# Mathematical Analysis

## Linear and Metric Structures and Continuity

• Mariano Giaquinta
• Giuseppe Modica
Textbook

1. Front Matter
Pages i-xix
2. ### Linear Algebra

1. Front Matter
Pages 1-1
2. Pages 3-39
3. Pages 41-78
4. Pages 79-110
5. Pages 111-145
3. ### Metrics and Topology

1. Front Matter
Pages 147-147
2. Pages 149-195
3. Pages 197-217
4. Pages 219-247
5. Pages 249-282
4. ### Continuity in Infinite-Dimensional Spaces

1. Front Matter
Pages 283-283
2. Pages 395-453
5. Back Matter
Pages 455-466

### Introduction

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.

The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.

Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.

### Keywords

calculus compactness differential equation self-adjoint operators spectral theorem topology of metric spaces vector spaces

#### Authors and affiliations

• Mariano Giaquinta
• 1
• Giuseppe Modica
• 2
1. 1.Dipartimento di MatematicaScuola Normale SuperiorePisaItaly
2. 2.Dipartimento di Matematica ApplicataUniversità degli Studi di FirenzeFirenzeItaly