Functional Analysis for Physics and Engineering An Introduction [Hardcover]

This book provides an introduction to functional analysis for non-experts in mathematics. As such, it is distinct from most other books on the subject that are intended for mathematicians. Concepts are explained concisely with visual materials, making it accessible for those unfamiliar with graduate-level mathematics. Topics include topology, vector spaces, tensor spaces, Lebesgue integrals, and operators, to name a few. Two central issuesthe theory of Hilbert space and the operator theoryand how they relate to quantum physics are covered extensively. Each chapter explains, concisely, the purpose of the specific topic and the benefit of understanding it. Researchers and graduate students in physics, mechanical engineering, and information science will benefit from this view of functional analysis.

Prologue

What Functional Analysis tells us

From perspective of the limit

From perspective of infinite dimension

From perspective of quantum mechanical theory

Topology

Fundamentals

Continuous mapping

Homeomorphism

Vector space

What is vector space?

Property of vector space