Principles of Analysis: Measure, Integration, Functional Analysis, and Applications

Principles of Analysis: Measure, Integration, Functional Analysis, and Applications is a comprehensive textbook that covers advanced topics in analysis, probability, harmonic analysis, and applied mathematics. It is designed for readers preparing for doctoral-level courses and qualifying exams in real analysis. The book is divided into four sections and includes direct proofs, examples, and exercises. It is written by Hugo D. Junghenn, a professor of mathematics at The George Washington University.

Format: Hardback
Length: 520 pages
Publication date: 30 April 2018
Publisher: Taylor & Francis Inc

Principles of Analysis: Measure, Integration, Functional Analysis, and Applications is a comprehensive textbook designed to prepare readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. It also serves as a valuable resource for preparing for qualifying exams in real analysis. The book is meticulously crafted to cater to the needs of both readers and instructors, allowing them to select topics that align with their specific interests and requirements.

The author presents the text in a clear and straightforward manner, making it accessible to a wide range of students. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration, and functional analysis. The book covers a wide range of detailed topics, making it an invaluable reference for scholars and professionals in the field.

The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration, Part II serves as a course in functional analysis, Part III discusses various advanced topics, building on material covered in the previous parts, and Part IV includes two appendices with proofs of the change of the variable theorem and a joint continuity theorem. Additionally, a preliminary chapter provides comprehensive coverage of the theory of metric spaces and general topological spaces.

One of the key features of this textbook is its direct and concise proofs, which are accompanied by attention to detail. The author has included a substantial variety of interesting and nontrivial examples to illustrate the concepts and theories discussed in the text. These examples not only help to deepen the reader's understanding but also provide practical applications of the analytical techniques covered.

To further enhance the learning experience, the book includes nearly 700 exercises ranging from routine to challenging. These exercises are designed to test the reader's knowledge and understanding of the material covered. Each exercise includes hints and solutions to assist the reader in solving the problems. This feature particularly benefits students who may need additional guidance and support in grasping the concepts.

In addition to its theoretical content, Principles of Analysis: Measure, Integration, Functional Analysis, and Applications also includes a diverse set of special topics and applications. These topics cover a wide range of fields, including mathematical physics, mathematical biology, economics, and computer science. By presenting these applications, the book demonstrates the practical significance of the analytical techniques discussed and their relevance in real-world scenarios.

The author of this textbook is Hugo D. Junghenn, a professor of mathematics at The George Washington University. He has an extensive academic background and has published numerous journal articles in the field of analysis. He is also the author of several other books, including Introduction to Functional Analysis and Measure Theory.

In conclusion, Principles of Analysis: Measure, Integration, Functional Analysis, and Applications is a must-have textbook for students and scholars seeking to advance their knowledge and understanding of analysis, probability, harmonic analysis, and applied mathematics. Its comprehensive coverage, direct and concise proofs, interesting examples, and diverse set of special topics and applications make it an invaluable resource for anyone interested in this field. Whether you are a beginner or an experienced analyst, this textbook will provide you with the necessary tools and knowledge to excel in your academic and professional pursuits.

Weight: 1154g
Dimension: 187 x 262 x 35 (mm)
ISBN-13: 9781498773287