## e-books in Real Analysis category

**A Primer of Real Analysis**

by

**Dan Sloughter**-

**Synechism.org**,

**2009**

This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, the author is assuming that the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses.

(

**1031**views)

**Irrational Numbers and Their Representation by Sequences and Series**

by

**Henry Parker Manning**-

**J. Wiley & sons**,

**1906**

This book is intended to explain the nature of irrational numbers, and those parts of Algebra which depend on the theory of limits. We have endeavored to show how the fundamental operations are to be performed in the case of irrational numbers.

(

**1524**views)

**An Introductory Course Of Mathematical Analysis**

by

**Charles Walmsley**-

**Cambridge University Press**,

**1920**

Originally published in 1926, this text was aimed at first-year undergraduates studying physics and chemistry, to help them become acquainted with the concepts and processes of differentiation and integration. A prominence is given to inequalities.

(

**1541**views)

**The General Theory of Dirichlet's Series**

by

**G.H. Hardy, Marcel Riesz**-

**Cambridge University Press**,

**1915**

This classic work explains the theory and formulas behind Dirichlet's series and offers the first systematic account of Riesz's theory of the summation of series by typical means. Its authors rank among the most distinguished mathematicians ...

(

**968**views)

**An Introduction to Real Analysis**

by

**John K. Hunter**-

**University of California Davis**,

**2014**

These are some notes on introductory real analysis. They cover the properties of the real numbers, sequences and series of real numbers, limits of functions, continuity, differentiability, sequences and series of functions, and Riemann integration.

(

**1312**views)

**Basic Real Analysis**

by

**Anthony W. Knapp**-

**BirkhĂ¤user**,

**2016**

A comprehensive treatment with a global view of the subject, emphasizing connections between real analysis and other branches of mathematics. Included throughout are many examples and hundreds of problems, with hints or complete solutions for most.

(

**1734**views)

**Foundations of Analysis**

by

**Joseph L. Taylor**,

**2011**

The goal is to develop in students the mathematical maturity they will need when they move on to senior level mathematics courses, and to present a rigorous development of the calculus, beginning with the properties of the real number system.

(

**1669**views)

**Introduction to Mathematical Analysis**

by

**B. Lafferriere, G. Lafferriere, N. Mau Nam**-

**Portland State University Library**,

**2015**

We provide students with a strong foundation in mathematical analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

(

**3972**views)

**A Course Of Mathematical Analysis**

by

**Shanti Narayan**-

**S.Chand And Company**,

**1962**

Contents: Dedekind's theory of Real Numbers; Bounds and Limiting Points; Sequences; Real Valued Functions of a Real Variable; The derivative; Riemann Theory of Integration; Uniform Convergence; Improper Integrals; Fourier Series; and more.

(

**15013**views)

**Introduction to Real Analysis**

by

**Lee Larson**-

**University of Louisville**,

**2014**

From the table of contents: Basic Ideas (Sets, Functions and Relations, Cardinality); The Real Numbers; Sequences; Series; The Topology of R; Limits of Functions; Differentiation; Integration; Sequences of Functions; Fourier Series.

(

**2373**views)

**How We Got From There to Here: A Story of Real Analysis**

by

**Robert Rogers, Eugene Boman**-

**Open SUNY Textbooks**,

**2013**

This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. The book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments.

(

**2158**views)

**Undergraduate Analysis Tools**

by

**Bruce K. Driver**-

**University of California, San Diego**,

**2013**

Contents: Natural, integer, and rational Numbers; Fields; Real Numbers; Complex Numbers; Set Operations, Functions, and Counting; Metric Spaces; Series and Sums in Banach Spaces; Topological Considerations; Differential Calculus in One Real Variable.

(

**2655**views)

**Notes on Measure and Integration**

by

**John Franks**-

**arXiv**,

**2009**

My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to investigate the standard convergence theorems and a brief introduction to the Hilbert space of L2 functions on the interval.

(

**2853**views)

**The Foundations of Analysis**

by

**Larry Clifton**-

**arXiv**,

**2013**

This is a detailed introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios, and then define the positive real numbers categorically.

(

**3476**views)

**Real Analysis**

by

**Martin Smith-Martinez, et al.**-

**Wikibooks**,

**2013**

This introductory book is concerned in particular with analysis in the context of the real numbers. It will first develop the basic concepts needed for the idea of functions, then move on to the more analysis-based topics.

(

**6832**views)

**Differential Calculus**

by

**Pierre Schapira**-

**UniversitĂ© Paris VI**,

**2011**

The notes provide a short presentation of the main concepts of differential calculus. Our point of view is the abstract setting of a real normed space, and when necessary to specialize to the case of a finite dimensional space endowed with a basis.

(

**3934**views)

**A Course of Pure Mathematics**

by

**G.H. Hardy**-

**Cambridge University Press**,

**1921**

This classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. Hardy explains the fundamental ideas of the differential and integral calculus, and the properties of infinite series.

(

**5366**views)

**Real Analysis for Graduate Students: Measure and Integration Theory**

by

**Richard F. Bass**-

**CreateSpace**,

**2011**

Nearly every Ph.D. student in mathematics needs to take a preliminary or qualifying examination in real analysis. This book provides the necessary tools to pass such an examination. The author presents the material in as clear a fashion as possible.

(

**7802**views)

**Orders of Infinity**

by

**G. H. Hardy**-

**Cambridge University Press**,

**1910**

The ideas of Du Bois-Reymond's 'Infinitarcalcul' are of great and growing importance in all branches of the theory of functions. The author brings the Infinitarcalcul up to date, stating explicitly and proving carefully a number of general theorems.

(

**5415**views)

**Lectures on Lipschitz Analysis**

by

**Juha Heinonen**,

**2005**

In these lectures, we concentrate on the theory of Lipschitz functions in Euclidean spaces. From the table of contents: Introduction; Extension; Differentiability; Sobolev spaces; Whitney flat forms; Locally standard Lipschitz structures.

(

**5964**views)

**An Introductory Single Variable Real Analysis**

by

**Marcel B. Finan**-

**Arkansas Tech University**,

**2009**

The text is designed for an introductory course in real analysis suitable to upper sophomore or junior level students who already had the calculus sequel and a course in discrete mathematics. The content is considered a moderate level of difficulty.

(

**6809**views)

**Elementary Real Analysis**

by

**B. S. Thomson, J. B. Bruckner, A. M. Bruckner**-

**Prentice Hall**,

**2001**

The book is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the big picture and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory and other.

(

**12649**views)

**Elliptic Functions**

by

**Arthur Latham Baker**-

**John Wiley & Sons**,

**1890**

The author used only such methods as are familiar to the ordinary student of Calculus, avoiding those methods of discussion dependent upon the properties of double periodicity, and also those depending upon Functions of Complex Variables.

(

**6937**views)

**Theory of the Integral**

by

**Brian S. Thomson**-

**ClassicalRealAnalysis.info**,

**2012**

This text is intended as a treatise for a rigorous course introducing the elements of integration theory on the real line. All of the important features of the Riemann integral, the Lebesgue integral, and the Henstock-Kurzweil integral are covered.

(

**12965**views)

**Mathematical Analysis II**

by

**Elias Zakon**-

**The TrilliaGroup**,

**2009**

This book follows the release of the author's Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses. The text is appropriate for any second course in real analysis or mathematical analysis.

(

**10652**views)

**Basic Analysis: Introduction to Real Analysis**

by

**Jiri Lebl**-

**Lulu.com**,

**2009**

This is a free online textbook for a first course in mathematical analysis. The text covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, and sequences of functions.

(

**14374**views)

**Applied Analysis**

by

**J. Hunter, B. Nachtergaele**-

**World Scientific Publishing Company**,

**2005**

Introduces applied analysis at the graduate level, particularly those parts of analysis useful in graduate applications. Only a background in basic calculus, linear algebra and ordinary differential equations, and functions and sets is required.

(

**8758**views)

**Analysis Tools with Applications**

by

**Bruce K. Driver**-

**Springer**,

**2003**

These are lecture notes from Real analysis and PDE: Basic Topological, Metric and Banach Space Notions; Riemann Integral and ODE; Lebesbgue Integration; Hilbert Spaces and Spectral Theory of Compact Operators; Complex Variable Theory; etc.

(

**9030**views)

**Topics in Real and Functional Analysis**

by

**Gerald Teschl**-

**Universitaet Wien**,

**2016**

This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis. It covers basic Hilbert and Banach space theory as well as basic measure theory including Lebesgue spaces and the Fourier transform.

(

**9348**views)

**Introduction to Infinitesimal Analysis: Functions of One Real Variable**

by

**N. J. Lennes**-

**John Wiley & Sons**,

**1907**

This volume is designed as a reference book for a course dealing with the fundamental theorems of infinitesimal calculus in a rigorous manner. The book may also be used as a basis for a rather short theoretical course on real functions.

(

**8028**views)

**Homeomorphisms in Analysis**

by

**Casper Goffman, at al.**-

**American Mathematical Society**,

**1997**

This book features the interplay of two main branches of mathematics: topology and real analysis. The text covers Lebesgue measurability, Baire classes of functions, differentiability, the Blumberg theorem, various theorems on Fourier series, etc.

(

**9612**views)

**Introduction to Real Analysis**

by

**William F. Trench**-

**Prentice Hall**,

**2003**

This book introduces readers to a rigorous understanding of mathematical analysis and presents challenging concepts as clearly as possible. Written for those who want to gain an understanding of mathematical analysis and challenging concepts.

(

**17958**views)

**Introduction to Lebesgue Integration**

by

**W W L Chen**-

**Macquarie University**,

**1996**

An introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory. Contents: the real numbers and countability, the Riemann integral, point sets, the Lebesgue integral, monotone convergence theorem, etc.

(

**10152**views)

**Fundamentals of Analysis**

by

**W W L Chen**-

**Macquarie University**,

**2008**

Set of notes suitable for an introduction to the basic ideas in analysis: the number system, sequences and limits, series, functions and continuity, differentiation, the Riemann integral, further treatment of limits, and uniform convergence.

(

**11272**views)

**Set Theoretic Real Analysis**

by

**Krzysztof Ciesielski**-

**Heldermann Verlag**,

**1997**

This text surveys the recent results that concern real functions whose statements involve the use of set theory. The choice of the topics follows the author's personal interest in the subject. Most of the results are left without the proofs.

(

**10155**views)

**Mathematical Analysis I**

by

**Elias Zakon**-

**The Trillia Group**,

**2004**

Topics include metric spaces, convergent sequences, open and closed sets, function limits and continuity, sequences and series of functions, compact sets, power series, Taylor's theorem, differentiation and integration, total variation, and more.

(

**10269**views)

**Interactive Real Analysis**

by

**Bert G. Wachsmuth**-

**Seton Hall University**,

**2007**

Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability, topology, power series, and more.

(

**10535**views)

**Real Variables: With Basic Metric Space Topology**

by

**Robert B. Ash**-

**Institute of Electrical & Electronics Engineering**,

**2007**

A text for a first course in real variables for students of engineering, physics, and economics, who need to know real analysis in order to cope with the professional literature. The subject matter is fundamental for more advanced mathematical work.

(

**54120**views)

**Real Analysis**

by

**A. M. Bruckner, J. B. Bruckner, B. S. Thomson**-

**Prentice Hall**,

**1997**

This book provides an introductory chapter containing background material as well as a mini-overview of much of the course, making the book accessible to readers with varied backgrounds. It uses a wealth of examples to illustrate important concepts.

(

**12402**views)

**Theory of Functions of a Real Variable**

by

**Shlomo Sternberg**,

**2005**

The topology of metric spaces, Hilbert spaces and compact operators, the Fourier transform, measure theory, the Lebesgue integral, the Daniell integral, Wiener measure, Brownian motion and white noise, Haar measure, Banach algebras, etc.

(

**28812**views)