Functional Analysis Tools for Practical Use in Sciences and Engineering

This textbook provides a solid foundation in functional analysis for applied mathematics, physics, and engineering, emphasizing motivation, justification, and practical techniques. It covers abstract spaces, function spaces, dual spaces, distributions, linear functional analysis, compactness, derivative, and Hilbert spaces, with elementary examples and a reader-friendly structure.

Format: Hardback
Length: 214 pages
Publication date: 14 October 2022
Publisher: Springer International Publishing AG

This comprehensive textbook delves into the realm of functional analysis, presenting a selection of powerful tools that find immediate applications in diverse fields such as applied mathematics, physics, and engineering. With a reader-friendly structure, it caters to individuals who require functional analysis expertise but may not have a strong background in this branch of mathematics. Each tool is accompanied by a clear motivation, justification for the chosen approaches, and proper usage techniques. Proofs are included only when necessary to ensure the safe application of the results.

The book begins with a roadmap to facilitate the reading experience. Subsequent chapters reintroduce definitions and notation for abstract spaces and specific function spaces, while Chapter 3 introduces dual spaces. Chapters 2 and 3's tools find utility in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet is covered in Chapter 5, followed by Chapter 6, which delves into the concept of compactness. Chapter 7 extends the concept of derivative to functions defined in normed spaces, while Chapter 8 discusses fundamental results about Hilbert spaces that are crucial for numerical approximations. The final chapter offers remarks on recent bibliographical items. Throughout the chapters, elementary examples serve as aids for understanding and self-study.

By offering a comprehensive and accessible approach, this textbook serves as a valuable resource for researchers, students, and practitioners alike who rely on solid functional analysis but do not require a deep understanding of the underlying theory. Its user-friendly format and comprehensive coverage make it an essential tool for anyone seeking to leverage the power of functional analysis in their respective fields.

Weight: 518g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031105975
Edition number: 1st ed. 2022