Integral and Functional Analysis

This textbook covers Integration and Metric Spaces, Lebesgue Integration, and Functional Analysis, designed for senior undergraduate students with a basic understanding of calculus and linear algebra.

Format: Hardback
Length: 398 pages
Publication date: 05 May 2021
Publisher: Nova Science Publishers Inc

This comprehensive textbook is a valuable resource for students studying three closely interconnected courses: Integration and Metric Spaces, Lebesgue Integration, and Functional Analysis. While the content has been successfully utilized in joint undergraduate and graduate courses, it is primarily tailored to advanced undergraduate students. The prerequisites for this textbook are intentionally modest, assuming that students have a foundational understanding of calculus and linear algebra, along with basic (direct and indirect) proof methods.

The book is organized into nine chapters, each dedicated to a specific topic within the aforementioned courses. The first chapter provides an introduction to the fundamental concepts and tools of integration and metric spaces, laying the foundation for the subsequent chapters. Chapter 2 delves into Lebesgue integration, a fundamental concept in measure theory and functional analysis. Chapter 3 explores functional analysis, a branch of mathematics that examines functions and their properties, including continuity, differentiability, and integration.

Throughout the textbook, numerous examples and exercises are provided to illustrate the theoretical concepts and help students grasp the practical applications. These examples range from simple to complex, ensuring that students of all levels can benefit from the material. Additionally, each chapter includes a comprehensive list of references, allowing students to further explore the topics in depth if desired.

In conclusion, this textbook is an essential resource for students seeking to excel in the study of Integration and Metric Spaces, Lebesgue Integration, and Functional Analysis. With its clear and concise explanations, numerous examples, and comprehensive exercises, it provides a solid foundation for understanding these complex subjects and prepares students for further academic pursuits in mathematics or related fields.

Weight: 658g
Dimension: 230 x 155 (mm)
ISBN-13: 9781536192803