Analysis In Euclidean Space

Analysis in Euclidean Space is a book for undergraduate students interested in acquiring a solid footing in analysis and expanding their background. It covers Differentiation and Integration theory in several real variables, measure theory, differential geometry, classical theory of curves, geometric measure theory, integral geometry, and others. With original results, new approaches, and an emphasis on concepts and rigorous proofs, it is suitable for mathematics and physics students.

Format: Hardback
Length: 580 pages
Publication date: 13 November 2022
Publisher: World Scientific Europe Ltd

Analysis in Euclidean Space is a comprehensive textbook that delves into the realm of analysis, a fundamental branch of mathematics. Authored by the renowned mathematician, the book offers a comprehensive coverage of Differentiation and Integration theory in several real variables. However, its scope extends far beyond this core subject, encompassing a diverse range of closely related areas such as measure theory, differential geometry, classical theory of curves, geometric measure theory, integral geometry, and many more.

What sets Analysis in Euclidean Space apart is its unique approach and emphasis on concepts and rigorous proofs. The author has drawn upon their extensive teaching experience to craft a textbook that is both accessible to undergraduate students and challenging enough for graduate students. With numerous original results, innovative approaches, and a strong focus on understanding the underlying principles, the book provides a solid foundation in analysis for those seeking to expand their knowledge in mathematics and physics.

The book is organized into 21 chapters, each accompanied by an introduction that provides a summary of its contents. Additionally, there is an additional chapter dedicated to miscellaneous exercises, allowing students to further reinforce their understanding and apply the concepts learned. Lecturers can utilize the diverse chapters of this book to tailor their undergraduate courses in analysis, making it an invaluable resource for both students and educators alike.

While the book assumes a basic understanding of linear algebra and a standard first-year calculus course in differentiation and integration, it gradually increases in difficulty as it progresses. This makes it suitable for students at various levels, from those embarking on their mathematical journey to those pursuing advanced studies. The comprehensive nature of the content and the clear explanations make it an ideal textbook for anyone seeking to deepen their understanding of analysis.

In conclusion, Analysis in Euclidean Space is a remarkable textbook that offers a comprehensive and rigorous introduction to analysis. Authored by a renowned mathematician, it provides students with a solid foundation in Differentiation and Integration theory, while also exploring a wide range of related areas. With its emphasis on concepts, rigorous proofs, and practical applications, the book is an invaluable resource for undergraduate students, particularly in mathematics and physics, who are eager to acquire a deep understanding of analysis and expand their academic horizons.

ISBN-13: 9781800611719