This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.
This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.
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.
Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.
Designed to fill the gaps left in the development of calculus as it is usually presented in the elementary course, this text introduces students to a rigorous understanding of mathematical analysis.
