# Top Ten Functional Analysis books

Functional analysis is a form of modern mathematics, which covers infinite dimensional spaces and simple and general functions. It’s essentially a generalized form of linear algebra studied from the infinite dimensional case. Functional analysis utilizes classical analysis and algebra in order to discover the relationship between two distant forms of math. The top ten finite mathematical books include:

**Introductory Functional Analysis with Applications**

Introductory Functional Analysis with Applications by Erwin Kreyszig is considered to be the number one book on the subject. A solid understanding in calculus and linear algebra is recommended. But this book is also accessible to beginning graduate students. The exercises and examples are well chosen and the theorems and problems in functional analysis are worked out in detail removing any guess work for the reader.

**Functional Analysis**

The text is comprehensive using real world investigation for the analysis of applied mathematics. It includes plenty of examples and exercise in order to develop the student’s proficiency and understanding. Theorems and problems in functional analysis are discussed from Kakutani’s fixed point theorem and Lamonosov’s invariant subspace theorem. It’s written for graduate students of functional analysis.

**Functional Analysis (Dover Books on Mathematics)**

Backhman and Narici designed this book especially for students with a strong background in advanced calculus, physics, algebra and engineering. Each chapter includes practice problems and exercises, which test students’ mastery of the material. Functional analysis books pdf format for kindle are available. The text does a great job of covering introductory topics such as inner-product spaces, normed; and metric spaces and topological spaces.

**A First Look at Numerical Functional Analysis (Dover Books on Mathematics)**

This book delivers clear-cut explanations of complex ideas. Some of the topics discussed are Banach and Hilbert spaces, criteria for convergence, contraction mappings and the Kantorovich test for convergence of iteration. There are plenty of examples throughout and it eloquently reveals how problems in numerical analysis can naturally lead to concepts of functional analysis.

**Elementary Functional Analysis (Dover Books on Mathematics)**

This is a great introductory text dealing with basic structures of mathematical analysis such as linear spaces, metric spaces, normed linear spaces, differential equations and Fourier transforms. The chapters are laid out for ease in understanding and provide exercise problems, hints and answers.

**Applied Functional Analysis (Dover Books on Mathematics)**

This introductory text is stimulating and delves deeply into the important aspects and applications of functional analysis. It covers the basic mechanics, diffusive growth and approximation. Griffel is very straightforward, which is great for those who are new to dealing with abstract analysis. The text covers functional analysis in four parts beginning with discussions of Green’s functions.

**Elements of the Theory of Functions and Functional Analysis (Dover Books on Mathematics)**

This two-part advanced level text is a compilation of the authors’ courses and lectures. There are exercises and lessons in each section and it includes a list of symbols, definitions and functional analysis theory. This book is laid out with superb clarity and explanation. It’s not only recommended for mathematicians but also the theoretical physicists.

**Functional Analysis: Theory and Applications (Dover Books on Mathematics)**

This volume includes broad coverage of the subject enabling those having basic knowledge in functional analysis a taste of its various aspects. The text is balanced in abstract theory and linear functional analysis. And it’s great for those with a basic knowledge of general topology, set theory and vector spaces. Included are various illustrative examples and exercises in each chapter.

**Functional Analysis: Introduction to Further Topics in Analysis (Princeton Lectures in Analysis) (Bk. 4)**

This text is based upon a lecture series given at Princeton University. Stein is a premiere authority on harmonic analysis. He was awarded the Wolf Prize for his excellence in communicating mathematical ideas. It covers the basics of functional analysis, Banach spaces, Lp spaces and distribution theory. This is a clear-cut comprehensive and authoritative text.