Fundamentals of Analysis with Applications

This book is a textbook in real analysis that focuses on the fundamentals of structural properties of metric spaces and analytical properties of functions defined between them. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. The targeted student readership is senior undergraduates in mathematics and engineering, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding.

Format: Paperback / softback
Length: 477 pages
Publication date: 17 March 2023
Publisher: Springer Verlag, Singapore

This comprehensive textbook serves as an essential resource in the field of real analysis, providing a thorough exploration of the fundamental concepts and applications of metric spaces and functions. It delves into the structural properties of these spaces, emphasizing their characteristics and relationships, while also examining the analytical properties of functions defined within them. The book covers a wide range of topics, including sets, functions, cardinality, real numbers, analysis on the real line, topology, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series.

Its primary objective is to demonstrate the practical use of analytical methods in solving partial differential equations, which are central to numerous important problems in mathematics, physics, engineering, and related fields. The presentation and treatment of these topics are carefully crafted to meet the expectations of readers engaged in various branches of science and technology. Specifically, senior undergraduates in mathematics and engineering are the targeted student readership, as the book's focus on real-world examples and applications will foster a deeper understanding of mathematics at the upper-level undergraduate level.

By presenting a balanced blend of theoretical concepts and practical applications, this textbook equips students with the necessary tools to excel in their studies and pursue careers in the fields of mathematics, physics, engineering, and beyond. Its comprehensive coverage and engaging writing style make it an invaluable resource for anyone seeking to advance their knowledge in real analysis and its applications.

Weight: 766g
Dimension: 155 x 235 x 32 (mm)
ISBN-13: 9789811683855
Edition number: 1st ed. 2022