## An Introduction to Real Analysis

This book is a set of notes for an elementary course in real analysis. It covers sequences, limits, continuity, differentiation, integration, and series.

This book is a set of notes for an elementary course in real analysis. It covers sequences, limits, continuity, differentiation, integration, and series.

## An Introduction to Real Analysis

This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.

This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.

## Spaces: An Introduction to Real Analysis

Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years.

The text has been tested in classes at the University of Oslo over a number of years.

## An Introduction to Real Analysis

AN INTRODUCTION TO REAL ANALYSIS covers some basic results pertaining to the set of real numbers. It is a foundational course for beginners. It includes chapters like real number system, sequences, limit and continuity of functions, differentiability and integration. A chapter on inequalities supplements other chapters. Each chapter contains some examples and an exercise set. Solving these exercises will make the subject interesting. Pre requistte for this book is the basic knowledge of real numbers.

A chapter on inequalities supplements other chapters. Each chapter contains some examples and an exercise set. Solving these exercises will make the subject interesting. Pre requistte for this book is the basic knowledge of real numbers.

## An Introduction to Real Analysis

##### The Commonwealth and International Library: Mathematical Topics

An Introduction to Real Analysis presents the concepts of real analysis and highlights the problems which necessitate the introduction of these concepts. Topics range from sets, relations, and functions to numbers, sequences, series, derivatives, and the Riemann integral. This volume begins with an introduction to some of the problems which are met in the use of numbers for measuring, and which provide motivation for the creation of real analysis. Attention then turns to real numbers that are built up from natural numbers, with emphasis on integers, rationals, and irrationals. The chapters that follow explore the conditions under which sequences have limits and derive the limits of many important sequences, along with functions of a real variable, Rolle's theorem and the nature of the derivative, and the theory of infinite series and how the concepts may be applied to decimal representation. The book also discusses some important functions and expansions before concluding with a chapter on the Riemann integral and the problem of area and its measurement. Throughout the text the stress has been upon concepts and interesting results rather than upon techniques. Each chapter contains exercises meant to facilitate understanding of the subject matter. This book is intended for students in colleges of education and others with similar needs.

Each chapter contains exercises meant to facilitate understanding of the subject matter. This book is intended for students in colleges of education and others with similar needs.