illustrations
We present the material in a clear and simple yet precise and accurate manner, with interesting examples illustrating each new concept. Many examples emphasize selected applications of electromagnetic waves. A total of 74 illustrative examples are detailed over six chapters, with two of the chapters having more than 20 examples. Each example is presented with an abbreviated topical title, a clear problem statement, and a detailed solution. Recognizing the importance of visualization in the reader's understanding, especially in view of the three-dimensional nature of electromagnetic wave phenomena, over 180 diagrams, graphs, and illustrations appear throughout the book.
Numerous End-of-Chapter Problems
Each chapter concludes with a variety of practice problems to allow the students to test their understanding of the material covered in the chapter, with a total of over 230 exercise problems spread over five chapters. The topical content of each problem is clearly identified in an abbreviated title (e.g., "Infrared antireflection coating" or "GPS signal transmission through the ionosphere"). Many of the problems explore interesting applications, and many practical "real-life" problems are included in each chapter to motivate students.
Historical Notes and Abbreviated Biographies
The history of the development of electromagnetic waves is laden with outstanding examples of pioneering scientists and development of scientific thought. Throughout our text we maintain a constant link with the pioneering giants and their work in order to bring about a better appreciation of the complex physical concepts and how they were discovered, which helps to motivate readers to keep their interest. We provide abbreviated biographies of the pioneers, emphasizing their scientific work in electromagnetics as well as in other fields, such as optics, heat, chemistry, and astronomy.
Emphasis on Clarity without Sacrificing Rigor and Completeness
This textbook presents the material at a simple enough level to be readable by senior undergraduate and first-year graduate students, but it is also rigorous in providing references and footnotes for in-depth analyses of selected concepts and applications. We provide the students with a taste of the rigor and completeness of classical reference texts, combined with a level of physical insight that was exemplified so well in some very old texts, while still maintaining the necessary level of organization and presentation clarity required for a modern textbook. We also provide not just a superficial but a sufficiently rigorous and in-depth exposure to a diverse range of applications of electromagnetic waves, in the body of the text, in examples, and in end-of-chapter problems.
Hundreds of Footnotes
In view of its fundamental physical nature, and its wide-encompassing generality, electromagnetic s is a subject that lends itself particularly well to alternative ways of thinking about physical and engineering problems and is also particularly rich in terms of available scientific literature and many outstanding textbooks. Almost every new concept encountered can be thought of in different ways, and its implications can be explored further by the interested reader. We encourage such scholarly pursuit of enhanced knowledge and understanding by providing tens to hundreds of footnotes in each chapter, providing further comments, qualifications of statements made in the text, and references for in-depth analyses of selected concepts and applications. A total of over 360 footnotes are spread over six chapters. These footnotes do not interrupt the flow of ideas and the development of the main topics, but they provide an unprecedented degree of completeness for a textbook at this level, with interesting and sometimes thought-provoking content to make the subject more appealing.
The organization as well as the philosophy of this textbook is motivated by our view of the current status of electromagnetic fundamentals and waves in engineering curricula. Electromagnetic Waves is designed specifically for what normally is the second fields and waves course in most schools, the first one being a course in electromagnetic fundamemals. This book is the second of a sequence of two books by the same authors, the first one, Engineering Electromagnetics, having been designed specifically for the one-semester first course.
Understanding electromagnetics and appreciating its applications require a generally higher level of abstraction than most other topics encountered by electrical engineering students. The first course in electromagnetics, which most students take after having had vector calculus, aims at the development and understanding of Maxwell's equations, which requires the utilization of the full three-dimensional vector form of the fields and their relationships. It is this very step that makes the subject of electromagnetics appear insurmountable to many students and turns off their interest, especially when coupled with a lack of presentation and discussion of important and stimulating applications and the physical (and experimental) bases of the fundamental laws of physics. In our first book, we attempt to overcome this difficulty by (i) using a modern chapter organization, starting with an initial exposure to transmission lines and transients on high-speed distributed circuits, to bridge electrical circuits and electromagnetics, and (ii) emphasizing a combination of physical understanding; practical applications; historical notes and biographies; clarity without sacrificing rigor; and abundant examples, illustrations, and end-of-chapter problems. A first course based on Engineering Electromagnetics provides the students with a working knowledge of transmission lines as well as a solid, physically based background and a firm understanding of Maxwell's equations and their experimental bases. At that point, the student is ready to study in detail the most important manifestation of Maxwell's equations: electromagnetic waves, which is the subject of the present book.
Since electromagnetics is a mature basic science, and the topics covered in introductory texts are well established, the various texts differ primarily in their organization as well as range and depth of coverage. In formulating our approach, we were cognizant of the many challenges and opportunities that lie ahead in teaching electromagnetic waves. Challenges include (i) the need to return to fundamentals (rather than rely on derived concepts), especially in view of the many emerging new applications that exploit unusual properties of materials and that rely on unconventional device concepts, and (ii) the need to maintain student interest, in spite of the reputation of electromagnetic s as a difficult and abstract subject. Opportunities are abundant, especially as the engineers working in electronics and computer science are now finding that as devices get smaller and faster, circuit theory is insufficient in describing system performance or facilitating design. The need for a basic understanding of electromagnetic waves and their guided propagation is underscored by the explosive expansion of the use of optical fibers and consideration of extremely high data rates (ranging to 10 Gb-s-1 ) and the emerging use of highperformance, high-density cables for communication within systems that will soon be required to carry digital signals at Gb-s-1 rates over distances of a few meters. The rapidly increasing demand for personal wireless communication systems similarly requires a thorough understanding of the electromagnetic propagation channel, varying from simple line of sight to one that is severely obstructed by buildings and foliage. In addition, issues of electromagnetic interference (EMI) and electromagnetic compatibility (EMC) are beginning to limit the performance of system-, board-, and chiplevel designs, and electrostatic discharge phenomena significantly impact the design and performance of integrated circuits.
This book is specifically designed for a one-term course in electromagnetic waves, nowadays typically the second (required or optional) fields and waves course in most electrical engineering curricula. The recommended course content for a regular three-unit one-semester course (42 contact hours) is provided in Table 1. The sections under "Cover" are recommended for complete coverage, including illustrative examples, while those marked "Skim" are recommended to be covered lightly, although the material provided is complete in case individual students want to go into more detail. The sections marked with a superscript asterisk are intended to provide flexibility to the individual instructor. For example, depending on the desired emphasis, one may want to choose between covering oblique reflection from lossy interfaces (Sec. 3.8), wave propagation in plasmas (Sec. 6.2), or ferrites (Sec. 6.4).
Table 1 also shows a recommended course content for a three-unit one-quarter course (27 contact hours) identical to the "Electromagnetic Waves" course (entry course for the fields and waves specialization for the BSEE degree) that one of us taught at Stanford for the past seven years. This topical coverage provides the students with a solid, physically based background and a working knowledge of electromagnetic wave phenomena and their applications.
| Quarter course (27 hours) | Semester course (42 hours) | |||||
|---|---|---|---|---|---|---|
| Chapter | Cover | Skim | Skip | Cover | Skim | Skip |
| 1 | All | All | ||||
| 2 | 2.1-2.6 | 2.7 | 2.4.4 | All | ||
| 3 | 3.1-3.7 | 3.1.1 | 3.8 | 3.1-3.7, 3.8* | ||
| 4 | All | All | ||||
| 5 | 5.1, 5.2.2 5.3.1 | 5.2.1 5.3.2, 5.3.3 | 5.2.3 | 5.1, 5.2 5.3 | 5.2.3* | |
| 6 | 6.1, 6.2.1 | 6.5.1, 6.5.2 | 6.2.2, 6.2.3 6.3-6.5, 6.5.3 | 6.1, 6.2*, 6.3* 6.4*, 6.5* |
As educators with a good deal of experience, we firmly believe that practice is the key to learning and that homework and exams are all instruments of teachingalthough they may not be regarded as such by the students at the time. In our own courses, we take pride in providing the students with detailed solutions of homework and exam problems, rather than cryptic and abbreviated answers. To aid the instructors who choose to use this text, we have thus taken it upon ourselves to prepare a well-laidout solutions manual, describing the solution of every end-of-chapter problem, in the same step-by-step detailed manner as our illustrative examples within the chapters. The solution for each end-of-chapter problem has been typeset by the authors themselves, with special attention to pedagogical detail. This instructor's manual is available to instructors upon request from Prentice Hall.
As authors of this book, we are looking forward to interacting with its users, both students and instructors, to collect and respond to their comments, questions, and corrections. We can most easily be reached by electronic mail at inan@nova.stanford.edu (URL: ...
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