First Course in Functional Analysis

A First Course in Functional Analysis provides an introduction to functional analysis and operator theory, emphasizing Hilbert space methods, without requiring prior knowledge in measure theory. It is written in a course-like structure, focusing on clarity and logical development with real-world applications in analysis. Minimal background knowledge in linear algebra, calculus, and topology is assumed.

Format: Paperback / softback
Length: 240 pages
Publication date: 30 September 2020
Publisher: Taylor & Francis Ltd

A First Course in Functional Analysis is a comprehensive textbook that provides an introduction to fundamental functional analysis and operator theory, with a strong emphasis on Hilbert space methods. The primary objective of this book is to introduce the core concepts of functional analysis and operator theory to students without the prerequisite of a course in measure theory. It is meticulously written and organized in a manner akin to a course curriculum, prioritizing clarity, logical progression, and real-world applications in analysis. The foundational knowledge required for a student enrolling in this course is relatively modest, encompassing basic linear algebra, calculus up to Riemann integration, and a basic understanding of topological and metric spaces.

Functional analysis is a branch of mathematics that studies functions and their properties, particularly in the context of linear operators and Hilbert spaces. It originated in the late 19th century as a way to analyze and solve mathematical problems in physics and engineering. Functional analysis is characterized by the use of mathematical techniques such as differentiation, integration, and matrix theory to analyze and manipulate functions.

One of the key concepts in functional analysis is the notion of a norm. A norm is a measure of the size or magnitude of a function, and it is used to define the topology of a Hilbert space. Different norms can be defined, such as the L2 norm, which measures the square of the function's magnitude, or the L1 norm, which measures the sum of the function's absolute values.

Another important concept in functional analysis is the idea of an operator. An operator is a mapping that takes one function to another, and it can be defined on a Hilbert space. Operators can be linear, such as the addition operator, or non-linear, such as the Laplace operator. Non-linear operators are often used to model complex systems, such as electrical circuits or fluid dynamics.

Functional analysis has many applications in fields such as physics, engineering, computer science, and mathematics. For example, it is used to model physical systems, such as electric circuits, and to solve differential equations. It is also used in signal processing and computer vision to analyze and process images and videos.

In conclusion, functional analysis is a powerful branch of mathematics that has many applications in various fields. It is characterized by the use of norms and operators to analyze and manipulate functions, and it has played a crucial role in the development of modern mathematics.

Weight: 398g
Dimension: 156 x 232 x 24 (mm)
ISBN-13: 9780367658137